Table of spherical codes

Maintained by Henry Cohn

This data is archived at https://dspace.mit.edu/handle/1721.1/153543. If you cite the table, please refer to that data set, not this web page.

A spherical code is a configuration of points on the surface of a sphere, with the goal of maximizing the minimal angle between the points. The following table lists the best codes known, with cases that are known to be optimal marked with *. The number of points links to coordinates for the code, and the cosine of the minimal angle links to an information page for the code. Cosines are rigorous upper bounds rounded up to twelve decimal places; a shorter decimal such as 0.5 means the cosine is exactly that value. Along with references, in some cases the table lists the minimal polynomial of the cosine of the minimal angle, in which case a code with this exact angle has been proved to exist.

The table is limited to 32 dimensions and 1024 points, with a few exceptions. It omits cases that have been systematically solved, namely dimensions below three and n-dimensional codes with at most 2n points (see R. A. Rankin, The closest packing of spherical caps in n dimensions, Proc. Glasgow Math. Assoc. 2 (1955), 139–144, doi:10.1017/S2040618500033219). There are two records listed in Ericson and Zinoviev's book (Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001) that I have not included below: for 80 points in 7 dimensions, their construction describes only 78 points, and for 1024 points in 16 dimensions, I am unable to get their construction to work.

You can access a plain text table here, which includes all minimal polynomials, and upload additions or improvements here.

Dimensions: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 52 64

Dimension	Number of points	Cosine of minimal angle	References and notes
3	7*	0.210138312731	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944. $3 x^{3} - 9 x^{2} - 3 x + 1$
3	8*	0.261203874964	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944. $7 x^{2} + 2 x - 1$
3	9*	0.333333333334	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944. $3 x - 1$
3	10*	0.404394325217	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S² with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6. $7 x^{3} - 4 x^{2} - 2 x + 1$
3	11*	0.447213595500	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S² with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6. $5 x^{2} - 1$
3	12*	0.447213595500	L. Fejes [Tóth], Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jber. Deutsch. Math.-Verein. 53 (1943), 66–68. $5 x^{2} - 1$
3	13*	0.542636486830	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom. 48 (2012), 128–141, doi:10.1007/s00454-011-9392-2. $x^{8} - 24 x^{7} - 12 x^{6} + 8 x^{5} + 38 x^{4} + 24 x^{3} - 12 x^{2} - 8 x + 1$
3	14*	0.563950300361	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015), 460–468, doi:10.1080/10586458.2015.1022842. $4 x^{4} - 2 x^{3} + 3 x^{2} - 1$
3	15*	0.592605902926	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370; mt0-svg, The Tammes problem for fifteen points, preprint, 2026, doi:10.5281/zenodo.23450670, https://github.com/mt0-svg/tammes-15. $13 x^{5} - x^{4} + 6 x^{3} + 2 x^{2} - 3 x - 1$
3	16	0.612294616483	K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944. $23 x^{6} + 6 x^{5} + 5 x^{4} + 4 x^{3} - 3 x^{2} - 2 x - 1$
3	17	0.628094415071	L. Danzer, Finite point-sets on S² with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6. $4 x^{10} - 92 x^{9} + 24 x^{8} + 128 x^{7} - 58 x^{6} - 78 x^{5} + 35 x^{4} + 32 x^{3} - 4 x^{2} - 6 x - 1$
3	18	0.648695832224	T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485. $216 x^{11} + 108 x^{10} + 118 x^{9} + 209 x^{8} - 100 x^{7} - 160 x^{6} + 40 x^{5} + 46 x^{4} - 20 x^{3} - 12 x^{2} + 2 x + 1$
3	19	0.673116887561	D. E. Lazić, V. Šenk, and I. Šeškar, Arrangements of points on a sphere which maximize the least distance, Bull. Appl. Math. (Technical University Budapest) 47 (1987), 7–21. Minimal polynomial of degree 75
3	20	0.676477138130	B. L. van der Waerden, Punkte auf der Kugel. Drei Zusätze, Math. Ann. 125 (1952), 213–222, doi:10.1007/BF01343118. $21 x^{3} - 9 x^{2} - 5 x + 1$
3	21	0.699498431067	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	22	0.710306258580	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370. Minimal polynomial of degree 18
3	23	0.722846984869	T. Tarnai and Zs. Gáspár, Arrangement of 23 points on a sphere (on a conjecture of R. M. Robinson), Proc. Roy. Soc. London Ser. A 433 (1991), 257–267, doi:10.1098/rspa.1991.0046.
3	24*	0.723078468334	R. M. Robinson, Arrangements of 24 points on a sphere, Math. Ann. 144 (1961), 17–48, doi:10.1007/BF01396539. $7 x^{3} + x^{2} - 3 x - 1$
3	25	0.747398628578	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370. Minimal polynomial of degree 89
3	26	0.754278177121	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370. Minimal polynomial of degree 101
3	27	0.758389210777	T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485. Minimal polynomial of degree 24
3	28	0.773230262338	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	29	0.780281415949	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	30	0.781551875095	B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056. Minimal polynomial of degree 29
3	31	0.791118613299	J. Strohmajer, Über die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 6 (1963), 49–53. Minimal polynomial of degree 66
3	32	0.793616614872	L. Danzer, Finite point-sets on S² with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6. Minimal polynomial of degree 22
3	33	0.806397613648	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	34	0.810984337204	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	35	0.815937771500	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	36	0.817248185290	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	37	0.824892480240	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	38	0.826583259422	E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf. $363 x^{14} + 7685 x^{12} + 34299 x^{10} - 77139 x^{8} + 68985 x^{6} - 31833 x^{4} + 6561 x^{2} - 729$
3	39	0.833991322411	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	40	0.837162072474	B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
3	41	0.841236343029	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	42	0.843331551639	E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf. Minimal polynomial of degree 58
3	43	0.847208865437	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	44	0.848201378305	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	45	0.854249474082	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	46	0.857534166865	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	47	0.859122361410	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	48	0.859292295076	R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775. $34 x^{5} + 15 x^{4} - 12 x^{3} - 14 x^{2} - 6 x - 1$
3	49	0.866691479049	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	50	0.868173209127	E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf. Minimal polynomial of degree 12
3	51	0.871484364931	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	52	0.872966708781	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370. Minimal polynomial of degree 16
3	53	0.876189803956	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	54	0.877004306358	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	55	0.880785046525	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	56	0.881731578410	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	57	0.884363737604	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	58	0.886555745177	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	59	0.887855737148	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	60	0.889473567590	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	61	0.892008443283	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	62	0.893496850569	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3	63	0.895036180815	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	64	0.896988167538	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	65	0.898259108584	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	66	0.899195777484	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	67	0.901198227760	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	68	0.902856921522	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	69	0.903831506358	James Buddenhagen and D. A. Kottwitz, 1997.
3	70	0.905043036803	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	71	0.906396736776	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	72	0.906849285445	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	73	0.909571628656	James Buddenhagen and D. A. Kottwitz, 1997.
3	74	0.910532623502	D. A. Kottwitz, 1997.
3	75	0.911390904652	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	76	0.912633133084	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3	77	0.913536344688	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3	78	0.914034438768	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	79	0.916195009441	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	80	0.916690360742	James Buddenhagen, 1997.
3	81	0.918117193791	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	82	0.919172412416	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	83	0.919937881756	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	84	0.920151698890	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	85	0.922004026342	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	86	0.922710627798	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	87	0.923567597265	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	88	0.924093912593	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	89	0.925099726146	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	90	0.926173483336	D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3	91	0.926844825210	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	92	0.927003416243	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	93	0.928418531906	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	94	0.928979461777	James Buddenhagen and D. A. Kottwitz, 1997.
3	95	0.929811497467	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	96	0.930285673249	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	97	0.931051674650	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	98	0.931239991046	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	99	0.932727363300	James Buddenhagen and D. A. Kottwitz, 1997.
3	100	0.933385128903	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	101	0.934025767057	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	102	0.934480088172	James Buddenhagen and D. A. Kottwitz, 1997.
3	103	0.935207723062	James Buddenhagen and D. A. Kottwitz, 1997.
3	104	0.935711381000	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	105	0.936434497689	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	106	0.937042014619	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	107	0.937517802204	James Buddenhagen and D. A. Kottwitz, 1997.
3	108	0.937862018289	James Buddenhagen and D. A. Kottwitz, 1997.
3	109	0.938798085650	James Buddenhagen and D. A. Kottwitz, 1997.
3	110	0.939026290863	James Buddenhagen and D. A. Kottwitz, 1997.
3	111	0.939729959842	Henry Cohn, 2024.
3	112	0.940339774660	James Buddenhagen and D. A. Kottwitz, 1997.
3	113	0.940847649045	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	114	0.941205445297	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	115	0.941916896842	James Buddenhagen and D. A. Kottwitz, 1997.
3	116	0.942351017116	James Buddenhagen and D. A. Kottwitz, 1997.
3	117	0.942866795114	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3	118	0.943283453359	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	119	0.943651453299	Antoine Jay, 2026.
3	120	0.943662307333	R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775. $1364 x^{10} + 1230 x^{9} - 709 x^{8} - 1468 x^{7} - 688 x^{6} + 136 x^{5} + 286 x^{4} + 108 x^{3} + 4 x^{2} - 6 x - 1$
3	121	0.944678061273	Henry Cohn, 2024.
3	122	0.945086237318	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	123	0.945482265531	James Buddenhagen and D. A. Kottwitz, 1997.
3	124	0.945780154584	James Buddenhagen and D. A. Kottwitz, 1997.
3	125	0.946395861103	Henry Cohn, 2026.
3	126	0.946752784732	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	127	0.947264465646	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	128	0.947573544865	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	129	0.947971561157	James Buddenhagen and D. A. Kottwitz, 1997.
3	130	0.948266309315	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3	131	0.948765511183	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	132	0.948962593971	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	133	0.949572658198	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	134	0.949971678353	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	135	0.950317557456	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	136	0.950634777737	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	137	0.951024783277	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	138	0.951358398188	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	139	0.951683443186	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	140	0.951979740880	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	141	0.952385754295	Henry Cohn, 2025.
3	142	0.952693726748	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	143	0.952998670435	Henry Cohn, 2024.
3	144	0.953228409663	Henry Cohn, 2025.
3	145	0.953609890346	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	146	0.953890527065	Henry Cohn, 2024.
3	147	0.954232032048	Henry Cohn, 2024.
3	148	0.954536757950	Henry Cohn, 2025.
3	149	0.954857978400	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	150	0.955020893900	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	151	0.955409384784	Henry Cohn, 2024.
3	152	0.955652691422	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	153	0.955934479813	Henry Cohn, 2025.
3	154	0.956200715693	Henry Cohn, 2024.
3	155	0.956523743427	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	156	0.956672320428	Henry Cohn, 2024.
3	157	0.957096132346	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	158	0.957339288658	Henry Cohn, 2024.
3	159	0.957588843682	Henry Cohn, 2024.
3	160	0.957856569962	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	161	0.958127174616	Antoine Jay, 2026.
3	162	0.958288809704	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	163	0.958615566728	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	164	0.958889976688	Henry Cohn, 2024.
3	165	0.959124889495	Henry Cohn, 2024.
3	166	0.959323846675	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	167	0.959625833713	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	168	0.959759331314	Henry Cohn, 2025.
3	169	0.960021869084	Henry Cohn, 2025.
3	170	0.960117137568	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121 (see footnote 1).
3	171	0.960456738161	Henry Cohn, 2025.
3	172	0.960629559055	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	173	0.960986405967	Antoine Jay, 2026.
3	174	0.961153945452	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	175	0.961330724045	Henry Cohn, 2024.
3	176	0.961593582498	Henry Cohn, 2024.
3	177	0.961828786663	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	178	0.961965173662	Henry Cohn, 2024.
3	179	0.962096013263	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	180	0.962128794086	T. Tarnai, Packing of 180 equal circles on a sphere, Elem. Math. 38 (1983), 119–122, doi:10.5169/seals-37194. Minimal polynomial of degree 18
3	181	0.962508969964	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	182	0.962801835015	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	183	0.962987454665	Antoine Jay, 2026.
3	184	0.963227493195	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	185	0.963400251151	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	186	0.963602302299	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	187	0.963858096099	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	188	0.964002261472	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	189	0.964190407206	Henry Cohn, 2024.
3	190	0.964292984546	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	191	0.964504935278	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	192	0.964585751396	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	193	0.964893730830	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	194	0.965083352280	Henry Cohn, 2024.
3	195	0.965251036900	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	196	0.965468009555	Antoine Jay, 2026.
3	197	0.965671400310	Henry Cohn, 2025.
3	198	0.965829315374	Henry Cohn, 2024.
3	199	0.965916172795	Henry Cohn, 2024.
3	200	0.965942044452	Henry Cohn, 2025.
3	201	0.966306900791	Henry Cohn, 2024.
3	202	0.966420203486	Antoine Jay, 2026.
3	203	0.966622724376	Henry Cohn, 2024.
3	204	0.966712897537	Henry Cohn, 2024.
3	205	0.966826978769	Henry Cohn, 2025.
3	206	0.967078415732	Henry Cohn, 2024.
3	207	0.967258049747	Henry Cohn, 2024.
3	208	0.967362842483	Henry Cohn, 2024.
3	209	0.967547223611	Henry Cohn, 2024.
3	210	0.967630597679	Henry Cohn, 2024.
3	211	0.967822897132	Henry Cohn, 2024.
3	212	0.967927157323	Henry Cohn, 2024.
3	213	0.968163116144	Henry Cohn, 2024.
3	214	0.968277360489	Henry Cohn, 2025.
3	215	0.968453681521	Henry Cohn, 2024.
3	216	0.968596893733	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	217	0.968776493956	Henry Cohn, 2025.
3	218	0.968881995145	Joseph Farland, 2026.
3	219	0.969051617681	Henry Cohn, 2025.
3	220	0.969138855053	Henry Cohn, 2024.
3	221	0.969215831481	Henry Cohn, 2024.
3	222	0.969434783107	Antoine Jay, 2026.
3	223	0.969554841105	Henry Cohn, 2024.
3	224	0.969694397387	Henry Cohn, 2024.
3	225	0.969832486673	Henry Cohn, 2024.
3	226	0.969908996450	Antoine Jay, 2026.
3	227	0.970127102957	Antoine Jay, 2026.
3	228	0.970249147842	Henry Cohn, 2024.
3	229	0.970369120893	Henry Cohn, 2025.
3	230	0.970483445180	Henry Cohn, 2024.
3	231	0.970608829668	Henry Cohn, 2024.
3	232	0.970693980479	Henry Cohn, 2024.
3	233	0.970846639234	Antoine Jay, 2026.
3	234	0.970903800528	Antoine Jay, 2026.
3	235	0.971108669673	Henry Cohn, 2025.
3	236	0.971194820033	Henry Cohn, 2024.
3	237	0.971302439718	Antoine Jay, 2026.
3	238	0.971450420857	Antoine Jay, 2026.
3	239	0.971569245430	Joseph Farland, 2026.
3	240	0.971657594484	Henry Cohn, 2024.
3	241	0.971802213952	Henry Cohn, 2024.
3	242	0.971893361216	Henry Cohn, 2025.
3	243	0.971985281550	Antoine Jay, 2026.
3	244	0.972112111081	Henry Cohn, 2025.
3	245	0.972207255147	Henry Cohn, 2024.
3	246	0.972337795891	Henry Cohn, 2024.
3	247	0.972484516196	Henry Cohn, 2024.
3	248	0.972577587182	Antoine Jay, 2026.
3	249	0.972727698402	Henry Cohn, 2024.
3	250	0.972802667761	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	251	0.972878488641	Henry Cohn, 2025.
3	252	0.973005270899	Henry Cohn, 2024.
3	253	0.973112111220	Henry Cohn, 2024.
3	254	0.973166293799	Antoine Jay, 2026.
3	255	0.973336098901	Henry Cohn, 2025.
3	256	0.973419418775	Henry Cohn, 2024.
3	257	0.973518713646	Henry Cohn, 2024.
3	258	0.973601287197	Henry Cohn, 2024.
3	259	0.973687576212	Henry Cohn, 2024.
3	260	0.973743009714	Henry Cohn, 2024.
3	261	0.973920627055	Joseph Farland, 2026.
3	262	0.974027125019	Henry Cohn, 2024.
3	263	0.974151173293	Antoine Jay, 2026.
3	264	0.974245195545	Henry Cohn, 2026.
3	265	0.974330655728	Henry Cohn, 2024.
3	266	0.974398317842	Antoine Jay, 2026.
3	267	0.974465984042	Henry Cohn, 2025.
3	268	0.974543890479	Henry Cohn, 2024.
3	269	0.974603593005	Henry Cohn, 2024.
3	270	0.974616849625	T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842. Minimal polynomial of degree 26
3	271	0.974808781632	Henry Cohn, 2024.
3	272	0.974950342892	Henry Cohn, 2024.
3	273	0.975065447378	Henry Cohn, 2024.
3	274	0.975124578016	Henry Cohn, 2024.
3	275	0.975240636386	Henry Cohn, 2024.
3	276	0.975319878521	Antoine Jay, 2026.
3	277	0.975403368414	Antoine Jay, 2026.
3	278	0.975464347279	Henry Cohn, 2024.
3	279	0.975521244170	Henry Cohn, 2024.
3	280	0.975556159117	Henry Cohn, 2024.
3	281	0.975696078155	Henry Cohn, 2024.
3	282	0.975817103894	X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3	283	0.975926949120	Henry Cohn, 2024.
3	284	0.976026277162	Henry Cohn, 2024.
3	285	0.976129872208	Henry Cohn, 2026.
3	286	0.976188040904	Antoine Jay, 2026.
3	287	0.976292535597	Henry Cohn, 2024.
3	288	0.976363799835	Henry Cohn, 2026.
3	289	0.976439859800	Henry Cohn, 2024.
3	290	0.976500970455	Henry Cohn, 2024.
3	291	0.976554670637	Joseph Farland, 2026.
3	292	0.976605721255	Antoine Jay, 2026.
3	293	0.976711107353	Henry Cohn, 2024.
3	294	0.976800018749	Antoine Jay, 2026.
3	295	0.976890767574	Henry Cohn, 2024.
3	296	0.976945912178	Henry Cohn, 2024.
3	297	0.977073329897	Henry Cohn, 2024.
3	298	0.977138830798	Henry Cohn, 2026.
3	299	0.977212395551	Antoine Jay, 2026.
3	300	0.977219217071	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000. Minimal polynomial of degree 58
3	301	0.977391298844	Antoine Jay, 2026.
3	302	0.977456318034	Antoine Jay, 2026.
3	303	0.977523317804	Antoine Jay, 2026.
3	304	0.977581836960	Antoine Jay, 2026.
3	305	0.977632490985	Henry Cohn, 2024.
3	306	0.977703964298	Antoine Jay, 2026.
3	307	0.977813103970	Antoine Jay, 2026.
3	308	0.977892051736	Henry Cohn, 2024.
3	309	0.977959537061	Antoine Jay, 2026.
3	310	0.978011833466	Antoine Jay, 2026.
3	311	0.978083973836	Antoine Jay, 2026.
3	312	0.978120238531	Antoine Jay, 2026.
3	313	0.978224489292	Antoine Jay, 2026.
3	314	0.978264314155	Henry Cohn, 2026.
3	315	0.978359778769	Henry Cohn, 2024.
3	316	0.978409720822	Antoine Jay, 2026.
3	317	0.978487475787	Henry Cohn, 2024.
3	318	0.978544186966	Henry Cohn, 2026.
3	319	0.978603060123	Henry Cohn, 2024.
3	320	0.978663214407	Joseph Farland, 2026.
3	321	0.978700877038	Antoine Jay, 2026.
3	322	0.978821099775	Antoine Jay, 2026.
3	323	0.978910839488	Antoine Jay, 2026.
3	324	0.978990321564	Antoine Jay, 2026.
3	325	0.979041935606	Henry Cohn, 2026.
3	326	0.979095312240	Henry Cohn, 2026.
3	327	0.979171371681	Antoine Jay, 2026.
3	328	0.979218332061	Antoine Jay, 2026.
3	329	0.979277581704	Antoine Jay, 2026.
3	330	0.979323231314	Joseph Farland, 2026.
3	331	0.979372582064	Antoine Jay, 2026.
3	332	0.979423808444	Antoine Jay, 2026.
3	333	0.979489346043	Antoine Jay, 2026.
3	334	0.979582034493	Henry Cohn, 2024.
3	335	0.979641442751	Antoine Jay, 2026.
3	336	0.979685624811	Antoine Jay, 2026.
3	337	0.979751239348	Antoine Jay, 2026.
3	338	0.979838818714	Henry Cohn, 2024.
3	339	0.979890536212	Antoine Jay, 2026.
3	340	0.979943505817	Antoine Jay, 2026.
3	341	0.979999218383	Henry Cohn, 2026.
3	342	0.980044047715	Henry Cohn, 2024.
3	343	0.980089563136	Antoine Jay, 2026.
3	344	0.980135977822	Henry Cohn, 2024.
3	345	0.980195528212	Antoine Jay, 2026.
3	346	0.980272636307	Antoine Jay, 2026.
3	347	0.980349152228	Henry Cohn, 2024.
3	348	0.980406401850	Antoine Jay, 2026.
3	349	0.980459098303	Antoine Jay, 2026.
3	350	0.980512031528	Antoine Jay, 2026.
3	351	0.980569488890	Henry Cohn, 2026.
3	352	0.980617038392	Antoine Jay, 2026.
3	353	0.980680058456	Joseph Farland, 2026.
3	354	0.980726877303	Antoine Jay, 2026.
3	355	0.980776809933	Antoine Jay, 2026.
3	356	0.980813672203	Antoine Jay, 2026.
3	357	0.980859420724	Joseph Farland, 2026.
3	358	0.980900744832	Antoine Jay, 2026.
3	359	0.980938721612	Henry Cohn, 2024.
3	360	0.980946761337	T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3	361	0.981088226426	Antoine Jay, 2026.
3	362	0.981160326747	Antoine Jay, 2026.
3	363	0.981225268927	Henry Cohn, 2024.
3	364	0.981270920689	Antoine Jay, 2026.
3	365	0.981314154564	Antoine Jay, 2026.
3	366	0.981353471401	Antoine Jay, 2026.
3	367	0.981411802995	Antoine Jay, 2026.
3	368	0.981459173258	Joseph Farland, 2026.
3	369	0.981497701713	Antoine Jay, 2026.
3	370	0.981557852196	Antoine Jay, 2026.
3	371	0.981609476686	Antoine Jay, 2026.
3	372	0.981655634463	Antoine Jay, 2026.
3	373	0.981698204635	Antoine Jay, 2026.
3	374	0.981743695439	Henry Cohn, 2024.
3	375	0.981791432540	Joseph Farland, 2026.
3	376	0.981823740017	Antoine Jay, 2026.
3	377	0.981882566817	Henry Cohn, 2026.
3	378	0.981910199675	Antoine Jay, 2026.
3	379	0.981950089856	Antoine Jay, 2026.
3	380	0.981966079866	Henry Cohn, 2025.
3	381	0.982053259851	Antoine Jay, 2026.
3	382	0.982136118975	Antoine Jay, 2026.
3	383	0.982191165481	Henry Cohn, 2024.
3	384	0.982230205834	Antoine Jay, 2026.
3	385	0.982275034690	Antoine Jay, 2026.
3	386	0.982306280672	Henry Cohn, 2026.
3	387	0.982343568478	Antoine Jay, 2026.
3	388	0.982373183313	Henry Cohn, 2024.
3	389	0.982413939800	Henry Cohn, 2026.
3	390	0.982435685538	Antoine Jay, 2026.
3	391	0.982506919253	Antoine Jay, 2026.
3	392	0.982576748727	Antoine Jay, 2026.
3	393	0.982649357699	Henry Cohn, 2024.
3	394	0.982692258634	Antoine Jay, 2026.
3	395	0.982725266501	Antoine Jay, 2026.
3	396	0.982755879143	Antoine Jay, 2026.
3	397	0.982794828038	Antoine Jay, 2026.
3	398	0.982818117650	Antoine Jay, 2026.
3	399	0.982854598025	Antoine Jay, 2026.
3	400	0.982905526758	Antoine Jay, 2026.
3	401	0.982946647764	Henry Cohn, 2026.
3	402	0.982976658773	Antoine Jay, 2026.
3	403	0.983046966156	Henry Cohn, 2026.
3	404	0.983108974861	Antoine Jay, 2026.
3	405	0.983167968174	Henry Cohn, 2026.
3	406	0.983204434317	Antoine Jay, 2026.
3	407	0.983235764397	Antoine Jay, 2026.
3	408	0.983284547279	Antoine Jay, 2026.
3	409	0.983324857501	Henry Cohn, 2024.
3	410	0.983353268157	Henry Cohn, 2026.
3	411	0.983397760620	Henry Cohn, 2024.
3	412	0.983427483278	Henry Cohn, 2026.
3	413	0.983461427167	Henry Cohn, 2024.
3	414	0.983491996915	Antoine Jay, 2026.
3	415	0.983543330326	Antoine Jay, 2026.
3	416	0.983572356049	Henry Cohn, 2024.
3	417	0.983606250324	Henry Cohn, 2026.
3	418	0.983665319836	Henry Cohn, 2026.
3	419	0.983706848253	Henry Cohn, 2026.
3	420	0.983733077420	Antoine Jay, 2026.
3	421	0.983788433471	Antoine Jay, 2026.
3	422	0.983819451048	Antoine Jay, 2026.
3	423	0.983864932171	Antoine Jay, 2026.
3	424	0.983899323392	Antoine Jay, 2026.
3	425	0.983936730938	Henry Cohn, 2026.
3	426	0.983967656850	Henry Cohn, 2024.
3	427	0.984016858976	Antoine Jay, 2026.
3	428	0.984055271687	Antoine Jay, 2026.
3	429	0.984081419316	Henry Cohn, 2026.
3	430	0.984128863366	Henry Cohn, 2026.
3	431	0.984165514392	Henry Cohn, 2024.
3	432	0.984201636678	Henry Cohn, 2024.
3	433	0.984244767708	Henry Cohn, 2026.
3	434	0.984271520387	Henry Cohn, 2026.
3	435	0.984318791801	Henry Cohn, 2026.
3	436	0.984353934697	Antoine Jay, 2026.
3	437	0.984376596212	Henry Cohn, 2024.
3	438	0.984418580619	Joseph Farland, 2026.
3	439	0.984449790237	Antoine Jay, 2026.
3	440	0.984472421765	Henry Cohn, 2024.
3	441	0.984527980944	Henry Cohn, 2024.
3	442	0.984558142424	Henry Cohn, 2026.
3	443	0.984590149553	Antoine Jay, 2026.
3	444	0.984628415926	Henry Cohn, 2024.
3	445	0.984659452674	Antoine Jay, 2026.
3	446	0.984697315281	Antoine Jay, 2026.
3	447	0.984730491574	Antoine Jay, 2026.
3	448	0.984758024752	Antoine Jay, 2026.
3	449	0.984783461265	Antoine Jay, 2026.
3	450	0.984833102924	Henry Cohn, 2026.
3	451	0.984869055427	Henry Cohn, 2026.
3	452	0.984909861454	Joseph Farland, 2026.
3	453	0.984937733146	Antoine Jay, 2026.
3	454	0.984965933474	Henry Cohn, 2026.
3	455	0.984992526693	Antoine Jay, 2026.
3	456	0.985025831529	Antoine Jay, 2026.
3	457	0.985063607349	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	458	0.985097884587	Henry Cohn, 2024.
3	459	0.985118722612	Antoine Jay, 2026.
3	460	0.985147607585	Henry Cohn, 2026.
3	461	0.985179263490	Antoine Jay, 2026.
3	462	0.985200918091	Antoine Jay, 2026.
3	463	0.985227838286	Antoine Jay, 2026.
3	464	0.985256999693	Antoine Jay, 2026.
3	465	0.985313255033	Antoine Jay, 2026.
3	466	0.985354555719	Antoine Jay, 2026.
3	467	0.985386081788	Henry Cohn, 2024.
3	468	0.985411837325	Henry Cohn, 2024.
3	469	0.985444627723	Henry Cohn, 2024.
3	470	0.985482640963	Henry Cohn, 2024.
3	471	0.985509915678	Henry Cohn, 2024.
3	472	0.985523632535	Henry Cohn, 2026.
3	473	0.985548106738	Antoine Jay, 2026.
3	474	0.985570497957	Antoine Jay, 2026.
3	475	0.985596615938	Henry Cohn, 2026.
3	476	0.985623062603	Antoine Jay, 2026.
3	477	0.985650741616	Henry Cohn, 2026.
3	478	0.985677664535	Antoine Jay, 2026.
3	479	0.985699793609	Henry Cohn, 2026.
3	480	0.985719122362	Antoine Jay, 2026.
3	481	0.985785156651	Antoine Jay, 2026.
3	482	0.985825013849	Antoine Jay, 2026.
3	483	0.985845956715	Antoine Jay, 2026.
3	484	0.985878240751	Antoine Jay, 2026.
3	485	0.985905879597	Antoine Jay, 2026.
3	486	0.985929368687	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	487	0.985979258599	Antoine Jay, 2026.
3	488	0.985998639323	Antoine Jay, 2026.
3	489	0.986025629765	Antoine Jay, 2026.
3	490	0.986059032195	Henry Cohn, 2026.
3	491	0.986086277740	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	492	0.986121402880	Antoine Jay, 2026.
3	493	0.986155833767	Antoine Jay, 2026.
3	494	0.986181734672	Henry Cohn, 2026.
3	495	0.986207408173	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	496	0.986232320520	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	497	0.986253840325	Antoine Jay, 2026.
3	498	0.986298103712	Henry Cohn, 2024.
3	499	0.986321351633	Antoine Jay, 2026.
3	500	0.986340427741	Henry Cohn, 2026.
3	501	0.986368564388	Henry Cohn, 2026.
3	502	0.986394969781	Henry Cohn, 2026.
3	503	0.986426087274	Antoine Jay, 2026.
3	504	0.986452475219	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	505	0.986468065101	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	506	0.986496795507	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	507	0.986514377548	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	508	0.986537171402	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	509	0.986554423539	Joseph Farland, 2026.
3	510	0.986562939593	Antoine Jay, 2026.
3	511	0.986616546465	Antoine Jay, 2026.
3	512	0.986663629828	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	513	0.986686329536	Antoine Jay, 2026.
3	514	0.986709721838	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	515	0.986744566867	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	516	0.986768384280	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	517	0.986792240600	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	518	0.986817808150	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	519	0.986838493720	Antoine Jay, 2026.
3	520	0.986867931339	Antoine Jay, 2026.
3	521	0.986893256455	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	522	0.986917151246	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	523	0.986938315059	Antoine Jay, 2026.
3	524	0.986963939788	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	525	0.986989421421	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	526	0.987009490347	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	527	0.987039988315	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	528	0.987061144390	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	529	0.987077262275	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	530	0.987104468645	Antoine Jay, 2026.
3	531	0.987135485578	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
3	532	0.987154387599	Antoine Jay, 2026.
3	533	0.987185368627	Henry Cohn, 2024.
3	534	0.987215557894	Henry Cohn, 2024.
3	535	0.987233366282	Henry Cohn, 2026.
3	536	0.987256919973	Antoine Jay, 2026.
3	537	0.987271183218	Henry Cohn, 2024.
3	538	0.987299318995	Henry Cohn, 2026.
3	539	0.987321991908	Antoine Jay, 2026.
3	540	0.987343988942	Antoine Jay, 2026.
3	541	0.987367192805	Antoine Jay, 2026.
3	542	0.987386297924	Antoine Jay, 2026.
3	543	0.987412608917	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	544	0.987437607152	Antoine Jay, 2026.
3	545	0.987453893787	Antoine Jay, 2026.
3	546	0.987478394579	Antoine Jay, 2026.
3	547	0.987509785826	Antoine Jay, 2026.
3	548	0.987533154648	Antoine Jay, 2026.
3	549	0.987547178470	Henry Cohn, 2026.
3	550	0.987571280344	Antoine Jay, 2026.
3	551	0.987602101320	Antoine Jay, 2026.
3	552	0.987621804564	Antoine Jay, 2026.
3	553	0.987639063720	Antoine Jay, 2026.
3	554	0.987655992944	Antoine Jay, 2026.
3	555	0.987683367461	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	556	0.987703437496	Antoine Jay, 2026.
3	557	0.987733289783	Antoine Jay, 2026.
3	558	0.987755845204	Joseph Farland, 2026.
3	559	0.987776637712	Antoine Jay, 2026.
3	560	0.987795764336	Antoine Jay, 2026.
3	561	0.987821080530	Antoine Jay, 2026.
3	562	0.987837720422	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	563	0.987857321321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
3	564	0.987882017649	Henry Cohn, 2026.
3	565	0.987908752724	Antoine Jay, 2026.
3	566	0.987930679295	Henry Cohn, 2024.
3	567	0.987952251042	Antoine Jay, 2026.
3	568	0.987974408939	Henry Cohn, 2024.
3	569	0.987986081388	Antoine Jay, 2026.
3	570	0.988006037936	Antoine Jay, 2026.
3	571	0.988035686717	Antoine Jay, 2026.
3	572	0.988045142899	Antoine Jay, 2026.
3	573	0.988070762308	Henry Cohn, 2026.
3	574	0.988092299430	Antoine Jay, 2026.
3	575	0.988116092887	Henry Cohn, 2024.
3	576	0.988134624923	Henry Cohn, 2026.
3	577	0.988154372704	Antoine Jay, 2026.
3	578	0.988175563349	Henry Cohn, 2026.
3	579	0.988195536872	Antoine Jay, 2026.
3	580	0.988214394071	Henry Cohn, 2024.
3	581	0.988236298890	Antoine Jay, 2026.
3	582	0.988253378024	Antoine Jay, 2026.
3	583	0.988275503344	Antoine Jay, 2026.
3	584	0.988296366139	Antoine Jay, 2026.
3	585	0.988316187693	Henry Cohn, 2024.
3	586	0.988336136398	Henry Cohn, 2024.
3	587	0.988354162127	Henry Cohn, 2026.
3	588	0.988367675855	Henry Cohn, 2026.
3	589	0.988390276053	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
3	590	0.988407003702	Antoine Jay, 2026.
3	591	0.988426256682	Henry Cohn, 2026.
3	592	0.988445621040	Antoine Jay, 2026.
3	593	0.988464934407	Henry Cohn, 2026.
3	594	0.988487475426	Henry Cohn, 2026.
3	595	0.988509243513	Henry Cohn, 2026.
3	596	0.988525221197	Henry Cohn, 2026.
3	597	0.988541463766	Henry Cohn, 2026.
3	598	0.988561538132	Antoine Jay, 2026.
3	599	0.988578635915	Antoine Jay, 2026.
3	600	0.988601034992	Henry Cohn, 2026.
3	601	0.988620184212	Antoine Jay, 2026.
3	602	0.988636075049	Henry Cohn, 2026.
3	603	0.988654856575	Antoine Jay, 2026.
3	604	0.988675027866	Henry Cohn, 2026.
3	605	0.988695531872	Antoine Jay, 2026.
3	606	0.988711666482	Antoine Jay, 2026.
3	607	0.988725982410	Henry Cohn, 2026.
3	608	0.988746033738	Antoine Jay, 2026.
3	609	0.988760157529	Henry Cohn, 2024.
3	610	0.988777012301	Antoine Jay, 2026.
3	611	0.988792490186	Antoine Jay, 2026.
3	612	0.988809317215	Antoine Jay, 2026.
3	613	0.988828386947	Antoine Jay, 2026.
3	614	0.988847477277	Antoine Jay, 2026.
3	615	0.988863827463	Antoine Jay, 2026.
3	616	0.988878602395	Antoine Jay, 2026.
3	617	0.988896185791	Antoine Jay, 2026.
3	618	0.988916078492	Antoine Jay, 2026.
3	619	0.988933057019	Antoine Jay, 2026.
3	620	0.988948235960	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	621	0.988977945194	Antoine Jay, 2026.
3	622	0.988998181125	Antoine Jay, 2026.
3	623	0.989012306487	Antoine Jay, 2026.
3	624	0.989027311465	Antoine Jay, 2026.
3	625	0.989045750434	Antoine Jay, 2026.
3	626	0.989070144515	Henry Cohn, 2026.
3	627	0.989079627522	Antoine Jay, 2026.
3	628	0.989098539879	Antoine Jay, 2026.
3	629	0.989116725768	Antoine Jay, 2026.
3	630	0.989134691942	Henry Cohn, 2024.
3	631	0.989153918243	Antoine Jay, 2026.
3	632	0.989172993109	Henry Cohn, 2024.
3	633	0.989186376920	Antoine Jay, 2026.
3	634	0.989199989773	Antoine Jay, 2026.
3	635	0.989215092854	Antoine Jay, 2026.
3	636	0.989239733363	Antoine Jay, 2026.
3	637	0.989255056858	Antoine Jay, 2026.
3	638	0.989267204518	Henry Cohn, 2024.
3	639	0.989281046840	Antoine Jay, 2026.
3	640	0.989297085361	Antoine Jay, 2026.
3	641	0.989312593081	Antoine Jay, 2026.
3	642	0.989329805069	Antoine Jay, 2026.
3	643	0.989348238645	Henry Cohn, 2026.
3	644	0.989365778020	Antoine Jay, 2026.
3	645	0.989382090433	Henry Cohn, 2026.
3	646	0.989398153265	Antoine Jay, 2026.
3	647	0.989412560581	Henry Cohn, 2026.
3	648	0.989430248098	Antoine Jay, 2026.
3	649	0.989448419535	Antoine Jay, 2026.
3	650	0.989461420595	Henry Cohn, 2026.
3	651	0.989477172719	Antoine Jay, 2026.
3	652	0.989492328439	Antoine Jay, 2026.
3	653	0.989514111691	Antoine Jay, 2026.
3	654	0.989528389272	Henry Cohn, 2024.
3	655	0.989542872527	Henry Cohn, 2026.
3	656	0.989556026849	Antoine Jay, 2026.
3	657	0.989574490806	Antoine Jay, 2026.
3	658	0.989586987026	Antoine Jay, 2026.
3	659	0.989608228928	Antoine Jay, 2026.
3	660	0.989620029682	Henry Cohn, 2026.
3	661	0.989637573715	Henry Cohn, 2026.
3	662	0.989651179949	Antoine Jay, 2026.
3	663	0.989664846590	Antoine Jay, 2026.
3	664	0.989677792146	Antoine Jay, 2026.
3	665	0.989689538393	Antoine Jay, 2026.
3	666	0.989709382193	Antoine Jay, 2026.
3	667	0.989717174328	Antoine Jay, 2026.
3	668	0.989728785522	Antoine Jay, 2026.
3	669	0.989745854740	Antoine Jay, 2026.
3	670	0.989765777159	Henry Cohn, 2024.
3	671	0.989779719224	Antoine Jay, 2026.
3	672	0.989791610602	Antoine Jay, 2026.
3	673	0.989803383306	Antoine Jay, 2026.
3	674	0.989822513451	Antoine Jay, 2026.
3	675	0.989824204407	Antoine Jay, 2026.
3	676	0.989844677872	Antoine Jay, 2026.
3	677	0.989858315152	Antoine Jay, 2026.
3	678	0.989876535128	Antoine Jay, 2026.
3	679	0.989897065545	Antoine Jay, 2026.
3	680	0.989910935742	Antoine Jay, 2026.
3	681	0.989928112762	Antoine Jay, 2026.
3	682	0.989945509386	Antoine Jay, 2026.
3	683	0.989964518656	Antoine Jay, 2026.
3	684	0.989976711497	Henry Cohn, 2026.
3	685	0.989995163911	Antoine Jay, 2026.
3	686	0.990003142707	Antoine Jay, 2026.
3	687	0.990010216029	Antoine Jay, 2026.
3	688	0.990015216226	Antoine Jay, 2026.
3	689	0.990024075153	Antoine Jay, 2026.
3	690	0.990030508982	Antoine Jay, 2026.
3	691	0.990043948471	Antoine Jay, 2026.
3	692	0.990049719467	Antoine Jay, 2026.
3	693	0.990072377412	Antoine Jay, 2026.
3	694	0.990088638584	Antoine Jay, 2026.
3	695	0.990112186137	Antoine Jay, 2026.
3	696	0.990130331424	Antoine Jay, 2026.
3	697	0.990147701774	Antoine Jay, 2026.
3	698	0.990161184258	Antoine Jay, 2026.
3	699	0.990166705398	Antoine Jay, 2026.
3	700	0.990174748139	Antoine Jay, 2026.
3	701	0.990184946152	Henry Cohn, 2026.
3	702	0.990195428201	Antoine Jay, 2026.
3	703	0.990213168813	Antoine Jay, 2026.
3	704	0.990233105514	Antoine Jay, 2026.
3	705	0.990244174304	Antoine Jay, 2026.
3	706	0.990259228929	Antoine Jay, 2026.
3	707	0.990275847056	Antoine Jay, 2026.
3	708	0.990299310428	Antoine Jay, 2026.
3	709	0.990313942630	Antoine Jay, 2026.
3	710	0.990328486808	Antoine Jay, 2026.
3	711	0.990343657516	Antoine Jay, 2026.
3	712	0.990354565437	Antoine Jay, 2026.
3	713	0.990370582233	Antoine Jay, 2026.
3	714	0.990386923851	Henry Cohn, 2026.
3	715	0.990398715014	Henry Cohn, 2026.
3	716	0.990417939893	Antoine Jay, 2026.
3	717	0.990434938173	Antoine Jay, 2026.
3	718	0.990448237688	Henry Cohn, 2024.
3	719	0.990458980758	Antoine Jay, 2026.
3	720	0.990470768988	Antoine Jay, 2026.
3	721	0.990482109810	Antoine Jay, 2026.
3	722	0.990494551328	Antoine Jay, 2026.
3	723	0.990507268425	Antoine Jay, 2026.
3	724	0.990518238914	Antoine Jay, 2026.
3	725	0.990527197765	Antoine Jay, 2026.
3	726	0.990540391364	Antoine Jay, 2026.
3	727	0.990553366436	Antoine Jay, 2026.
3	728	0.990566754002	Antoine Jay, 2026.
3	729	0.990579328611	Antoine Jay, 2026.
3	730	0.990593018922	Antoine Jay, 2026.
3	731	0.990606383200	Antoine Jay, 2026.
3	732	0.990620520226	Antoine Jay, 2026.
3	733	0.990632985385	Antoine Jay, 2026.
3	734	0.990650031145	Antoine Jay, 2026.
3	735	0.990663385058	Henry Cohn, 2026.
3	736	0.990676301529	Antoine Jay, 2026.
3	737	0.990689150380	Henry Cohn, 2026.
3	738	0.990704677084	Henry Cohn, 2024.
3	739	0.990712590288	Henry Cohn, 2026.
3	740	0.990721213799	Antoine Jay, 2026.
3	741	0.990733794060	Antoine Jay, 2026.
3	742	0.990745808407	Antoine Jay, 2026.
3	743	0.990758583077	Antoine Jay, 2026.
3	744	0.990774050675	Antoine Jay, 2026.
3	745	0.990782069775	Antoine Jay, 2026.
3	746	0.990790403691	Antoine Jay, 2026.
3	747	0.990798752530	Antoine Jay, 2026.
3	748	0.990804855397	Antoine Jay, 2026.
3	749	0.990823444501	Antoine Jay, 2026.
3	750	0.990838051026	Antoine Jay, 2026.
3	751	0.990848217974	Antoine Jay, 2026.
3	752	0.990863314275	Antoine Jay, 2026.
3	753	0.990870643929	Antoine Jay, 2026.
3	754	0.990891813894	Antoine Jay, 2026.
3	755	0.990898642484	Henry Cohn, 2026.
3	756	0.990907385040	Antoine Jay, 2026.
3	757	0.990919004877	Antoine Jay, 2026.
3	758	0.990931791504	Antoine Jay, 2026.
3	759	0.990948080272	Antoine Jay, 2026.
3	760	0.990957023242	Antoine Jay, 2026.
3	761	0.990973445618	Antoine Jay, 2026.
3	762	0.990981734597	Antoine Jay, 2026.
3	763	0.990993431032	Antoine Jay, 2026.
3	764	0.991001594495	Antoine Jay, 2026.
3	765	0.991018496613	Antoine Jay, 2026.
3	766	0.991034013908	Henry Cohn, 2026.
3	767	0.991054056532	Antoine Jay, 2026.
3	768	0.991061479408	Henry Cohn, 2026.
3	769	0.991069201953	Antoine Jay, 2026.
3	770	0.991083942446	Antoine Jay, 2026.
3	771	0.991091079354	Henry Cohn, 2026.
3	772	0.991105143241	Antoine Jay, 2026.
3	773	0.991117205198	Antoine Jay, 2026.
3	774	0.991127072576	Antoine Jay, 2026.
3	775	0.991136894702	Antoine Jay, 2026.
3	776	0.991145168494	Antoine Jay, 2026.
3	777	0.991155507750	Antoine Jay, 2026.
3	778	0.991167453340	Antoine Jay, 2026.
3	779	0.991179257795	Antoine Jay, 2026.
3	780	0.991194037221	Antoine Jay, 2026.
3	781	0.991201092291	Antoine Jay, 2026.
3	782	0.991209823270	Antoine Jay, 2026.
3	783	0.991220308032	Antoine Jay, 2026.
3	784	0.991231480431	Antoine Jay, 2026.
3	785	0.991241878022	Antoine Jay, 2026.
3	786	0.991257179931	Antoine Jay, 2026.
3	787	0.991267590682	Henry Cohn, 2026.
3	788	0.991272827701	Antoine Jay, 2026.
3	789	0.991284297051	Antoine Jay, 2026.
3	790	0.991293857653	Antoine Jay, 2026.
3	791	0.991308010128	Antoine Jay, 2026.
3	792	0.991321548698	Antoine Jay, 2026.
3	793	0.991334012066	Antoine Jay, 2026.
3	794	0.991342884325	Antoine Jay, 2026.
3	795	0.991355304584	Antoine Jay, 2026.
3	796	0.991369426758	Antoine Jay, 2026.
3	797	0.991379427026	Antoine Jay, 2026.
3	798	0.991387368744	Antoine Jay, 2026.
3	799	0.991401562374	Antoine Jay, 2026.
3	800	0.991412852948	Antoine Jay, 2026.
3	801	0.991420587755	Antoine Jay, 2026.
3	802	0.991433978804	Henry Cohn, 2026.
3	803	0.991445422902	Antoine Jay, 2026.
3	804	0.991453184032	Henry Cohn, 2026.
3	805	0.991465077808	Antoine Jay, 2026.
3	806	0.991476886053	Antoine Jay, 2026.
3	807	0.991488929992	Henry Cohn, 2026.
3	808	0.991493793941	Antoine Jay, 2026.
3	809	0.991501492895	Antoine Jay, 2026.
3	810	0.991511034948	Antoine Jay, 2026.
3	811	0.991520983395	Antoine Jay, 2026.
3	812	0.991526678194	Antoine Jay, 2026.
3	813	0.991537189112	Antoine Jay, 2026.
3	814	0.991545807128	Antoine Jay, 2026.
3	815	0.991555319558	Antoine Jay, 2026.
3	816	0.991569882781	Antoine Jay, 2026.
3	817	0.991578450781	Antoine Jay, 2026.
3	818	0.991589801252	Antoine Jay, 2026.
3	819	0.991604428530	Antoine Jay, 2026.
3	820	0.991612217714	Antoine Jay, 2026.
3	821	0.991622680066	Antoine Jay, 2026.
3	822	0.991629380413	Antoine Jay, 2026.
3	823	0.991637880056	Antoine Jay, 2026.
3	824	0.991646552805	Antoine Jay, 2026.
3	825	0.991657054580	Antoine Jay, 2026.
3	826	0.991665648672	Antoine Jay, 2026.
3	827	0.991679718253	Antoine Jay, 2026.
3	828	0.991691393645	Antoine Jay, 2026.
3	829	0.991703450922	Antoine Jay, 2026.
3	830	0.991715253156	Antoine Jay, 2026.
3	831	0.991721242520	Antoine Jay, 2026.
3	832	0.991732788637	Antoine Jay, 2026.
3	833	0.991741159913	Antoine Jay, 2026.
3	834	0.991752722437	Antoine Jay, 2026.
3	835	0.991760041337	Henry Cohn, 2026.
3	836	0.991769617104	Henry Cohn, 2026.
3	837	0.991780131221	Henry Cohn, 2026.
3	838	0.991793296667	Antoine Jay, 2026.
3	839	0.991798530900	Antoine Jay, 2026.
3	840	0.991804754582	Henry Cohn, 2026.
3	841	0.991814323308	Henry Cohn, 2026.
3	842	0.991823210380	Henry Cohn, 2026.
3	843	0.991831775406	Henry Cohn, 2026.
3	844	0.991840474750	Henry Cohn, 2026.
3	845	0.991848392337	Antoine Jay, 2026.
3	846	0.991856641148	Antoine Jay, 2026.
3	847	0.991864742782	Antoine Jay, 2026.
3	848	0.991873396735	Antoine Jay, 2026.
3	849	0.991880802104	Antoine Jay, 2026.
3	850	0.991888525780	Henry Cohn, 2026.
3	851	0.991896793561	Antoine Jay, 2026.
3	852	0.991904228280	Antoine Jay, 2026.
3	853	0.991917862343	Henry Cohn, 2026.
3	854	0.991932276509	Antoine Jay, 2026.
3	855	0.991947953670	Antoine Jay, 2026.
3	856	0.991957977192	Antoine Jay, 2026.
3	857	0.991970551877	Antoine Jay, 2026.
3	858	0.991978577813	Antoine Jay, 2026.
3	859	0.991988241941	Antoine Jay, 2026.
3	860	0.991995730812	Antoine Jay, 2026.
3	861	0.992005674809	Antoine Jay, 2026.
3	862	0.992017778445	Antoine Jay, 2026.
3	863	0.992022892213	Antoine Jay, 2026.
3	864	0.992032415887	Antoine Jay, 2026.
3	865	0.992040102992	Antoine Jay, 2026.
3	866	0.992047814017	Antoine Jay, 2026.
3	867	0.992053956655	Antoine Jay, 2026.
3	868	0.992064131252	Antoine Jay, 2026.
3	869	0.992072857610	Antoine Jay, 2026.
3	870	0.992080865839	Antoine Jay, 2026.
3	871	0.992089958881	Antoine Jay, 2026.
3	872	0.992098609076	Antoine Jay, 2026.
3	873	0.992109594640	Antoine Jay, 2026.
3	874	0.992123631704	Antoine Jay, 2026.
3	875	0.992132177747	Antoine Jay, 2026.
3	876	0.992140936121	Antoine Jay, 2026.
3	877	0.992149947046	Antoine Jay, 2026.
3	878	0.992160175361	Antoine Jay, 2026.
3	879	0.992168459233	Antoine Jay, 2026.
3	880	0.992178909104	Antoine Jay, 2026.
3	881	0.992188247941	Antoine Jay, 2026.
3	882	0.992194602267	Antoine Jay, 2026.
3	883	0.992199976372	Antoine Jay, 2026.
3	884	0.992209467978	Antoine Jay, 2026.
3	885	0.992218883899	Antoine Jay, 2026.
3	886	0.992228098391	Joseph Farland, 2026.
3	887	0.992236502483	Antoine Jay, 2026.
3	888	0.992244856127	Antoine Jay, 2026.
3	889	0.992249403258	Antoine Jay, 2026.
3	890	0.992255071734	Antoine Jay, 2026.
3	891	0.992264482521	Antoine Jay, 2026.
3	892	0.992273559041	Antoine Jay, 2026.
3	893	0.992285198532	Antoine Jay, 2026.
3	894	0.992295144198	Antoine Jay, 2026.
3	895	0.992303398480	Antoine Jay, 2026.
3	896	0.992314948574	Antoine Jay, 2026.
3	897	0.992320289977	Antoine Jay, 2026.
3	898	0.992326804829	Antoine Jay, 2026.
3	899	0.992342930514	Antoine Jay, 2026.
3	900	0.992351846776	Antoine Jay, 2026.
3	901	0.992359234184	Henry Cohn, 2026.
3	902	0.992363270295	Antoine Jay, 2026.
3	903	0.992368790115	Antoine Jay, 2026.
3	904	0.992373967239	Antoine Jay, 2026.
3	905	0.992379504116	Antoine Jay, 2026.
3	906	0.992385013796	Antoine Jay, 2026.
3	907	0.992390525784	Antoine Jay, 2026.
3	908	0.992398251421	Antoine Jay, 2026.
3	909	0.992406650098	Antoine Jay, 2026.
3	910	0.992414829941	Antoine Jay, 2026.
3	911	0.992427714754	Antoine Jay, 2026.
3	912	0.992442625898	Antoine Jay, 2026.
3	913	0.992453873099	Antoine Jay, 2026.
3	914	0.992461451057	Antoine Jay, 2026.
3	915	0.992469119083	Antoine Jay, 2026.
3	916	0.992475396191	Antoine Jay, 2026.
3	917	0.992483130594	Antoine Jay, 2026.
3	918	0.992493179809	Antoine Jay, 2026.
3	919	0.992500045108	Antoine Jay, 2026.
3	920	0.992508200184	Antoine Jay, 2026.
3	921	0.992517795902	Antoine Jay, 2026.
3	922	0.992524652841	Antoine Jay, 2026.
3	923	0.992532627473	Antoine Jay, 2026.
3	924	0.992542488232	Antoine Jay, 2026.
3	925	0.992551181847	Antoine Jay, 2026.
3	926	0.992560570552	Antoine Jay, 2026.
3	927	0.992571835258	Antoine Jay, 2026.
3	928	0.992578857578	Antoine Jay, 2026.
3	929	0.992585214902	Antoine Jay, 2026.
3	930	0.992591337458	Antoine Jay, 2026.
3	931	0.992600310245	Antoine Jay, 2026.
3	932	0.992609227455	Antoine Jay, 2026.
3	933	0.992617089891	Antoine Jay, 2026.
3	934	0.992625097925	Antoine Jay, 2026.
3	935	0.992632212491	Antoine Jay, 2026.
3	936	0.992639564779	Antoine Jay, 2026.
3	937	0.992648583886	Joseph Farland, 2026.
3	938	0.992657288761	Antoine Jay, 2026.
3	939	0.992666642244	Antoine Jay, 2026.
3	940	0.992674971819	Antoine Jay, 2026.
3	941	0.992684277552	Henry Cohn, 2026.
3	942	0.992692529469	Antoine Jay, 2026.
3	943	0.992696458600	Antoine Jay, 2026.
3	944	0.992702830822	Antoine Jay, 2026.
3	945	0.992709333379	Antoine Jay, 2026.
3	946	0.992717742353	Antoine Jay, 2026.
3	947	0.992723773131	Antoine Jay, 2026.
3	948	0.992729424666	Antoine Jay, 2026.
3	949	0.992736449021	Antoine Jay, 2026.
3	950	0.992747116974	Henry Cohn, 2026.
3	951	0.992757674072	Antoine Jay, 2026.
3	952	0.992764719358	Arhan Canli, 2026.
3	953	0.992771437613	Antoine Jay, 2026.
3	954	0.992777313007	Antoine Jay, 2026.
3	955	0.992785473328	Antoine Jay, 2026.
3	956	0.992798700278	Antoine Jay, 2026.
3	957	0.992803751946	Antoine Jay, 2026.
3	958	0.992812773362	Antoine Jay, 2026.
3	959	0.992820236118	Antoine Jay, 2026.
3	960	0.992825883272	Antoine Jay, 2026.
3	961	0.992831944498	Antoine Jay, 2026.
3	962	0.992838208362	Antoine Jay, 2026.
3	963	0.992847143563	Antoine Jay, 2026.
3	964	0.992854000711	Antoine Jay, 2026.
3	965	0.992859391632	Antoine Jay, 2026.
3	966	0.992866627528	Antoine Jay, 2026.
3	967	0.992874137738	Antoine Jay, 2026.
3	968	0.992878711395	Antoine Jay, 2026.
3	969	0.992882639475	Antoine Jay, 2026.
3	970	0.992892561078	Antoine Jay, 2026.
3	971	0.992896819831	Antoine Jay, 2026.
3	972	0.992902815460	Antoine Jay, 2026.
3	973	0.992910779257	Antoine Jay, 2026.
3	974	0.992922858070	Antoine Jay, 2026.
3	975	0.992930655144	Antoine Jay, 2026.
3	976	0.992935632714	Antoine Jay, 2026.
3	977	0.992942151792	Antoine Jay, 2026.
3	978	0.992949777445	Antoine Jay, 2026.
3	979	0.992960469870	Antoine Jay, 2026.
3	980	0.992966741992	Antoine Jay, 2026.
3	981	0.992973232097	Antoine Jay, 2026.
3	982	0.992980289896	Antoine Jay, 2026.
3	983	0.992987990572	Antoine Jay, 2026.
3	984	0.992995021125	Antoine Jay, 2026.
3	985	0.993002596190	Antoine Jay, 2026.
3	986	0.993010363243	Antoine Jay, 2026.
3	987	0.993015620954	Henry Cohn, 2026.
3	988	0.993022276224	Henry Cohn, 2026.
3	989	0.993033146692	Antoine Jay, 2026.
3	990	0.993035618327	Antoine Jay, 2026.
3	991	0.993043384691	Joseph Farland, 2026.
3	992	0.993050281399	Antoine Jay, 2026.
3	993	0.993054265702	Antoine Jay, 2026.
3	994	0.993059717229	Antoine Jay, 2026.
3	995	0.993066714676	Antoine Jay, 2026.
3	996	0.993072572268	Antoine Jay, 2026.
3	997	0.993080560471	Antoine Jay, 2026.
3	998	0.993087960168	Antoine Jay, 2026.
3	999	0.993095371140	Antoine Jay, 2026.
3	1000	0.993103336080	Antoine Jay, 2026.
3	1001	0.993111229583	Antoine Jay, 2026.
3	1002	0.993117686502	Antoine Jay, 2026.
3	1003	0.993124139513	Antoine Jay, 2026.
3	1004	0.993133111254	Antoine Jay, 2026.
3	1005	0.993142171134	Antoine Jay, 2026.
3	1006	0.993150204240	Antoine Jay, 2026.
3	1007	0.993154661343	Antoine Jay, 2026.
3	1008	0.993157819766	Antoine Jay, 2026.
3	1009	0.993163272197	Antoine Jay, 2026.
3	1010	0.993170318002	Antoine Jay, 2026.
3	1011	0.993175076360	Antoine Jay, 2026.
3	1012	0.993181260702	Antoine Jay, 2026.
3	1013	0.993189485118	Antoine Jay, 2026.
3	1014	0.993195726531	Antoine Jay, 2026.
3	1015	0.993198966173	Antoine Jay, 2026.
3	1016	0.993206239653	Antoine Jay, 2026.
3	1017	0.993212860337	Antoine Jay, 2026.
3	1018	0.993219384861	Antoine Jay, 2026.
3	1019	0.993226370050	Antoine Jay, 2026.
3	1020	0.993235373238	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	1021	0.993241517009	Antoine Jay, 2026.
3	1022	0.993248664953	Antoine Jay, 2026.
3	1023	0.993255294103	Antoine Jay, 2026.
3	1024	0.993262211836	Antoine Jay, 2026.
4	9	0.162015199612	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $16 x^{3} - 16 x^{2} - 4 x + 1$
4	10*	0.166666666667	A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011; C. Bachoc and F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, J. Combin. Theory Ser. A 116 (2009), 195–204, doi:10.1016/j.jcta.2008.05.001. $6 x - 1$
4	11	0.230405563595	L. T. Wille, Close packing in curved space by simulated annealing, Journal of Physics A: Mathematical and General 20 (1987), L1211–L1218, doi:10.1088/0305-4470/20/17/014. $8 x^{3} - 12 x^{2} - 2 x + 1$
4	12*	0.25	A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011; D. de Laat, N. M. Leijenhorst, and W. H. H. de Muinck Keizer, Traceless projection of tensors with applications to hierarchies in discrete geometry, in preparation, 2026+; N. M. Leijenhorst, On the computation of three and four-point bounds in discrete geometry and analytic number theory, doctoral thesis, TU Delft, 2025, doi:10.4233/uuid:91af805a-376c-4ef8-aec5-e6ce08ae20a7. $4 x - 1$
4	13	0.307295653982	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $5632 x^{9} + 9472 x^{8} - 3072 x^{7} - 5888 x^{6} + 544 x^{5} + 944 x^{4} + 152 x^{3} - 44 x^{2} - 14 x - 1$
4	14	0.319518594213	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $58 x^{7} + 174 x^{6} + 140 x^{5} - 16 x^{4} - 54 x^{3} - 10 x^{2} + 4 x + 1$
4	15	0.350992175946	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $36 x^{4} - 18 x^{3} + 10 x^{2} - 1$
4	16	0.387628177123	A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011. $256 x^{10} + 1024 x^{9} + 256 x^{8} - 1152 x^{7} + 160 x^{6} + 176 x^{5} - 144 x^{4} + 36 x^{3} + 37 x^{2} - 6 x - 3$
4	17	0.412259362694	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	18	0.422819414074	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. Minimal polynomial of degree 16
4	19	0.434258545911	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $3 x^{2} + x - 1$
4	20	0.434258545911	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $3 x^{2} + x - 1$
4	21	0.471380858508	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $16 x^{8} - 128 x^{7} - 64 x^{6} + 32 x^{5} + 72 x^{4} + 32 x^{3} - 16 x^{2} - 8 x + 1$
4	22	0.497884130844	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	23	0.5	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $2 x - 1$
4	24*	0.5	L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; D. de Laat, N. Leijenhorst, and W. H. H. de Muinck Keizer, Optimality and uniqueness of the D₄ root system, preprint, 2024, arXiv:2404.18794. $2 x - 1$
4	25	0.537316056656	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	26	0.540789617698	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $3392 x^{6} + 2112 x^{5} - 496 x^{4} - 656 x^{3} - 132 x^{2} + 6 x - 1$
4	27	0.557591351181	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $794 x^{5} + 393 x^{4} - 344 x^{3} - 82 x^{2} + 6 x + 1$
4	28	0.567338804075	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	29	0.573148530449	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. Minimal polynomial of degree 58
4	30	0.584232813931	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	31	0.590765838581	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
4	32	0.595720149236	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	33	0.600755407756	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	34	0.610128556790	Henry Cohn, 2024.
4	35	0.621523986641	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	36	0.628309089475	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	37	0.630368722499	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	38	0.640732732793	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	39	0.646928247960	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	40	0.650497801063	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4	41	0.655274051124	Henry Cohn, 2024.
4	42	0.658420878517	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	43	0.662667198430	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4	44	0.668804906276	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $36 x^{8} - 60 x^{7} + 481 x^{6} + 166 x^{5} - 205 x^{4} - 116 x^{3} + 11 x^{2} + 10 x + 1$
4	45	0.676924957837	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	46	0.682325866078	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	47	0.685400852293	Henry Cohn, 2025.
4	48	0.689831186714	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	49	0.693413660571	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	50	0.693726127145	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. Minimal polynomial of degree 10
4	51	0.701375493264	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	52	0.703627792371	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	53	0.707671488219	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	54	0.709714380727	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	55	0.715661893754	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	56	0.719201427062	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	57	0.722366203194	Henry Cohn, 2025.
4	58	0.724963759986	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	59	0.726684594037	Henry Cohn, 2025.
4	60	0.728768479335	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	61	0.731517689032	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	62	0.733882910506	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	63	0.738725371284	Henry Cohn, 2025.
4	64	0.739558032728	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	65	0.742483255369	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	66	0.745996162085	Henry Cohn, 2025.
4	67	0.748966563154	Henry Cohn, 2025.
4	68	0.751044149551	Henry Cohn, 2025.
4	69	0.752628993819	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	70	0.753734038368	Henry Cohn, 2025.
4	71	0.756373364760	Henry Cohn, 2025.
4	72	0.758022144348	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	73	0.759191014470	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	74	0.759545691353	Henry Cohn, 2025.
4	75	0.760558878464	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	76	0.761064664765	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. Minimal polynomial of degree 56
4	77	0.765200782016	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	78	0.768765601292	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	79	0.773060404397	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	80	0.775691894892	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	81	0.777799033764	Henry Cohn, 2025.
4	82	0.779753559198	Henry Cohn, 2025.
4	83	0.781053544402	Henry Cohn, 2025.
4	84	0.782373204314	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	85	0.783715044186	Henry Cohn, 2024.
4	86	0.784899010819	Henry Cohn, 2026.
4	87	0.785487328991	Henry Cohn, 2025.
4	88	0.785927649195	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	89	0.788520093069	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	90	0.790391197000	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	91	0.791393154383	Henry Cohn, 2025.
4	92	0.792211293351	Henry Cohn, 2025.
4	93	0.793047017514	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	94	0.793553793569	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	95	0.796982807052	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	96	0.797980534415	Henry Cohn, 2025.
4	97	0.799480375605	Henry Cohn, 2023.
4	98	0.800757084766	Henry Cohn, 2026.
4	99	0.801793100994	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	100	0.803178722499	Henry Cohn, 2025.
4	101	0.803884649087	Henry Cohn, 2025.
4	102	0.804699654814	Henry Cohn, 2025.
4	103	0.805093331367	Henry Cohn, 2025.
4	104	0.806308735044	Henry Cohn, 2025.
4	105	0.807104881635	Henry Cohn, 2026.
4	106	0.807600771583	Henry Cohn, 2025.
4	107	0.808031793624	Henry Cohn, 2025.
4	108	0.808461453357	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	109	0.808686924144	Henry Cohn, 2026.
4	110	0.808927278464	Henry Cohn, 2026.
4	111	0.808991157916	Henry Cohn, 2025.
4	112	0.809016055614	Henry Cohn, 2025.
4	113	0.809016993589	Henry Cohn, 2026.
4	114	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	115	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	116	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	117	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	118	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	119	0.809016994375	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $4 x^{2} - 2 x - 1$
4	120*	0.809016994375	L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Mathematica Academiae Scientiarum Hungarica 32 (1978), 243–261, doi:10.1007/BF01902361. $4 x^{2} - 2 x - 1$
4	121	0.824637992952	Henry Cohn, 2026.
4	122	0.826366133292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	123	0.827329141763	Henry Cohn, 2026.
4	124	0.829076814196	Henry Cohn, 2025.
4	125	0.830275122838	Henry Cohn, 2025.
4	126	0.831265387603	Henry Cohn, 2026.
4	127	0.832257256453	Henry Cohn, 2026.
4	128	0.833179033616	Henry Cohn, 2026.
4	129	0.833853106202	Henry Cohn, 2025.
4	130	0.834729130389	Henry Cohn, 2025.
4	131	0.835330073631	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	132	0.835824295438	WolfFrogs, 2026.
4	133	0.836898862653	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	134	0.837404919734	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	135	0.837973296726	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	136	0.838381205119	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	137	0.838774742033	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	138	0.839060498538	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	139	0.839472488807	Antoine Jay, 2026.
4	140	0.839788592759	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	141	0.840151651527	Antoine Jay, 2026.
4	142	0.840928789319	Henry Cohn, 2025.
4	143	0.842625863066	Henry Cohn, 2025.
4	144	0.843224738610	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	145	0.845004703395	Henry Cohn, 2025.
4	146	0.846032955845	Antoine Jay, 2026.
4	147	0.846808291003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	148	0.847320837337	Henry Cohn, 2025.
4	149	0.847701351395	Henry Cohn, 2025.
4	150	0.848007962329	Henry Cohn, 2026.
4	151	0.848381266848	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	152	0.848701931506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	153	0.849102358280	Henry Cohn, 2026.
4	154	0.849441145118	Antoine Jay, 2026.
4	155	0.850521509148	Antoine Jay, 2026.
4	156	0.852364181174	Henry Cohn, 2025.
4	157	0.853098036527	Henry Cohn, 2025.
4	158	0.853541001367	Henry Cohn, 2025.
4	159	0.853832223138	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	160	0.854015402705	Henry Cohn, 2025.
4	161	0.855034788504	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	162	0.856011990176	Henry Cohn, 2025.
4	163	0.856415430312	Henry Cohn, 2026.
4	164	0.856668082967	Henry Cohn, 2025.
4	165	0.856908324217	Henry Cohn, 2024.
4	166	0.857225212584	Antoine Jay, 2026.
4	167	0.857623781724	Henry Cohn, 2025.
4	168	0.859313315479	Henry Cohn, 2026.
4	169	0.860416214468	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	170	0.861163976919	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	171	0.861860457084	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	172	0.862259278969	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	173	0.862713337568	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	174	0.863032216222	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	175	0.863219626411	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	176	0.863541636392	Antoine Jay, 2026.
4	177	0.863735316880	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	178	0.863916425407	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	179	0.864723195011	Henry Cohn, 2025.
4	180	0.865779496303	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	181	0.866478028994	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	182	0.866999103714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	183	0.867321728092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	184	0.867752439883	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	185	0.868210887137	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	186	0.868503854814	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	187	0.868812628892	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	188	0.869170807232	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	189	0.869490893942	Antoine Jay, 2026.
4	190	0.870034930876	Antoine Jay, 2026.
4	191	0.870814241870	Henry Cohn, 2025.
4	192	0.871291918040	Antoine Jay, 2026.
4	193	0.871542554779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	194	0.871792013221	Henry Cohn, 2025.
4	195	0.872104790050	Antoine Jay, 2026.
4	196	0.872618344187	Antoine Jay, 2026.
4	197	0.873486718836	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	198	0.874154745460	Antoine Jay, 2026.
4	199	0.874934007957	Antoine Jay, 2026.
4	200	0.875565480080	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	201	0.875972803452	Antoine Jay, 2026.
4	202	0.876364532678	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	203	0.876769879845	Antoine Jay, 2026.
4	204	0.877141575051	Antoine Jay, 2026.
4	205	0.877397692359	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	206	0.877688778825	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	207	0.877931193622	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	208	0.878149163396	Antoine Jay, 2026.
4	209	0.878612898618	Antoine Jay, 2026.
4	210	0.879170006117	Antoine Jay, 2026.
4	211	0.879424605083	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	212	0.879588052399	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	213	0.879782298893	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	214	0.879945189010	Antoine Jay, 2026.
4	215	0.880272662054	Henry Cohn, 2025.
4	216	0.880886649220	Henry Cohn, 2026.
4	217	0.881471958903	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	218	0.881811305066	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	219	0.881951865237	Antoine Jay, 2026.
4	220	0.882544919478	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	221	0.882998375696	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	222	0.883456069925	Henry Cohn, 2025.
4	223	0.884116929277	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	224	0.884567598136	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	225	0.884939723272	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	226	0.885215992226	Antoine Jay, 2026.
4	227	0.885494793921	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	228	0.885767422205	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	229	0.886031940795	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	230	0.886364304610	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	231	0.886733709714	Antoine Jay, 2026.
4	232	0.887068100429	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	233	0.887295434839	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	234	0.887585611623	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	235	0.887849817683	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	236	0.888072337269	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	237	0.888442766077	Antoine Jay, 2026.
4	238	0.888868274572	Antoine Jay, 2026.
4	239	0.889105362853	Henry Cohn, 2026.
4	240	0.889477098095	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	241	0.889798189525	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	242	0.890094523657	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	243	0.890327494714	Henry Cohn, 2025.
4	244	0.890617063831	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	245	0.890928343137	Antoine Jay, 2026.
4	246	0.891229627359	Antoine Jay, 2026.
4	247	0.891664059840	Henry Cohn, 2026.
4	248	0.891976307814	Antoine Jay, 2026.
4	249	0.892189641969	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	250	0.892630822838	Henry Cohn, 2026.
4	251	0.892919512389	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	252	0.893141824147	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	253	0.893447011118	Antoine Jay, 2026.
4	254	0.893683630257	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	255	0.893979929375	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	256	0.894458817070	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	257	0.894676913068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	258	0.894979744467	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	259	0.895312799200	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	260	0.895514991230	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	261	0.895719186710	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	262	0.895872566241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	263	0.896110999549	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	264	0.896385068073	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	265	0.896712282757	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	266	0.896886624454	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	267	0.897043320127	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	268	0.897211713567	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	269	0.897441326108	Antoine Jay, 2026.
4	270	0.897703831823	Antoine Jay, 2026.
4	271	0.897956854415	WolfFrogs, 2026.
4	272	0.898160315150	Henry Cohn, 2026.
4	273	0.898312901925	WolfFrogs, 2026.
4	274	0.898501943447	Antoine Jay, 2026.
4	275	0.898694169669	Antoine Jay, 2026.
4	276	0.898928185300	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	277	0.899220630949	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	278	0.899374768251	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	279	0.899512341354	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	280	0.899632074734	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	281	0.900108840945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	282	0.900626807599	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	283	0.900975636655	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	284	0.901133046719	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	285	0.901205680841	Antoine Jay, 2026.
4	286	0.901347768965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	287	0.901396418795	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	288	0.901415628271	Antoine Jay, 2026.
4	289	0.902147118232	Antoine Jay, 2026.
4	290	0.902628071679	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	291	0.903091733725	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	292	0.903471504338	Henry Cohn, 2026.
4	293	0.903697039427	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	294	0.903946299821	Antoine Jay, 2026.
4	295	0.904181784760	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	296	0.904396588445	Antoine Jay, 2026.
4	297	0.904599994876	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	298	0.904829436006	Antoine Jay, 2026.
4	299	0.905018028171	Antoine Jay, 2026.
4	300	0.905130142401	Antoine Jay, 2026.
4	301	0.905236043122	Antoine Jay, 2026.
4	302	0.905620556225	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	303	0.905822596112	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	304	0.905940433081	Antoine Jay, 2026.
4	305	0.906204165764	Antoine Jay, 2026.
4	306	0.906439446769	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	307	0.906617510667	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	308	0.906838944174	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	309	0.906997560706	Antoine Jay, 2026.
4	310	0.907191157217	Arhan Canli, 2026.
4	311	0.907399977535	Antoine Jay, 2026.
4	312	0.907603233813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	313	0.907775211720	Antoine Jay, 2026.
4	314	0.908030505206	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	315	0.908206562009	Antoine Jay, 2026.
4	316	0.908393194062	Antoine Jay, 2026.
4	317	0.908606509747	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	318	0.908752248940	Antoine Jay, 2026.
4	319	0.908967805697	Antoine Jay, 2026.
4	320	0.909064991593	Antoine Jay, 2026.
4	321	0.909394517495	Antoine Jay, 2026.
4	322	0.909515466459	Antoine Jay, 2026.
4	323	0.909658884266	Antoine Jay, 2026.
4	324	0.909779049491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	325	0.909962141544	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	326	0.910100840900	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	327	0.910270353608	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	328	0.910387032754	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	329	0.910628876799	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	330	0.910807685798	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	331	0.911047740827	Antoine Jay, 2026.
4	332	0.911267635211	Antoine Jay, 2026.
4	333	0.911437609294	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	334	0.911626472720	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	335	0.911849672707	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	336	0.911992187992	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	337	0.912164170114	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	338	0.912352631153	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	339	0.912515606927	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	340	0.912640809843	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	341	0.912704448322	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	342	0.912908591861	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	343	0.913079603359	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	344	0.913225557771	Antoine Jay, 2026.
4	345	0.913344098227	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	346	0.913474514501	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	347	0.913618377940	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	348	0.913874985347	Antoine Jay, 2026.
4	349	0.914223948768	Antoine Jay, 2026.
4	350	0.914423114200	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	351	0.914622374712	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	352	0.914759341781	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	353	0.914881983628	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	354	0.915025153648	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	355	0.915181026254	Antoine Jay, 2026.
4	356	0.915333949173	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	357	0.915491374249	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	358	0.915665862738	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	359	0.915796345877	Antoine Jay, 2026.
4	360	0.915905644540	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	361	0.916062572957	Antoine Jay, 2026.
4	362	0.916201824684	Antoine Jay, 2026.
4	363	0.916327076943	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	364	0.916486139182	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	365	0.916624016013	Antoine Jay, 2026.
4	366	0.916748136675	Antoine Jay, 2026.
4	367	0.916882943297	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	368	0.916997602816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	369	0.917088962587	Antoine Jay, 2026.
4	370	0.917242999091	Antoine Jay, 2026.
4	371	0.917382656503	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	372	0.917501189734	Antoine Jay, 2026.
4	373	0.917605928234	Antoine Jay, 2026.
4	374	0.917757694308	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	375	0.917869187384	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	376	0.918057159734	Antoine Jay, 2026.
4	377	0.918237978677	Antoine Jay, 2026.
4	378	0.918436180707	Antoine Jay, 2026.
4	379	0.918579341419	Antoine Jay, 2026.
4	380	0.918650510876	Antoine Jay, 2026.
4	381	0.918761170508	Antoine Jay, 2026.
4	382	0.918926834738	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	383	0.919074727790	Antoine Jay, 2026.
4	384	0.919224095482	Antoine Jay, 2026.
4	385	0.919317490909	Antoine Jay, 2026.
4	386	0.919407387144	Antoine Jay, 2026.
4	387	0.919468891854	Antoine Jay, 2026.
4	388	0.919495433313	Antoine Jay, 2026.
4	389	0.919655370440	Antoine Jay, 2026.
4	390	0.919818909563	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	391	0.920025487324	Antoine Jay, 2026.
4	392	0.920159769845	Antoine Jay, 2026.
4	393	0.920319488453	Antoine Jay, 2026.
4	394	0.920398990111	Antoine Jay, 2026.
4	395	0.920431996327	Antoine Jay, 2026.
4	396	0.920515273268	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	397	0.920799688032	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	398	0.920982368400	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	399	0.921120613530	Antoine Jay, 2026.
4	400	0.921271378028	Antoine Jay, 2026.
4	401	0.921415910405	Antoine Jay, 2026.
4	402	0.921500254339	Antoine Jay, 2026.
4	403	0.921588234009	Antoine Jay, 2026.
4	404	0.921665001170	Antoine Jay, 2026.
4	405	0.921735617973	Antoine Jay, 2026.
4	406	0.921817043314	Antoine Jay, 2026.
4	407	0.921904519375	Antoine Jay, 2026.
4	408	0.921990208825	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
4	409	0.922310560935	Antoine Jay, 2026.
4	410	0.922611954286	Antoine Jay, 2026.
4	411	0.922695906836	Antoine Jay, 2026.
4	412	0.922837605398	Antoine Jay, 2026.
4	413	0.922993812241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	414	0.923098742885	Antoine Jay, 2026.
4	415	0.923223858695	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	416	0.923319766287	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	417	0.923435660747	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	418	0.923537420842	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	419	0.923705957474	Antoine Jay, 2026.
4	420	0.923815406748	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	421	0.923926199694	Antoine Jay, 2026.
4	422	0.924019686431	Antoine Jay, 2026.
4	423	0.924253108786	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	424	0.924438407236	Antoine Jay, 2026.
4	425	0.924562704668	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	426	0.924680167639	Antoine Jay, 2026.
4	427	0.924813846888	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	428	0.924925377332	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	429	0.925038323965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	430	0.925156636548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	431	0.925274677385	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	432	0.925422507023	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	433	0.925585967502	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	434	0.925724159711	Antoine Jay, 2026.
4	435	0.925826576113	Antoine Jay, 2026.
4	436	0.925981018356	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	437	0.926142953257	Antoine Jay, 2026.
4	438	0.926222764221	Antoine Jay, 2026.
4	439	0.926352153124	Antoine Jay, 2026.
4	440	0.926432496857	Antoine Jay, 2026.
4	441	0.926550948849	Antoine Jay, 2026.
4	442	0.926643796223	Antoine Jay, 2026.
4	443	0.926720036198	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	444	0.926799468241	Antoine Jay, 2026.
4	445	0.926866032028	Antoine Jay, 2026.
4	446	0.927011244619	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	447	0.927110541819	Antoine Jay, 2026.
4	448	0.927263989666	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	449	0.927408966142	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	450	0.927512002189	Antoine Jay, 2026.
4	451	0.927609985866	Antoine Jay, 2026.
4	452	0.927687890534	Antoine Jay, 2026.
4	453	0.927823502476	Antoine Jay, 2026.
4	454	0.927912677204	Antoine Jay, 2026.
4	455	0.927984392982	Antoine Jay, 2026.
4	456	0.928040782158	Antoine Jay, 2026.
4	457	0.928131810371	Antoine Jay, 2026.
4	458	0.928268618523	Antoine Jay, 2026.
4	459	0.928412017167	Antoine Jay, 2026.
4	460	0.928491680630	Antoine Jay, 2026.
4	461	0.928585263252	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	462	0.928647375151	Antoine Jay, 2026.
4	463	0.928750831263	Antoine Jay, 2026.
4	464	0.928857519838	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	465	0.928935726341	Antoine Jay, 2026.
4	466	0.929012388008	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	467	0.929098825548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	468	0.929159239546	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	469	0.929313415841	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	470	0.929424756820	Antoine Jay, 2026.
4	471	0.929596568928	Antoine Jay, 2026.
4	472	0.929720316348	Antoine Jay, 2026.
4	473	0.929807687242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	474	0.929899574513	Antoine Jay, 2026.
4	475	0.929962794498	Antoine Jay, 2026.
4	476	0.930097236129	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	477	0.930184048740	Antoine Jay, 2026.
4	478	0.930296064018	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	479	0.930399562072	Antoine Jay, 2026.
4	480	0.930544019004	Antoine Jay, 2026.
4	481	0.930618385950	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	482	0.930743558099	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	483	0.930829856163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	484	0.930910368024	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	485	0.931022746840	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	486	0.931061346666	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	487	0.931186917778	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	488	0.931282048328	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	489	0.931375886074	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	490	0.931461221147	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	491	0.931593595014	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	492	0.931665131260	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	493	0.931713675705	Antoine Jay, 2026.
4	494	0.931747016166	Antoine Jay, 2026.
4	495	0.931762755191	Antoine Jay, 2026.
4	496	0.931801843087	Antoine Jay, 2026.
4	497	0.931831971337	Antoine Jay, 2026.
4	498	0.931900726504	Antoine Jay, 2026.
4	499	0.931971011451	Antoine Jay, 2026.
4	500	0.932058577211	Antoine Jay, 2026.
4	501	0.932126145628	Antoine Jay, 2026.
4	502	0.932164943908	Antoine Jay, 2026.
4	503	0.932308604670	Antoine Jay, 2026.
4	504	0.932405823075	Antoine Jay, 2026.
4	505	0.932635493928	Antoine Jay, 2026.
4	506	0.932720030385	Antoine Jay, 2026.
4	507	0.932811334891	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	508	0.932906571563	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	509	0.932975547025	Antoine Jay, 2026.
4	510	0.933043859071	Antoine Jay, 2026.
4	511	0.933123032165	Antoine Jay, 2026.
4	512	0.933210925674	Antoine Jay, 2026.
4	513	0.933275988108	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	514	0.933376754077	Antoine Jay, 2026.
4	515	0.933438700706	Antoine Jay, 2026.
4	516	0.933507267485	Antoine Jay, 2026.
4	517	0.933693250256	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	518	0.933819334444	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	519	0.933909136763	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	520	0.933982317772	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	521	0.934095470596	Antoine Jay, 2026.
4	522	0.934205969613	Antoine Jay, 2026.
4	523	0.934327053585	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	524	0.934392219426	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	525	0.934502863359	Antoine Jay, 2026.
4	526	0.934622453189	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	527	0.934702597820	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	528	0.934795043814	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	529	0.934876829410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	530	0.934951125065	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	531	0.935026090394	Antoine Jay, 2026.
4	532	0.935107225574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	533	0.935242552051	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	534	0.935351572128	Antoine Jay, 2026.
4	535	0.935439854771	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	536	0.935545287532	Antoine Jay, 2026.
4	537	0.935633330312	Antoine Jay, 2026.
4	538	0.935698279752	Antoine Jay, 2026.
4	539	0.935737935789	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	540	0.935802498782	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	541	0.935873515729	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	542	0.935944032615	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	543	0.936006304478	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	544	0.936146771276	Antoine Jay, 2026.
4	545	0.936194816493	Antoine Jay, 2026.
4	546	0.936309391047	Antoine Jay, 2026.
4	547	0.936471207403	Antoine Jay, 2026.
4	548	0.936534159036	Antoine Jay, 2026.
4	549	0.936569382634	Antoine Jay, 2026.
4	550	0.936628412875	Antoine Jay, 2026.
4	551	0.936702283265	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	552	0.936736944373	Antoine Jay, 2026.
4	553	0.936824741407	Antoine Jay, 2026.
4	554	0.936873884813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	555	0.936961298805	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	556	0.937012725975	Antoine Jay, 2026.
4	557	0.937077507502	Antoine Jay, 2026.
4	558	0.937133748534	Antoine Jay, 2026.
4	559	0.937221549550	Antoine Jay, 2026.
4	560	0.937331393950	Antoine Jay, 2026.
4	561	0.937424775190	Antoine Jay, 2026.
4	562	0.937491593628	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	563	0.937564329856	Antoine Jay, 2026.
4	564	0.937680472008	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	565	0.937778623404	Antoine Jay, 2026.
4	566	0.937885258165	Antoine Jay, 2026.
4	567	0.937918186208	Vadim Borisov, 2026.
4	568	0.937918197905	Antoine Jay, 2026.
4	569	0.937951796919	Antoine Jay, 2026.
4	570	0.938079468057	Antoine Jay, 2026.
4	571	0.938144494988	Antoine Jay, 2026.
4	572	0.938277913341	Antoine Jay, 2026.
4	573	0.938345897242	Antoine Jay, 2026.
4	574	0.938426367808	Antoine Jay, 2026.
4	575	0.938495269462	Antoine Jay, 2026.
4	576	0.938572386987	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	577	0.938641427650	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	578	0.938695588156	Antoine Jay, 2026.
4	579	0.938760741068	Antoine Jay, 2026.
4	580	0.938824156225	Antoine Jay, 2026.
4	581	0.938917159242	Antoine Jay, 2026.
4	582	0.938947495343	Antoine Jay, 2026.
4	583	0.939021020888	Antoine Jay, 2026.
4	584	0.939098702765	Antoine Jay, 2026.
4	585	0.939214060656	Antoine Jay, 2026.
4	586	0.939269665555	Antoine Jay, 2026.
4	587	0.939369719894	Antoine Jay, 2026.
4	588	0.939464069169	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	589	0.939528916278	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	590	0.939540327353	Antoine Jay, 2026.
4	591	0.939560404638	Antoine Jay, 2026.
4	592	0.939623600169	Antoine Jay, 2026.
4	593	0.939679435497	Antoine Jay, 2026.
4	594	0.939736776202	Antoine Jay, 2026.
4	595	0.939788592086	Antoine Jay, 2026.
4	596	0.939849244530	Antoine Jay, 2026.
4	597	0.939869311199	Antoine Jay, 2026.
4	598	0.939935146640	Antoine Jay, 2026.
4	599	0.940006873883	Antoine Jay, 2026.
4	600	0.940069406815	Antoine Jay, 2026.
4	601	0.940162784403	Antoine Jay, 2026.
4	602	0.940202529909	Antoine Jay, 2026.
4	603	0.940264189437	Antoine Jay, 2026.
4	604	0.940314706849	Antoine Jay, 2026.
4	605	0.940391305031	Antoine Jay, 2026.
4	606	0.940432158290	Antoine Jay, 2026.
4	607	0.940513609731	Antoine Jay, 2026.
4	608	0.940607279084	Antoine Jay, 2026.
4	609	0.940646235969	Antoine Jay, 2026.
4	610	0.940702142551	Antoine Jay, 2026.
4	611	0.940770737362	Antoine Jay, 2026.
4	612	0.940859393191	Antoine Jay, 2026.
4	613	0.940922045907	Henry Cohn, 2026.
4	614	0.940999770899	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	615	0.941050631714	Antoine Jay, 2026.
4	616	0.941140227508	Antoine Jay, 2026.
4	617	0.941222268047	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	618	0.941307989175	Antoine Jay, 2026.
4	619	0.941366332376	Antoine Jay, 2026.
4	620	0.941456959639	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	621	0.941489300583	Antoine Jay, 2026.
4	622	0.941592089348	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	623	0.941606007928	Antoine Jay, 2026.
4	624	0.941708052094	Antoine Jay, 2026.
4	625	0.941769899299	Antoine Jay, 2026.
4	626	0.941809937192	Antoine Jay, 2026.
4	627	0.941894242904	Antoine Jay, 2026.
4	628	0.941949734067	Antoine Jay, 2026.
4	629	0.941993192756	Antoine Jay, 2026.
4	630	0.942106278778	Antoine Jay, 2026.
4	631	0.942124632798	Antoine Jay, 2026.
4	632	0.942182128345	Antoine Jay, 2026.
4	633	0.942211399547	Antoine Jay, 2026.
4	634	0.942245337985	Antoine Jay, 2026.
4	635	0.942335502780	Antoine Jay, 2026.
4	636	0.942419594360	Antoine Jay, 2026.
4	637	0.942476467147	Antoine Jay, 2026.
4	638	0.942480747963	Antoine Jay, 2026.
4	639	0.942531458499	Antoine Jay, 2026.
4	640	0.942573563632	Antoine Jay, 2026.
4	641	0.942627906051	Antoine Jay, 2026.
4	642	0.942664286261	Antoine Jay, 2026.
4	643	0.942744679211	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	644	0.942780033896	Antoine Jay, 2026.
4	645	0.942807321199	Antoine Jay, 2026.
4	646	0.942835224259	Antoine Jay, 2026.
4	647	0.942871404532	Antoine Jay, 2026.
4	648	0.942950516392	Antoine Jay, 2026.
4	649	0.942981438067	Antoine Jay, 2026.
4	650	0.943058001580	Antoine Jay, 2026.
4	651	0.943145893831	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	652	0.943217190688	Antoine Jay, 2026.
4	653	0.943282422509	Antoine Jay, 2026.
4	654	0.943316093009	Antoine Jay, 2026.
4	655	0.943350276535	Antoine Jay, 2026.
4	656	0.943401605464	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	657	0.943435674331	Antoine Jay, 2026.
4	658	0.943473318383	Antoine Jay, 2026.
4	659	0.943526401460	Antoine Jay, 2026.
4	660	0.943574911641	Antoine Jay, 2026.
4	661	0.943616081172	Antoine Jay, 2026.
4	662	0.943639385120	Antoine Jay, 2026.
4	663	0.943676068419	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	664	0.943693804047	Antoine Jay, 2026.
4	665	0.943736136913	Henry Cohn, 2026.
4	666	0.943767303116	Antoine Jay, 2026.
4	667	0.943789305502	Antoine Jay, 2026.
4	668	0.943837757151	Antoine Jay, 2026.
4	669	0.943883434305	Antoine Jay, 2026.
4	670	0.943905533715	Antoine Jay, 2026.
4	671	0.943966174144	Antoine Jay, 2026.
4	672	0.944024794646	Antoine Jay, 2026.
4	673	0.944105028323	Antoine Jay, 2026.
4	674	0.944143110437	Antoine Jay, 2026.
4	675	0.944211115487	Antoine Jay, 2026.
4	676	0.944265216810	Antoine Jay, 2026.
4	677	0.944326538482	Antoine Jay, 2026.
4	678	0.944363147553	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	679	0.944401746694	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	680	0.944431798875	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	681	0.944507262202	Antoine Jay, 2026.
4	682	0.944551428296	Antoine Jay, 2026.
4	683	0.944649809111	Antoine Jay, 2026.
4	684	0.944718310569	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	685	0.944768305408	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	686	0.944813921100	Antoine Jay, 2026.
4	687	0.944855357331	Antoine Jay, 2026.
4	688	0.944929051057	Antoine Jay, 2026.
4	689	0.945028309292	Antoine Jay, 2026.
4	690	0.945107898662	Antoine Jay, 2026.
4	691	0.945207077177	Antoine Jay, 2026.
4	692	0.945317570761	Antoine Jay, 2026.
4	693	0.945372890900	Antoine Jay, 2026.
4	694	0.945421977689	Antoine Jay, 2026.
4	695	0.945490673722	Antoine Jay, 2026.
4	696	0.945556552158	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	697	0.945616550543	Antoine Jay, 2026.
4	698	0.945693766748	Vadim Borisov, 2026.
4	699	0.945693769130	Antoine Jay, 2026.
4	700	0.945777885363	Antoine Jay, 2026.
4	701	0.945837840027	Antoine Jay, 2026.
4	702	0.945901543839	Antoine Jay, 2026.
4	703	0.945953748853	Antoine Jay, 2026.
4	704	0.946024676505	Antoine Jay, 2026.
4	705	0.946092309183	Antoine Jay, 2026.
4	706	0.946114015992	Antoine Jay, 2026.
4	707	0.946187307547	Antoine Jay, 2026.
4	708	0.946269538988	Antoine Jay, 2026.
4	709	0.946322854117	Antoine Jay, 2026.
4	710	0.946364793128	Antoine Jay, 2026.
4	711	0.946400348855	Antoine Jay, 2026.
4	712	0.946441695893	Antoine Jay, 2026.
4	713	0.946479398920	Antoine Jay, 2026.
4	714	0.946531765363	Antoine Jay, 2026.
4	715	0.946590497594	Antoine Jay, 2026.
4	716	0.946648379370	Antoine Jay, 2026.
4	717	0.946693991179	Antoine Jay, 2026.
4	718	0.946754785388	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	719	0.946782439899	Antoine Jay, 2026.
4	720	0.946814930479	Antoine Jay, 2026.
4	721	0.946842543091	Antoine Jay, 2026.
4	722	0.946907452604	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	723	0.946941981933	Antoine Jay, 2026.
4	724	0.946971748245	Antoine Jay, 2026.
4	725	0.947014045250	Antoine Jay, 2026.
4	726	0.947025044931	Antoine Jay, 2026.
4	727	0.947084064371	Antoine Jay, 2026.
4	728	0.947113040170	Antoine Jay, 2026.
4	729	0.947168832135	Antoine Jay, 2026.
4	730	0.947220429013	Antoine Jay, 2026.
4	731	0.947261324030	Antoine Jay, 2026.
4	732	0.947301598311	Antoine Jay, 2026.
4	733	0.947350935934	Antoine Jay, 2026.
4	734	0.947394067886	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	735	0.947434426704	Antoine Jay, 2026.
4	736	0.947462655645	Antoine Jay, 2026.
4	737	0.947511993090	Antoine Jay, 2026.
4	738	0.947546140466	Antoine Jay, 2026.
4	739	0.947625664343	Antoine Jay, 2026.
4	740	0.947673097259	Antoine Jay, 2026.
4	741	0.947729852081	Antoine Jay, 2026.
4	742	0.947808051524	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	743	0.947844839839	Antoine Jay, 2026.
4	744	0.947865855613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	745	0.947905615771	Antoine Jay, 2026.
4	746	0.947921008196	Antoine Jay, 2026.
4	747	0.947966846408	Antoine Jay, 2026.
4	748	0.947996252076	Antoine Jay, 2026.
4	749	0.948018433909	Antoine Jay, 2026.
4	750	0.948065838734	Antoine Jay, 2026.
4	751	0.948138703777	Antoine Jay, 2026.
4	752	0.948165835240	Antoine Jay, 2026.
4	753	0.948207433680	Antoine Jay, 2026.
4	754	0.948269198988	Antoine Jay, 2026.
4	755	0.948290259594	Antoine Jay, 2026.
4	756	0.948353468191	Antoine Jay, 2026.
4	757	0.948390773470	Antoine Jay, 2026.
4	758	0.948417124868	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	759	0.948482596375	Antoine Jay, 2026.
4	760	0.948508436355	Antoine Jay, 2026.
4	761	0.948561257489	Antoine Jay, 2026.
4	762	0.948620439130	Antoine Jay, 2026.
4	763	0.948675030405	Antoine Jay, 2026.
4	764	0.948717162506	Antoine Jay, 2026.
4	765	0.948758687260	Antoine Jay, 2026.
4	766	0.948781426119	Antoine Jay, 2026.
4	767	0.948831173242	Antoine Jay, 2026.
4	768	0.948872350261	Antoine Jay, 2026.
4	769	0.948928657859	Antoine Jay, 2026.
4	770	0.948948039365	Antoine Jay, 2026.
4	771	0.949001880467	Antoine Jay, 2026.
4	772	0.949050577613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	773	0.949096008541	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	774	0.949136209658	Antoine Jay, 2026.
4	775	0.949165750644	Antoine Jay, 2026.
4	776	0.949208197875	Antoine Jay, 2026.
4	777	0.949257739389	Antoine Jay, 2026.
4	778	0.949281830124	Antoine Jay, 2026.
4	779	0.949315900763	Antoine Jay, 2026.
4	780	0.949375011354	Antoine Jay, 2026.
4	781	0.949409185866	Antoine Jay, 2026.
4	782	0.949429754459	Antoine Jay, 2026.
4	783	0.949466669203	Antoine Jay, 2026.
4	784	0.949516062604	Antoine Jay, 2026.
4	785	0.949536410174	Antoine Jay, 2026.
4	786	0.949584637959	Antoine Jay, 2026.
4	787	0.949617880796	Antoine Jay, 2026.
4	788	0.949658271568	Antoine Jay, 2026.
4	789	0.949684427169	Antoine Jay, 2026.
4	790	0.949732393620	Antoine Jay, 2026.
4	791	0.949758449546	Antoine Jay, 2026.
4	792	0.949806623377	Antoine Jay, 2026.
4	793	0.949836200277	Antoine Jay, 2026.
4	794	0.949860669967	Antoine Jay, 2026.
4	795	0.949908786714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	796	0.949929673572	Antoine Jay, 2026.
4	797	0.949966944148	Antoine Jay, 2026.
4	798	0.949983976797	Antoine Jay, 2026.
4	799	0.949999564906	Antoine Jay, 2026.
4	800	0.950029568300	Antoine Jay, 2026.
4	801	0.950071284222	Antoine Jay, 2026.
4	802	0.950109031048	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	803	0.950132603230	Antoine Jay, 2026.
4	804	0.950161177809	Antoine Jay, 2026.
4	805	0.950199424060	Antoine Jay, 2026.
4	806	0.950224337197	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	807	0.950246632070	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	808	0.950268594113	Antoine Jay, 2026.
4	809	0.950296638182	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	810	0.950298831657	Antoine Jay, 2026.
4	811	0.950320091622	Antoine Jay, 2026.
4	812	0.950357272130	Antoine Jay, 2026.
4	813	0.950369416788	Antoine Jay, 2026.
4	814	0.950376508774	Antoine Jay, 2026.
4	815	0.950407316019	Antoine Jay, 2026.
4	816	0.950448275553	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	817	0.950469091176	Antoine Jay, 2026.
4	818	0.950489956980	Antoine Jay, 2026.
4	819	0.950528775384	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	820	0.950555041324	Antoine Jay, 2026.
4	821	0.950567739679	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	822	0.950595331679	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	823	0.950598961936	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	824	0.950622331945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	825	0.950638530449	Antoine Jay, 2026.
4	826	0.950649733200	Antoine Jay, 2026.
4	827	0.950666151522	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	828	0.950682657517	Vadim Borisov, 2026.
4	829	0.950682659515	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	830	0.950699235322	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	831	0.950707846321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	832	0.950732492617	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	833	0.950745012895	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	834	0.950749338051	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	835	0.950760231063	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	836	0.950761230198	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	837	0.950764138804	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	838	0.950779009109	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	839	0.950791291943	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	840	0.950791926923	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	841	0.950938141957	Antoine Jay, 2026.
4	843	0.951014101360	Antoine Jay, 2026.
4	844	0.951162769106	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	845	0.951266655116	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	846	0.951316305793	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	847	0.951318556932	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	848	0.951335141900	Antoine Jay, 2026.
4	849	0.951382211178	Antoine Jay, 2026.
4	850	0.951426191024	Antoine Jay, 2026.
4	851	0.951458010177	Antoine Jay, 2026.
4	852	0.951485690024	Antoine Jay, 2026.
4	853	0.951615490044	Antoine Jay, 2026.
4	854	0.951704137402	Antoine Jay, 2026.
4	855	0.951809705736	Antoine Jay, 2026.
4	856	0.951855140389	Antoine Jay, 2026.
4	857	0.951907792562	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	858	0.951977842370	Antoine Jay, 2026.
4	859	0.952054110722	Antoine Jay, 2026.
4	860	0.952130645617	Antoine Jay, 2026.
4	861	0.952247731685	Antoine Jay, 2026.
4	862	0.952320345036	Antoine Jay, 2026.
4	863	0.952354991043	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	864	0.952428106277	Antoine Jay, 2026.
4	865	0.952508093113	Antoine Jay, 2026.
4	866	0.952534007654	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	867	0.952549573810	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	868	0.952594614901	Antoine Jay, 2026.
4	869	0.952676731659	Antoine Jay, 2026.
4	870	0.952703974614	Antoine Jay, 2026.
4	871	0.952762468675	Antoine Jay, 2026.
4	872	0.952808088493	Antoine Jay, 2026.
4	873	0.952835461232	Antoine Jay, 2026.
4	874	0.952847567854	Antoine Jay, 2026.
4	875	0.952900167793	Antoine Jay, 2026.
4	876	0.952939435727	Antoine Jay, 2026.
4	877	0.952980893005	Antoine Jay, 2026.
4	878	0.953014122236	Antoine Jay, 2026.
4	879	0.953058701325	Antoine Jay, 2026.
4	880	0.953065581534	Antoine Jay, 2026.
4	881	0.953096665472	Antoine Jay, 2026.
4	882	0.953139130347	Antoine Jay, 2026.
4	883	0.953174632212	Antoine Jay, 2026.
4	884	0.953185498287	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	885	0.953196940320	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	886	0.953223340798	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	887	0.953236565202	Antoine Jay, 2026.
4	888	0.953270170768	Antoine Jay, 2026.
4	889	0.953313712496	Antoine Jay, 2026.
4	890	0.953334597229	Antoine Jay, 2026.
4	891	0.953361963661	Antoine Jay, 2026.
4	892	0.953395569622	Antoine Jay, 2026.
4	894	0.953424501654	Antoine Jay, 2026.
4	895	0.953481968238	Antoine Jay, 2026.
4	896	0.953489360670	Antoine Jay, 2026.
4	897	0.953536429924	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	898	0.953584396279	Antoine Jay, 2026.
4	899	0.953599381548	Antoine Jay, 2026.
4	900	0.953654112934	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	901	0.953708108364	Antoine Jay, 2026.
4	902	0.953746829963	Antoine Jay, 2026.
4	903	0.953777766643	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	904	0.953807774525	Antoine Jay, 2026.
4	905	0.953854675752	Antoine Jay, 2026.
4	906	0.953900972254	Antoine Jay, 2026.
4	907	0.953929422532	Antoine Jay, 2026.
4	908	0.954020967398	Antoine Jay, 2026.
4	909	0.954033665429	Antoine Jay, 2026.
4	910	0.954057276222	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	911	0.954079716175	Antoine Jay, 2026.
4	912	0.954108411543	Antoine Jay, 2026.
4	913	0.954123330655	Antoine Jay, 2026.
4	914	0.954137704921	Vadim Borisov, 2026.
4	915	0.954140611905	Antoine Jay, 2026.
4	916	0.954154925308	Antoine Jay, 2026.
4	917	0.954178206228	Antoine Jay, 2026.
4	918	0.954233609796	Antoine Jay, 2026.
4	919	0.954283477370	Antoine Jay, 2026.
4	920	0.954312003460	Antoine Jay, 2026.
4	921	0.954367803728	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	922	0.954400991480	Antoine Jay, 2026.
4	923	0.954456191741	Antoine Jay, 2026.
4	924	0.954495727281	Antoine Jay, 2026.
4	925	0.954544340310	Antoine Jay, 2026.
4	926	0.954575173847	Antoine Jay, 2026.
4	927	0.954638435261	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	928	0.954674703124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	929	0.954707865092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	930	0.954752285298	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	931	0.954782163365	Antoine Jay, 2026.
4	932	0.954814046648	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	933	0.954823410275	Antoine Jay, 2026.
4	934	0.954874918764	Antoine Jay, 2026.
4	935	0.954904068935	Antoine Jay, 2026.
4	936	0.954948804824	Antoine Jay, 2026.
4	937	0.954991117846	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	938	0.955016196101	Antoine Jay, 2026.
4	939	0.955048351662	Antoine Jay, 2026.
4	940	0.955081999691	Antoine Jay, 2026.
4	941	0.955135576551	Antoine Jay, 2026.
4	942	0.955182775968	Antoine Jay, 2026.
4	943	0.955200031999	Antoine Jay, 2026.
4	944	0.955227589648	Antoine Jay, 2026.
4	945	0.955257353403	Antoine Jay, 2026.
4	946	0.955285371487	Antoine Jay, 2026.
4	947	0.955315440983	Antoine Jay, 2026.
4	948	0.955330266361	Antoine Jay, 2026.
4	949	0.955356995814	Antoine Jay, 2026.
4	950	0.955384584056	Antoine Jay, 2026.
4	951	0.955413714247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	952	0.955429640040	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	953	0.955469964086	Antoine Jay, 2026.
4	954	0.955502049951	Antoine Jay, 2026.
4	955	0.955543342145	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	956	0.955587905426	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	957	0.955607193287	Antoine Jay, 2026.
4	958	0.955665015195	Antoine Jay, 2026.
4	959	0.955695008272	Antoine Jay, 2026.
4	960	0.955719198813	Antoine Jay, 2026.
4	961	0.955747396324	Antoine Jay, 2026.
4	962	0.955790188398	Antoine Jay, 2026.
4	963	0.955837825935	Antoine Jay, 2026.
4	964	0.955856915800	Antoine Jay, 2026.
4	965	0.955903676415	Antoine Jay, 2026.
4	966	0.955963651010	Antoine Jay, 2026.
4	967	0.955975653685	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	968	0.956002872174	Antoine Jay, 2026.
4	969	0.956017995605	Antoine Jay, 2026.
4	970	0.956033687083	Antoine Jay, 2026.
4	971	0.956053552535	Antoine Jay, 2026.
4	972	0.956070824334	Antoine Jay, 2026.
4	973	0.956092924044	Antoine Jay, 2026.
4	974	0.956120441097	Antoine Jay, 2026.
4	975	0.956146734357	Antoine Jay, 2026.
4	976	0.956194544485	Antoine Jay, 2026.
4	977	0.956236080980	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	978	0.956262897204	Antoine Jay, 2026.
4	979	0.956293823289	Antoine Jay, 2026.
4	980	0.956337914727	Antoine Jay, 2026.
4	981	0.956384953967	Antoine Jay, 2026.
4	982	0.956417991917	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	983	0.956429489231	Antoine Jay, 2026.
4	984	0.956456919257	Antoine Jay, 2026.
4	985	0.956486992678	Antoine Jay, 2026.
4	986	0.956541819679	Antoine Jay, 2026.
4	987	0.956567648348	Antoine Jay, 2026.
4	988	0.956605515415	Antoine Jay, 2026.
4	989	0.956645897755	Antoine Jay, 2026.
4	990	0.956686780822	Antoine Jay, 2026.
4	991	0.956698206925	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	992	0.956722283956	Antoine Jay, 2026.
4	993	0.956785770810	Antoine Jay, 2026.
4	994	0.956801812989	Antoine Jay, 2026.
4	995	0.956815550039	Antoine Jay, 2026.
4	996	0.956822818959	Antoine Jay, 2026.
4	997	0.956849777283	Antoine Jay, 2026.
4	998	0.956895370350	Antoine Jay, 2026.
4	999	0.956921202335	Antoine Jay, 2026.
4	1000	0.956932809823	Antoine Jay, 2026.
4	1001	0.956945137748	Antoine Jay, 2026.
4	1002	0.956976811817	Antoine Jay, 2026.
4	1003	0.957004222861	Antoine Jay, 2026.
4	1004	0.957045046110	Antoine Jay, 2026.
4	1005	0.957068688785	Antoine Jay, 2026.
4	1006	0.957107747701	Antoine Jay, 2026.
4	1007	0.957153161551	Antoine Jay, 2026.
4	1008	0.957158784667	Antoine Jay, 2026.
4	1009	0.957185456107	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
4	1010	0.957210341761	Antoine Jay, 2026.
4	1011	0.957252505228	Antoine Jay, 2026.
4	1012	0.957279762016	Antoine Jay, 2026.
4	1013	0.957334548490	Antoine Jay, 2026.
4	1014	0.957366579339	Antoine Jay, 2026.
4	1015	0.957397725916	Antoine Jay, 2026.
4	1016	0.957473104805	Antoine Jay, 2026.
4	1017	0.957478953210	Antoine Jay, 2026.
4	1018	0.957486053484	Antoine Jay, 2026.
4	1019	0.957516607178	Antoine Jay, 2026.
4	1020	0.957558575451	Antoine Jay, 2026.
4	1021	0.957582722209	Antoine Jay, 2026.
4	1022	0.957596953155	Antoine Jay, 2026.
4	1023	0.957631917750	Antoine Jay, 2026.
4	1024	0.957669668284	Antoine Jay, 2026.
5	11	0.132853542599	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $45 x^{3} - 25 x^{2} - 5 x + 1$
5	12	0.153931605034	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $25 x^{4} + 30 x^{3} + 24 x^{2} + 2 x - 1$
5	13	0.187259851883	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $17 x^{3} - 5 x^{2} - 5 x + 1$
5	14	0.2	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $5 x - 1$
5	15	0.2	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $5 x - 1$
5	16*	0.2	T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $5 x - 1$
5	17	0.270475835269	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $9 x^{4} - 16 x^{3} - 10 x^{2} + 1$
5	18	0.275501741660	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $484 x^{5} - 488 x^{4} + 97 x^{3} + 17 x^{2} - x - 1$
5	19	0.291822399025	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $57 x^{6} - 38 x^{5} - 109 x^{4} + 32 x^{3} + 23 x^{2} - 10 x + 1$
5	20	0.299385692900	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $5 x^{3} + 13 x^{2} - x - 1$
5	21	0.314916957176	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. Minimal polynomial of degree 14
5	22	0.354995034167	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	23	0.369772696944	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	24	0.374232982466	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $1620 x^{10} + 5508 x^{9} - 5751 x^{8} - 2406 x^{7} + 2055 x^{6} + 276 x^{5} + 559 x^{4} - 210 x^{3} - 127 x^{2} + 48 x - 4$
5	25	0.379621025394	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5	26	0.390240659505	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. Minimal polynomial of degree 23
5	27	0.401659264277	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 15
5	28	0.408169699093	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	29	0.411034435092	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. Minimal polynomial of degree 31
5	30	0.413029776123	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. $269 x^{7} - 1419 x^{6} - 283 x^{5} + 405 x^{4} + 15 x^{3} - 9 x^{2} - x - 1$
5	31	0.433911863960	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml. Minimal polynomial of degree 20
5	32	0.441830743928	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $8 x^{10} - 40 x^{9} + 74 x^{8} - 78 x^{7} + 73 x^{6} - 10 x^{5} - 3 x^{4} + 18 x^{3} - 9 x^{2} - 2 x + 1$
5	33	0.460004535963	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5	34	0.470482910392	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	35	0.478437929066	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	36	0.483999000231	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $49 x^{6} - 6 x^{5} - 53 x^{4} + 12 x^{3} + 13 x^{2} - 2 x - 1$
5	37	0.493828518526	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	38	0.496243746648	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	39	0.499971927191	Henry Cohn, 2025.
5	40	0.5	A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Five dimensional non-lattice sphere packings, Canad. Math. Bull. 10 (1967), 387–393, doi:10.4153/CMB-1967-037-5; F. Szöllősi, A note on five dimensional kissing arrangements, Math. Res. Lett. 30 (2023), no. 5, 1609–1615, doi:10.4310/MRL.2023.v30.n5.a13, arXiv:2301.08272; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937. $2 x - 1$
5	41	0.514705973641	Kevin Li, 2026.
5	42	0.518241155863	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	43	0.524709601830	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	44	0.527457712324	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	45	0.535068808289	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	46	0.538291308677	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	47	0.540668770936	Henry Cohn, 2025.
5	48	0.545112501822	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	49	0.546918160679	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $7 x^{2} - 2 x - 1$
5	50	0.546918160679	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x^{2} - 2 x - 1$
5	51	0.554740414282	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	52	0.560107395820	Henry Cohn, 2025.
5	53	0.566883217391	Henry Cohn, 2025.
5	54	0.571075948469	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	55	0.574604319465	Henry Cohn, 2025.
5	56	0.577211861101	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	57	0.577350269190	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $3 x^{2} - 1$
5	58	0.581466614772	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	59	0.586915485192	Henry Cohn, 2025.
5	60	0.593346597794	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	61	0.596251134208	Henry Cohn, 2025.
5	62	0.599005179291	Henry Cohn, 2023.
5	63	0.603554375176	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	64	0.605837370318	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	65	0.608465017856	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	66	0.608980005147	Henry Cohn, 2025.
5	67	0.611900403428	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	68	0.615240038880	Henry Cohn, 2025.
5	69	0.616793716634	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	70	0.617072261706	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	71	0.617972684614	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	72	0.617972684614	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	73	0.618033988750	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $x^{2} + x - 1$
5	74	0.618033988750	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $x^{2} + x - 1$
5	75	0.624659315083	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	76	0.631404527694	Henry Cohn, 2025.
5	77	0.636485570257	Henry Cohn, 2025.
5	78	0.640234003194	Henry Cohn, 2026.
5	79	0.643522691535	Henry Cohn, 2026.
5	80	0.643720731795	Henry Cohn, 2026.
5	81	0.643769373768	Kevin Li, 2026. $7 x^{4} + 12 x^{3} - 2 x^{2} - 4 x - 1$
5	82	0.651451517528	Henry Cohn, 2025.
5	83	0.655397827372	Henry Cohn, 2026.
5	84	0.657233125821	Antoine Jay, 2026.
5	85	0.659252981910	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	86	0.660931731561	Henry Cohn, 2025.
5	87	0.662618952049	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	88	0.664474200258	Henry Cohn, 2026.
5	89	0.666241382508	Henry Cohn, 2025.
5	90	0.666666666667	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $3 x - 2$
5	91	0.670415108805	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	92	0.671609349084	Henry Cohn, 2026.
5	93	0.673569382595	Henry Cohn, 2026.
5	94	0.674223122932	Henry Cohn, 2026.
5	95	0.674300440403	Henry Cohn, 2026.
5	96	0.674322195935	Antoine Jay, 2026.
5	98	0.674324398545	Kevin Li, 2026. $71 x^{6} - 26 x^{5} + 21 x^{4} - 12 x^{3} - 3 x^{2} - 2 x - 1$
5	99	0.681881045310	Henry Cohn, 2025.
5	100	0.683153263764	Henry Cohn, 2025.
5	101	0.685186090412	Henry Cohn, 2025.
5	102	0.687426161854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	103	0.688556975924	Henry Cohn, 2026.
5	104	0.689316429043	Henry Cohn, 2026.
5	105	0.690711966676	Henry Cohn, 2026.
5	106	0.692005491905	Henry Cohn, 2025.
5	107	0.693863512900	Henry Cohn, 2025.
5	108	0.695186314989	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	109	0.696434500115	Henry Cohn, 2025.
5	110	0.697959104275	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	111	0.699314980427	Henry Cohn, 2026.
5	112	0.700442780805	Henry Cohn, 2026.
5	113	0.701786576995	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	114	0.702924665447	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	115	0.704050978289	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	116	0.705292505873	Henry Cohn, 2025.
5	117	0.706815348305	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	118	0.707921087441	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	119	0.709175837480	Henry Cohn, 2026.
5	120	0.710234646534	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	121	0.711494596608	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	122	0.712249276837	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	123	0.713918633096	Henry Cohn, 2025.
5	124	0.715011517303	Henry Cohn, 2026.
5	125	0.716280109450	Henry Cohn, 2026.
5	126	0.717123270108	Henry Cohn, 2026.
5	127	0.718579275824	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	128	0.719621301444	Henry Cohn, 2025.
5	129	0.720741141724	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	130	0.721711816020	Henry Cohn, 2025.
5	131	0.722525538501	Antoine Jay, 2026.
5	132	0.723020248315	Antoine Jay, 2026.
5	133	0.725045590778	WolfFrogs, 2026.
5	134	0.726115703492	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	135	0.726958825422	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	136	0.727714141126	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	137	0.728315486874	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	138	0.729419676746	Antoine Jay, 2026.
5	139	0.730458979416	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	140	0.731114679118	Antoine Jay, 2026.
5	141	0.731999804745	Antoine Jay, 2026.
5	142	0.732990908903	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	143	0.733987775534	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	144	0.734665201204	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	145	0.735475119910	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	146	0.736013872443	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	147	0.736834565433	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	148	0.737153573850	Antoine Jay, 2026.
5	149	0.737526889466	Antoine Jay, 2026.
5	150	0.737851059324	Antoine Jay, 2026.
5	151	0.739099171806	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	152	0.739610877133	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	153	0.740466081028	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	154	0.741203903697	Antoine Jay, 2026.
5	155	0.742130735822	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	156	0.742620793805	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	157	0.743138069744	Antoine Jay, 2026.
5	158	0.743483529478	Antoine Jay, 2026.
5	159	0.743809855738	Henry Cohn, 2026.
5	160	0.744133760181	Antoine Jay, 2026.
5	161	0.747604595136	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	162	0.748758439671	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	163	0.750006570111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	164	0.750869025261	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	165	0.751869035248	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	166	0.752534073395	Henry Cohn, 2025.
5	167	0.752840051918	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	168	0.753135300368	Antoine Jay, 2026.
5	169	0.753180014210	Antoine Jay, 2026.
5	170	0.753195472216	Antoine Jay, 2026.
5	171	0.756593661726	Antoine Jay, 2026.
5	172	0.757288337753	Antoine Jay, 2026.
5	173	0.758561688405	Henry Cohn, 2026.
5	174	0.759545327556	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	175	0.760533290441	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	176	0.760864184788	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	177	0.761596904179	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	178	0.762101626550	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	179	0.762744044321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	180	0.763133113335	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	181	0.763905351722	Antoine Jay, 2026.
5	182	0.764073518798	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	183	0.764295534277	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	184	0.764714208622	Antoine Jay, 2026.
5	185	0.764792667513	Antoine Jay, 2026.
5	186	0.765091547589	Antoine Jay, 2026.
5	187	0.765206110974	Antoine Jay, 2026.
5	188	0.765422791038	Antoine Jay, 2026.
5	189	0.765492265227	Antoine Jay, 2026.
5	190	0.765637783019	Antoine Jay, 2026.
5	191	0.767840675119	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	192	0.768816129099	Antoine Jay, 2026.
5	193	0.769633202690	Antoine Jay, 2026.
5	194	0.770445250738	Antoine Jay, 2026.
5	195	0.770838844751	Antoine Jay, 2026.
5	196	0.771956694297	Antoine Jay, 2026.
5	197	0.772961996501	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	198	0.773535098509	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	199	0.773844972790	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	200	0.774612560000	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	201	0.775298152139	Antoine Jay, 2026.
5	202	0.775876129293	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	203	0.776547362696	Antoine Jay, 2026.
5	204	0.777218408765	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	205	0.777873615436	Antoine Jay, 2026.
5	206	0.778512531189	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	207	0.778983311076	Antoine Jay, 2026.
5	208	0.779695418936	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	209	0.780183809735	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	210	0.780691953810	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	211	0.781052621611	Antoine Jay, 2026.
5	212	0.781582875276	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	213	0.782186899352	Antoine Jay, 2026.
5	214	0.782805412055	Antoine Jay, 2026.
5	215	0.783426456313	Antoine Jay, 2026.
5	216	0.783729678347	Antoine Jay, 2026.
5	217	0.784096583393	Antoine Jay, 2026.
5	218	0.784300794595	Antoine Jay, 2026.
5	219	0.784564320285	Antoine Jay, 2026.
5	220	0.785603539656	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	221	0.786035542595	Antoine Jay, 2026.
5	222	0.786422813492	Antoine Jay, 2026.
5	223	0.786872293767	Antoine Jay, 2026.
5	224	0.787292850446	Antoine Jay, 2026.
5	225	0.787663431317	Antoine Jay, 2026.
5	226	0.788135770872	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	227	0.788528450686	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	228	0.788961582006	Antoine Jay, 2026.
5	229	0.789353134102	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	230	0.789650157925	Antoine Jay, 2026.
5	231	0.789984155832	Antoine Jay, 2026.
5	232	0.790719277661	Antoine Jay, 2026.
5	233	0.791209625064	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	234	0.791716682704	Antoine Jay, 2026.
5	235	0.792059162750	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	236	0.792438145486	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	237	0.792747940452	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	238	0.793086013310	Antoine Jay, 2026.
5	239	0.793430770551	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	240	0.793736551712	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	241	0.794252820625	Antoine Jay, 2026.
5	242	0.794849340301	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	243	0.795395579950	Antoine Jay, 2026.
5	244	0.795769860964	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	245	0.796368395673	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	246	0.796583641774	Antoine Jay, 2026.
5	247	0.797176517939	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	248	0.797637065905	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	249	0.797966052517	Antoine Jay, 2026.
5	250	0.798443969205	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	251	0.798896482290	Antoine Jay, 2026.
5	252	0.799168813403	Antoine Jay, 2026.
5	253	0.799593674183	Antoine Jay, 2026.
5	254	0.799857479527	Antoine Jay, 2026.
5	255	0.799990834566	Antoine Jay, 2026.
5	256	0.800310006410	Antoine Jay, 2026.
5	257	0.800818692158	Antoine Jay, 2026.
5	259	0.801200931811	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	260	0.801250113822	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	261	0.801436643839	Antoine Jay, 2026.
5	262	0.801490989565	Antoine Jay, 2026.
5	263	0.801604957676	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	264	0.802014744029	Antoine Jay, 2026.
5	265	0.802450551720	Antoine Jay, 2026.
5	266	0.803273861578	Antoine Jay, 2026.
5	267	0.803752858726	Arhan Canli, 2026.
5	268	0.804314152110	Antoine Jay, 2026.
5	269	0.804649040254	Antoine Jay, 2026.
5	270	0.805037286643	Antoine Jay, 2026.
5	271	0.805251516373	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	272	0.805301665051	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	274	0.805305136045	Antoine Jay, 2026.
5	275	0.805369010863	Antoine Jay, 2026.
5	276	0.805496583191	Antoine Jay, 2026.
5	277	0.806035649643	Antoine Jay, 2026.
5	278	0.806184804918	Antoine Jay, 2026.
5	279	0.806563273377	Antoine Jay, 2026.
5	280	0.806760206269	Antoine Jay, 2026.
5	281	0.806945159687	Antoine Jay, 2026.
5	282	0.807123589667	Antoine Jay, 2026.
5	283	0.807596704143	Antoine Jay, 2026.
5	284	0.808036122156	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	285	0.808532269541	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	286	0.808822971693	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	287	0.809372999783	Antoine Jay, 2026.
5	288	0.809722302880	Antoine Jay, 2026.
5	289	0.810375110877	Antoine Jay, 2026.
5	290	0.810952500751	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	291	0.811481566299	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	292	0.812007994085	Antoine Jay, 2026.
5	293	0.812400958598	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	294	0.812930870163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	295	0.813367847792	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	296	0.813903277123	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	297	0.814351054082	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	298	0.814815971786	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	299	0.815220879730	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	300	0.815455960214	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	301	0.815794486759	Antoine Jay, 2026.
5	302	0.816182382413	Antoine Jay, 2026.
5	303	0.816529147352	Antoine Jay, 2026.
5	304	0.816712516388	Antoine Jay, 2026.
5	305	0.817219722806	Antoine Jay, 2026.
5	306	0.817485960430	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	307	0.817702248404	Antoine Jay, 2026.
5	308	0.817955896571	Antoine Jay, 2026.
5	309	0.818260825883	Antoine Jay, 2026.
5	310	0.818593349239	Antoine Jay, 2026.
5	311	0.818791535138	Antoine Jay, 2026.
5	312	0.819115259720	Antoine Jay, 2026.
5	313	0.819392937598	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	314	0.819673799486	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	315	0.819713888197	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	316	0.819894901443	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	317	0.819911400032	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	318	0.820075031148	Antoine Jay, 2026.
5	319	0.820581706781	Henry Cohn, 2026.
5	320	0.820663041593	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	321	0.820793321161	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	322	0.820795477220	Antoine Jay, 2026.
5	323	0.820929681275	Antoine Jay, 2026.
5	324	0.821612444666	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
5	325	0.821794671527	Antoine Jay, 2026.
5	326	0.822207521093	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	327	0.822365452419	Antoine Jay, 2026.
5	328	0.822423204306	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	329	0.822969421207	Antoine Jay, 2026.
5	330	0.823137690011	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	331	0.823206071311	Antoine Jay, 2026.
5	332	0.823568736062	Antoine Jay, 2026.
5	333	0.823641824250	Antoine Jay, 2026.
5	334	0.823946813724	Antoine Jay, 2026.
5	335	0.824397846335	Antoine Jay, 2026.
5	336	0.824790785706	Antoine Jay, 2026.
5	337	0.825004249797	Antoine Jay, 2026.
5	338	0.825288968466	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	339	0.825584742608	Antoine Jay, 2026.
5	340	0.825988826068	Antoine Jay, 2026.
5	341	0.826260404451	Antoine Jay, 2026.
5	342	0.826621552014	Antoine Jay, 2026.
5	343	0.826828979790	Antoine Jay, 2026.
5	344	0.827224428941	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	345	0.827516615966	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	346	0.827771444702	Antoine Jay, 2026.
5	347	0.828083835189	Antoine Jay, 2026.
5	348	0.828204620793	Antoine Jay, 2026.
5	349	0.828485700297	Antoine Jay, 2026.
5	350	0.828861581314	Antoine Jay, 2026.
5	351	0.829081509690	Arhan Canli, 2026.
5	352	0.829512669912	Antoine Jay, 2026.
5	353	0.829762402883	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	354	0.830268971287	Antoine Jay, 2026.
5	355	0.830367467483	Antoine Jay, 2026.
5	356	0.830726989923	Antoine Jay, 2026.
5	357	0.830961923290	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	358	0.831100939988	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	359	0.831496548248	Antoine Jay, 2026.
5	360	0.831850886248	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	361	0.832095195023	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	362	0.832315309956	Antoine Jay, 2026.
5	363	0.832599718356	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	364	0.832858426319	Antoine Jay, 2026.
5	365	0.833122229267	Antoine Jay, 2026.
5	366	0.833148844992	Antoine Jay, 2026.
5	367	0.833258278154	Antoine Jay, 2026.
5	368	0.833330736450	Antoine Jay, 2026.
5	369	0.833416779863	Antoine Jay, 2026.
5	370	0.833527879590	Antoine Jay, 2026.
5	371	0.833679834217	Antoine Jay, 2026.
5	372	0.833840754589	Antoine Jay, 2026.
5	373	0.833974045958	Antoine Jay, 2026.
5	374	0.834407407111	Antoine Jay, 2026.
5	375	0.834580752886	Antoine Jay, 2026.
5	376	0.834731934205	Antoine Jay, 2026.
5	377	0.835047660432	Antoine Jay, 2026.
5	378	0.835412175423	Antoine Jay, 2026.
5	379	0.835587707928	Antoine Jay, 2026.
5	380	0.835788987393	Antoine Jay, 2026.
5	381	0.835995431589	Antoine Jay, 2026.
5	382	0.836325448636	Antoine Jay, 2026.
5	383	0.836604396820	Arhan Canli, 2026.
5	384	0.836941928919	Antoine Jay, 2026.
5	385	0.837124638430	Antoine Jay, 2026.
5	386	0.837384071313	Antoine Jay, 2026.
5	387	0.837545006851	Antoine Jay, 2026.
5	388	0.837773312829	Antoine Jay, 2026.
5	389	0.838235508527	Antoine Jay, 2026.
5	390	0.838261046337	Antoine Jay, 2026.
5	391	0.838751475806	Antoine Jay, 2026.
5	392	0.838979765400	Antoine Jay, 2026.
5	393	0.839092143707	Antoine Jay, 2026.
5	394	0.839448820589	Antoine Jay, 2026.
5	395	0.839695098455	Antoine Jay, 2026.
5	396	0.839977066438	Antoine Jay, 2026.
5	397	0.840165965307	Antoine Jay, 2026.
5	398	0.840242489571	Antoine Jay, 2026.
5	399	0.840452019119	Antoine Jay, 2026.
5	400	0.840676033455	Antoine Jay, 2026.
5	401	0.841007706450	Antoine Jay, 2026.
5	402	0.841263847774	Antoine Jay, 2026.
5	403	0.841563344355	Antoine Jay, 2026.
5	404	0.841802565822	Antoine Jay, 2026.
5	405	0.841994801864	Antoine Jay, 2026.
5	406	0.842390258263	Antoine Jay, 2026.
5	407	0.842529150118	Antoine Jay, 2026.
5	408	0.842704893647	Vadim Borisov, 2026.
5	409	0.842704908197	Antoine Jay, 2026.
5	410	0.842792728355	Antoine Jay, 2026.
5	411	0.842849131793	Antoine Jay, 2026.
5	412	0.842984575227	Antoine Jay, 2026.
5	413	0.843046068151	Antoine Jay, 2026.
5	414	0.843157473848	Antoine Jay, 2026.
5	415	0.843244790970	Antoine Jay, 2026.
5	416	0.843360131784	Antoine Jay, 2026.
5	417	0.843464510038	Antoine Jay, 2026.
5	418	0.843647788490	Antoine Jay, 2026.
5	419	0.843650399788	Antoine Jay, 2026.
5	420	0.843801811042	Antoine Jay, 2026.
5	421	0.843841991330	Antoine Jay, 2026.
5	422	0.843911291137	Arhan Canli, 2026.
5	423	0.843924186580	Antoine Jay, 2026.
5	424	0.843990322240	Antoine Jay, 2026.
5	425	0.844122162002	Antoine Jay, 2026.
5	426	0.844202846604	Antoine Jay, 2026.
5	427	0.844427943151	Antoine Jay, 2026.
5	428	0.844543990853	Antoine Jay, 2026.
5	429	0.844594126882	Antoine Jay, 2026.
5	430	0.844663079843	Antoine Jay, 2026.
5	431	0.844739183243	Antoine Jay, 2026.
5	432	0.844856609653	Antoine Jay, 2026.
5	433	0.845127619967	Antoine Jay, 2026.
5	434	0.845230861201	Henry Cohn, 2026.
5	435	0.845298817494	Antoine Jay, 2026.
5	436	0.845317551512	Antoine Jay, 2026.
5	437	0.845444967146	Antoine Jay, 2026.
5	438	0.845554678683	Antoine Jay, 2026.
5	439	0.845747072131	Antoine Jay, 2026.
5	440	0.846258925584	Antoine Jay, 2026.
5	441	0.846391467690	Antoine Jay, 2026.
5	442	0.846458239635	Antoine Jay, 2026.
5	443	0.846697494137	Antoine Jay, 2026.
5	444	0.847062785020	Arhan Canli, 2026.
5	445	0.847144729479	Antoine Jay, 2026.
5	446	0.847466887392	Antoine Jay, 2026.
5	447	0.847698830258	Antoine Jay, 2026.
5	449	0.847853902241	Antoine Jay, 2026.
5	450	0.847879753800	Antoine Jay, 2026.
5	451	0.847939995199	Antoine Jay, 2026.
5	452	0.848131275720	Antoine Jay, 2026.
5	453	0.848240312001	Christopher Smolen, 2026.
5	454	0.848483888107	Antoine Jay, 2026.
5	455	0.848609221231	Antoine Jay, 2026.
5	456	0.848777017872	Antoine Jay, 2026.
5	457	0.848874366967	Antoine Jay, 2026.
5	458	0.849025448595	Antoine Jay, 2026.
5	459	0.849205607657	Antoine Jay, 2026.
5	460	0.849308073437	Antoine Jay, 2026.
5	461	0.849537521644	Antoine Jay, 2026.
5	462	0.849661007844	Antoine Jay, 2026.
5	463	0.849885938310	Antoine Jay, 2026.
5	464	0.850142479393	Antoine Jay, 2026.
5	465	0.850380474317	Antoine Jay, 2026.
5	466	0.850792549224	Antoine Jay, 2026.
5	467	0.851112088087	Antoine Jay, 2026.
5	468	0.851367384767	Antoine Jay, 2026.
5	469	0.851659182607	Antoine Jay, 2026.
5	470	0.852023098059	Antoine Jay, 2026.
5	471	0.852224972256	Antoine Jay, 2026.
5	472	0.852512716254	Antoine Jay, 2026.
5	473	0.852753248365	Antoine Jay, 2026.
5	474	0.852956281593	Antoine Jay, 2026.
5	475	0.853253309078	Antoine Jay, 2026.
5	476	0.853467558079	Antoine Jay, 2026.
5	477	0.853615768410	Antoine Jay, 2026.
5	478	0.853805819714	Antoine Jay, 2026.
5	479	0.854112108623	Antoine Jay, 2026.
5	480	0.854330440330	Antoine Jay, 2026.
5	481	0.854550087363	Antoine Jay, 2026.
5	482	0.854710151285	Antoine Jay, 2026.
5	483	0.856208249793	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	484	0.856362782599	Antoine Jay, 2026.
5	485	0.856463812595	Antoine Jay, 2026.
5	486	0.856651783818	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	487	0.856831067866	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	488	0.856932073246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	489	0.857147443193	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	490	0.857315360501	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	491	0.857419798181	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	492	0.857605788666	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	493	0.857744196019	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	494	0.857798082994	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	495	0.857974025889	Antoine Jay, 2026.
5	496	0.858096902788	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	497	0.858223837016	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	498	0.858334201741	Antoine Jay, 2026.
5	499	0.858529178829	Antoine Jay, 2026.
5	500	0.858614419424	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	501	0.858770766773	Antoine Jay, 2026.
5	502	0.858857096539	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	503	0.859123404081	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	504	0.859298772137	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	505	0.859300480916	Antoine Jay, 2026.
5	506	0.859416897020	Antoine Jay, 2026.
5	507	0.859520084588	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	508	0.859581607033	Antoine Jay, 2026.
5	509	0.859680531155	Antoine Jay, 2026.
5	510	0.859864345276	Antoine Jay, 2026.
5	511	0.860122041544	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	512	0.860264330493	Antoine Jay, 2026.
5	513	0.860326098574	Antoine Jay, 2026.
5	514	0.860475773200	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	515	0.860631058314	Antoine Jay, 2026.
5	516	0.860815206899	Antoine Jay, 2026.
5	517	0.860940537434	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	518	0.861027755729	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	519	0.861061832183	Antoine Jay, 2026.
5	520	0.861238844744	Christopher Smolen, 2026.
5	521	0.861380747184	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	522	0.861466972413	Antoine Jay, 2026.
5	523	0.861534830308	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	525	0.861687115155	Vadim Borisov, 2026.
5	526	0.861687116303	Vadim Borisov, 2026.
5	527	0.861687127229	Antoine Jay, 2026.
5	528	0.861801720358	Antoine Jay, 2026.
5	529	0.861875827372	Antoine Jay, 2026.
5	530	0.862024646924	Antoine Jay, 2026.
5	531	0.862234954291	Antoine Jay, 2026.
5	532	0.862376958506	Antoine Jay, 2026.
5	533	0.862444417944	Antoine Jay, 2026.
5	534	0.862555810002	Antoine Jay, 2026.
5	535	0.862659522886	Antoine Jay, 2026.
5	536	0.862924656814	Antoine Jay, 2026.
5	537	0.863066727526	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
5	538	0.863095188406	Antoine Jay, 2026.
5	539	0.863283573294	Antoine Jay, 2026.
5	540	0.863552661265	Antoine Jay, 2026.
5	541	0.863625824025	Antoine Jay, 2026.
5	542	0.863852499141	Antoine Jay, 2026.
5	543	0.863919185599	Antoine Jay, 2026.
5	544	0.864241559583	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	545	0.864343141486	Vadim Borisov, 2026.
5	546	0.864343144834	Antoine Jay, 2026.
5	547	0.864425652630	Antoine Jay, 2026.
5	548	0.864511531839	Antoine Jay, 2026.
5	549	0.864823855690	Antoine Jay, 2026.
5	550	0.864870547245	Antoine Jay, 2026.
5	551	0.865085385406	Antoine Jay, 2026.
5	552	0.865226068520	Antoine Jay, 2026.
5	553	0.865341127919	Antoine Jay, 2026.
5	554	0.865461219888	Antoine Jay, 2026.
5	555	0.865615895537	Antoine Jay, 2026.
5	556	0.865722151918	Antoine Jay, 2026.
5	557	0.865899868104	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	558	0.866161974541	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	559	0.866258580364	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	560	0.866455723651	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	561	0.866579303573	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	562	0.866678859091	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	563	0.866775178964	Christopher Smolen, 2026.
5	564	0.866956214816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	565	0.867096375304	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	566	0.867207770084	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	567	0.867291597306	Antoine Jay, 2026.
5	568	0.867435664103	Antoine Jay, 2026.
5	569	0.867558511328	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	570	0.867679706052	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	571	0.867787396856	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	572	0.867953424250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	573	0.868058923848	Antoine Jay, 2026.
5	574	0.868112300703	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	575	0.868287981882	Antoine Jay, 2026.
5	576	0.868383480008	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	577	0.868500876232	Antoine Jay, 2026.
5	578	0.868613495633	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	579	0.868755234557	Antoine Jay, 2026.
5	580	0.868808998200	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	581	0.868920983430	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	582	0.869025723732	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	583	0.869181573798	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	584	0.869272836074	Antoine Jay, 2026.
5	585	0.869395016544	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	586	0.869554368178	Antoine Jay, 2026.
5	587	0.869617716332	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	588	0.869803304618	Antoine Jay, 2026.
5	589	0.869902221188	Antoine Jay, 2026.
5	590	0.870013320573	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	591	0.870116485875	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	592	0.870219835228	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	593	0.870339089875	Antoine Jay, 2026.
5	594	0.870424810492	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	595	0.870532997385	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	596	0.870695802435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	597	0.870728910840	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	598	0.870825163591	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	599	0.870960375160	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	600	0.871062947258	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	601	0.871192535830	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	602	0.871318464852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	603	0.871401636390	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	604	0.871532281625	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	605	0.871578432315	Antoine Jay, 2026.
5	606	0.871654569730	Antoine Jay, 2026.
5	607	0.871817394296	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	608	0.871909596713	Antoine Jay, 2026.
5	609	0.872025622321	Antoine Jay, 2026.
5	610	0.872140831428	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	611	0.872250281013	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	612	0.872321472657	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	613	0.872449453449	Antoine Jay, 2026.
5	614	0.872525176391	Antoine Jay, 2026.
5	615	0.872608962316	Antoine Jay, 2026.
5	616	0.872728869281	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	617	0.872864990617	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	618	0.872935737589	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	619	0.873052135335	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	620	0.873198597259	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	621	0.873277174768	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	622	0.873366418033	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	623	0.873472343608	Antoine Jay, 2026.
5	624	0.873580612680	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	625	0.873655536592	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	626	0.873707502795	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	627	0.873803079662	Antoine Jay, 2026.
5	628	0.873965064776	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	629	0.874067705789	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	630	0.874158573803	Antoine Jay, 2026.
5	631	0.874241097100	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	632	0.874339664844	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	633	0.874515666749	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	634	0.874570578183	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	635	0.874642875247	Antoine Jay, 2026.
5	636	0.874724604965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	637	0.874905348680	Antoine Jay, 2026.
5	638	0.874970066288	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	639	0.875063126196	Antoine Jay, 2026.
5	640	0.875149162627	Antoine Jay, 2026.
5	641	0.875227562311	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	642	0.875361260474	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	643	0.875449705428	Antoine Jay, 2026.
5	644	0.875552242003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	645	0.875641663613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	646	0.875734540475	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	647	0.875856663860	Antoine Jay, 2026.
5	648	0.875943721872	Antoine Jay, 2026.
5	649	0.876062872052	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	650	0.876142108193	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	651	0.876262494697	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	652	0.876342234743	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	653	0.876401534879	Antoine Jay, 2026.
5	654	0.876505123194	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	655	0.876608697412	Antoine Jay, 2026.
5	656	0.876679653518	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	657	0.876732204804	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	658	0.876933180225	Antoine Jay, 2026.
5	659	0.876979572838	Antoine Jay, 2026.
5	660	0.877056961930	Antoine Jay, 2026.
5	661	0.877139503750	Henry Cohn, 2026.
5	662	0.877219648562	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	663	0.877383543123	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	664	0.877441215109	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	665	0.877543704634	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	666	0.877656043970	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	667	0.877736492441	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	668	0.877840617758	Antoine Jay, 2026.
5	669	0.877931904708	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	670	0.877961310546	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	671	0.878059543968	Antoine Jay, 2026.
5	672	0.878106473545	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	673	0.878239675647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	674	0.878341862036	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	675	0.878426368658	Antoine Jay, 2026.
5	676	0.878532279625	Antoine Jay, 2026.
5	677	0.878641029088	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	678	0.878725344170	Antoine Jay, 2026.
5	679	0.878844642884	Antoine Jay, 2026.
5	680	0.878871026021	Antoine Jay, 2026.
5	681	0.878942566657	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	682	0.879094298148	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	683	0.879141705411	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	684	0.879237842244	Antoine Jay, 2026.
5	685	0.879349888018	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	686	0.879443262160	Antoine Jay, 2026.
5	687	0.879533216997	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	688	0.879603756205	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	689	0.879692797949	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	690	0.879760932845	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	691	0.879867389212	Antoine Jay, 2026.
5	692	0.879949429244	Antoine Jay, 2026.
5	693	0.880058582402	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	694	0.880108704289	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	695	0.880213636234	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	696	0.880332768217	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	697	0.880384639767	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	698	0.880410324681	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	699	0.880540761391	Antoine Jay, 2026.
5	700	0.880672293297	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	701	0.880706756421	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	702	0.880772437966	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	703	0.880898082445	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	704	0.880960334097	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	705	0.881059691286	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	706	0.881133230108	Antoine Jay, 2026.
5	707	0.881182594816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	708	0.881298041533	Antoine Jay, 2026.
5	709	0.881346559134	Antoine Jay, 2026.
5	710	0.881458543984	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	711	0.881544977440	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	712	0.881657972498	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	713	0.881748520102	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	714	0.881794374156	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	715	0.881873334904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	716	0.881982666327	Antoine Jay, 2026.
5	717	0.882071939111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	718	0.882139968837	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	719	0.882224968633	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	720	0.882266596886	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	721	0.882401477806	Antoine Jay, 2026.
5	722	0.882457861841	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	723	0.882545360336	Antoine Jay, 2026.
5	724	0.882632103713	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	725	0.882725242725	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	726	0.882788294800	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	727	0.882883992680	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	728	0.882938873892	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	729	0.883047979603	Antoine Jay, 2026.
5	730	0.883111870454	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	731	0.883215765216	Antoine Jay, 2026.
5	732	0.883261763530	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	733	0.883357902437	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	734	0.883432234104	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	735	0.883509237096	Antoine Jay, 2026.
5	736	0.883584603057	Antoine Jay, 2026.
5	737	0.883629005615	Antoine Jay, 2026.
5	738	0.883716322005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	739	0.883805870856	Antoine Jay, 2026.
5	740	0.883867770448	Antoine Jay, 2026.
5	741	0.883964648457	Antoine Jay, 2026.
5	742	0.884083702770	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	743	0.884161919689	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	744	0.884208812247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	745	0.884290133150	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	746	0.884376124134	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	747	0.884426830079	Antoine Jay, 2026.
5	748	0.884541491879	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	749	0.884600158731	Antoine Jay, 2026.
5	750	0.884671353816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	751	0.884736212722	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	752	0.884864170513	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	753	0.884902972182	Antoine Jay, 2026.
5	754	0.885004683554	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	755	0.885083474369	Antoine Jay, 2026.
5	756	0.885134705092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	757	0.885222853780	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	758	0.885326027552	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	759	0.885411821274	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	760	0.885488429544	Antoine Jay, 2026.
5	761	0.885563468054	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	762	0.885593120865	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	763	0.885656126630	Antoine Jay, 2026.
5	764	0.885785862977	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	765	0.885800134228	Antoine Jay, 2026.
5	766	0.885897941963	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	767	0.886015608336	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	768	0.886064170265	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	769	0.886144919190	Antoine Jay, 2026.
5	770	0.886228806560	Antoine Jay, 2026.
5	771	0.886293141628	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	772	0.886369768127	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	773	0.886443709050	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	774	0.886507926861	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	775	0.886601193191	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	776	0.886689306183	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	777	0.886714172678	Antoine Jay, 2026.
5	778	0.886822324082	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	779	0.886872091882	Antoine Jay, 2026.
5	780	0.886973487256	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	781	0.887067739177	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	782	0.887085127000	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	783	0.887170865163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	784	0.887213788641	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	785	0.887305545859	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	786	0.887357278715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	787	0.887448997918	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	788	0.887514049646	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	789	0.887612054907	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	790	0.887692321112	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	791	0.887717034398	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	792	0.887797932005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	793	0.887848221630	Antoine Jay, 2026.
5	794	0.887879771283	Antoine Jay, 2026.
5	795	0.888020208743	Antoine Jay, 2026.
5	796	0.888056445268	Antoine Jay, 2026.
5	797	0.888181830093	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	798	0.888226749919	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	799	0.888318273498	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	800	0.888367047936	Antoine Jay, 2026.
5	801	0.888425844635	Antoine Jay, 2026.
5	802	0.888468978315	Antoine Jay, 2026.
5	803	0.888580801185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	804	0.888659360745	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	805	0.888734299200	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	806	0.888800209584	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	807	0.888827652037	Antoine Jay, 2026.
5	808	0.888905338931	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	809	0.889018756766	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	810	0.889043738514	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	811	0.889146635876	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	812	0.889250805116	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	813	0.889261672686	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	814	0.889325016017	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	815	0.889407379830	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	816	0.889470236806	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	817	0.889553078118	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	818	0.889618783143	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	819	0.889679547196	Antoine Jay, 2026.
5	820	0.889735701941	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	821	0.889821307224	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	822	0.889860688652	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	823	0.889936960552	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	824	0.890008181372	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	825	0.890043890079	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	826	0.890157516714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	827	0.890173347579	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	828	0.890236833482	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	829	0.890308039858	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	830	0.890397801907	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	831	0.890468378790	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	832	0.890525855437	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	833	0.890610368416	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	834	0.890648092955	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	835	0.890779873362	Antoine Jay, 2026.
5	836	0.890791406406	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	837	0.890858956942	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	838	0.890913836226	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	839	0.890970107101	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	840	0.891050350215	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	841	0.891103375488	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	842	0.891181467827	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	843	0.891287528997	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	844	0.891315359906	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	845	0.891366882579	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	846	0.891416522489	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	847	0.891498599926	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	848	0.891576307617	Antoine Jay, 2026.
5	849	0.891611082414	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	850	0.891673831647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	851	0.891739350063	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	852	0.891810297767	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	853	0.891850160871	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	854	0.891956707177	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	855	0.891965720226	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	856	0.892053055855	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	857	0.892127562822	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	858	0.892166065271	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	859	0.892260947209	Antoine Jay, 2026.
5	860	0.892292283359	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	861	0.892394014607	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	862	0.892459840076	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	863	0.892525541140	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	864	0.892559715160	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	865	0.892632427725	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	866	0.892702069525	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	867	0.892751013515	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	868	0.892809229362	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	869	0.892927787737	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	870	0.892943373078	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	871	0.892998933779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	872	0.893045194309	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	873	0.893081811788	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	874	0.893191833046	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	875	0.893237705351	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	876	0.893266165998	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	877	0.893354663005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	878	0.893437197037	Antoine Jay, 2026.
5	879	0.893488848864	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	880	0.893552331464	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	881	0.893575492667	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	882	0.893675788240	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	883	0.893733990506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	884	0.893786740471	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	885	0.893819617758	Antoine Jay, 2026.
5	886	0.893906543970	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	887	0.893941779196	Antoine Jay, 2026.
5	888	0.894043500282	Antoine Jay, 2026.
5	889	0.894089122049	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	890	0.894168649562	Henry Cohn, 2026.
5	891	0.894206192531	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	892	0.894272661135	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	893	0.894332397388	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	894	0.894381185578	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	895	0.894439511963	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	896	0.894453112570	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	897	0.894592703204	Antoine Jay, 2026.
5	898	0.894645575810	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	899	0.894699961145	Antoine Jay, 2026.
5	900	0.894750689132	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	901	0.894798436537	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	902	0.894877029648	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	903	0.894922398858	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	904	0.894933018553	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	905	0.895056844323	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	906	0.895091614755	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	907	0.895177756885	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	908	0.895251827393	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	909	0.895283685929	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	910	0.895318680374	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	911	0.895386383067	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	912	0.895452016376	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	913	0.895508733659	Antoine Jay, 2026.
5	914	0.895584948003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	915	0.895665942688	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	916	0.895691383929	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	917	0.895740480766	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	918	0.895831153040	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	919	0.895857949737	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	920	0.895910062110	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	921	0.895978570522	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	922	0.896070532630	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	923	0.896081376210	Antoine Jay, 2026.
5	924	0.896160415742	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	925	0.896217259694	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	926	0.896270974493	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	927	0.896285975480	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	928	0.896371344685	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	929	0.896434284151	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	930	0.896506262521	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	931	0.896529629616	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	932	0.896551683898	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	933	0.896626742167	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	934	0.896719653714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	935	0.896763483292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	936	0.896822491668	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	937	0.896870010527	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	938	0.896912246115	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	939	0.896968294866	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	940	0.897050423715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	941	0.897115311646	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	942	0.897153317616	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	943	0.897218447907	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	944	0.897245854677	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	945	0.897332215849	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	946	0.897404796551	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	947	0.897419903128	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	948	0.897464730124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	949	0.897542820640	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	950	0.897615339891	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	951	0.897661595719	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	952	0.897698572916	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	953	0.897740693517	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	954	0.897818894651	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	955	0.897830841153	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	956	0.897922194428	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	957	0.897940422059	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	958	0.898018939564	Antoine Jay, 2026.
5	959	0.898054066517	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	960	0.898147031984	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	961	0.898172205817	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	962	0.898249545624	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	963	0.898280407909	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	964	0.898352042876	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	965	0.898415605881	Antoine Jay, 2026.
5	966	0.898447868707	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	967	0.898494542041	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	968	0.898543794039	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	969	0.898601309092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	970	0.898671723338	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	971	0.898678157520	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	972	0.898748952988	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	973	0.898781074626	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	974	0.898899770013	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	975	0.898912774169	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	976	0.898978510818	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	977	0.899025382787	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	978	0.899070452280	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	979	0.899100256178	Antoine Jay, 2026.
5	980	0.899138620026	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	981	0.899188273829	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	982	0.899281995922	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	983	0.899324578625	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	984	0.899374160785	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	985	0.899437609794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	986	0.899486396167	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	987	0.899518008089	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	988	0.899581022491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	989	0.899629951347	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	990	0.899676165613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	991	0.899739473462	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	992	0.899780402942	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	993	0.899856048564	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	994	0.899902503331	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	995	0.899956906140	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	996	0.899984046871	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	997	0.900033044264	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	998	0.900064691715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	999	0.900098883567	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1000	0.900174175250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1001	0.900244563003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1002	0.900277773975	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1003	0.900353351881	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1004	0.900397756303	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1005	0.900429604194	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1006	0.900484991293	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1007	0.900518956466	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1008	0.900533203441	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1009	0.900634564655	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1010	0.900685145043	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1011	0.900761606647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1012	0.900778836214	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1013	0.900831683587	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1014	0.900884196291	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1015	0.900937789989	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1016	0.900971199638	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1017	0.900991127152	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1018	0.901089895682	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1019	0.901110584229	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1020	0.901193127219	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1021	0.901207891090	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1022	0.901289678756	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1023	0.901330344619	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
5	1024	0.901352078641	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	13	0.113079752148	P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911 . $96 x^{3} - 36 x^{2} - 6 x + 1$
6	14	0.132490920324	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. Minimal polynomial of degree 13
6	15	0.144948974279	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $20 x^{2} + 4 x - 1$
6	16	0.171071421043	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $6400 x^{5} + 960 x^{4} - 1024 x^{3} - 32 x^{2} + 31 x - 1$
6	17	0.183274337024	P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911 . $400 x^{4} + 240 x^{3} + 16 x^{2} - 8 x - 1$
6	18	0.197812188602	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $784 x^{8} - 280 x^{7} - 1191 x^{6} + 120 x^{5} + 218 x^{4} - 62 x^{3} - 31 x^{2} + 2 x + 1$
6	19	0.200226025892	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6	20	0.214285714286	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $14 x - 3$
6	21	0.242852848014	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6	22	0.248865699460	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6	23	0.25	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $4 x - 1$
6	24	0.25	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $4 x - 1$
6	25	0.25	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $4 x - 1$
6	26	0.25	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $4 x - 1$
6	27*	0.25	T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $4 x - 1$
6	28	0.3	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $10 x - 3$
6	29	0.327844830882	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6	30	0.333157886299	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6	31	0.333333333334	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $3 x - 1$
6	32	0.333333333334	J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335–348, https://research.tue.nl/en/publications/equilateral-point-sets-in-elliptic-geometry. $3 x - 1$
6	33	0.344948974279	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $20 x^{2} - 4 x - 1$
6	34	0.346451336111	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $64 x^{5} + 64 x^{4} - 76 x^{3} + 7 x^{2} + 6 x - 1$
6	35	0.358257569496	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $5 x^{2} + x - 1$
6	36	0.358257569496	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x^{2} + x - 1$
6	37	0.366623377687	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $64 x^{4} + 96 x^{3} - 80 x^{2} + 16 x - 1$
6	38	0.367688450451	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $7424 x^{8} + 1280 x^{7} - 3904 x^{6} - 768 x^{5} + 448 x^{4} + 80 x^{3} - 1$
6	39	0.384936289161	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6	40	0.386096677606	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $31 x^{4} - 12 x^{3} - 14 x^{2} + 8 x - 1$
6	41	0.389434811673	Henry Cohn, 2023.
6	42	0.390388203203	J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4 x^{2} + x - 1$
6	43	0.399773924374	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $1024 x^{9} - 4096 x^{8} - 1536 x^{7} + 1024 x^{6} + 704 x^{5} + 64 x^{4} - 96 x^{3} - 16 x^{2} + 4 x - 1$
6	44	0.405666616164	Henry Cohn, 2023.
6	45	0.426943864061	Henry Cohn, 2025.
6	46	0.434834721516	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	47	0.441020734927	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	48	0.443609864234	Henry Cohn, 2025.
6	49	0.446060501890	Henry Cohn, 2023.
6	50	0.446739131277	Henry Cohn, 2023. $58 x^{3} - 50 x^{2} + 13 x - 1$
6	51	0.456479386398	Henry Cohn, 2025.
6	52	0.458253528717	Henry Cohn, 2023.
6	53	0.459145031877	Henry Cohn, 2025.
6	54	0.462714285892	Henry Cohn, 2023. $4104 x^{4} - 216 x^{3} - 3654 x^{2} + 1955 x - 289$
6	55	0.472467412878	Henry Cohn, 2024.
6	56	0.475645784548	Henry Cohn, 2023. $33024 x^{6} + 14848 x^{5} - 45568 x^{4} + 5832 x^{3} + 12257 x^{2} - 4922 x + 529$
6	57	0.479790821500	Henry Cohn, 2025.
6	58	0.482548584905	Henry Cohn, 2024. $20 x^{2} + 9 x - 9$
6	59	0.485942488798	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	60	0.486876290376	Henry Cohn, 2025.
6	61	0.491730182082	Henry Cohn, 2025.
6	62	0.495160643621	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	63	0.498122491823	Henry Cohn, 2023.
6	64	0.498345393899	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	65	0.499869061666	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	66	0.499921169601	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	67	0.499961868008	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	68	0.499999950782	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	69	0.499999977407	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	72	0.5	A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060. $2 x - 1$
6	73	0.513985952311	Henry Cohn, 2025.
6	74	0.521539568537	Henry Cohn, 2025.
6	75	0.523076433656	Antoine Jay, 2026.
6	76	0.524813970537	Antoine Jay, 2026.
6	77	0.527287929827	Henry Cohn, 2025.
6	78	0.528662896579	Henry Cohn, 2025.
6	79	0.533648501058	Henry Cohn, 2025.
6	80	0.536468893038	Henry Cohn, 2025.
6	81	0.538396586915	Henry Cohn, 2026.
6	82	0.539382071135	Henry Cohn, 2026.
6	83	0.543248902467	Henry Cohn, 2026.
6	84	0.545752285862	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	85	0.546038397748	Henry Cohn, 2026.
6	86	0.548916479202	Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6	87	0.550379697504	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	88	0.552456735670	Henry Cohn, 2025.
6	89	0.555561660912	Henry Cohn, 2025.
6	90	0.557491741124	Antoine Jay, 2026.
6	91	0.557588802583	Henry Cohn, 2026.
6	92	0.560333303162	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	93	0.563013323310	Henry Cohn, 2023.
6	94	0.564644480982	Antoine Jay, 2026.
6	95	0.565789396150	Henry Cohn, 2023.
6	96	0.565950871118	Henry Cohn, 2023.
6	97	0.568133461901	Henry Cohn, 2025.
6	98	0.571037776392	Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6	99	0.573881665753	Henry Cohn, 2023.
6	100	0.574916276575	Henry Cohn, 2024.
6	101	0.578318097782	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	102	0.580736682189	Henry Cohn, 2023.
6	103	0.580814970721	Antoine Jay, 2026.
6	104	0.582120078379	Henry Cohn, 2026.
6	105	0.582634862975	Antoine Jay, 2026.
6	106	0.582644233425	Antoine Jay, 2026.
6	107	0.583371498649	Henry Cohn, 2026.
6	108	0.584228700283	Henry Cohn, 2026.
6	109	0.585348750770	Henry Cohn, 2026.
6	110	0.585555924412	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	111	0.585638229827	Henry Cohn, 2026.
6	112	0.585693130025	Henry Cohn, 2026.
6	113	0.586622932873	Henry Cohn, 2025.
6	114	0.588109690133	Henry Cohn, 2023.
6	115	0.596004657476	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	116	0.596362762500	Henry Cohn, 2026.
6	117	0.596421582866	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	118	0.596439256863	Antoine Jay, 2026.
6	119	0.598418929486	Antoine Jay, 2026.
6	120	0.599016149465	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	121	0.603688760597	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	122	0.605232558247	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	123	0.606415945860	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6	124	0.607936838904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	125	0.607973280226	Henry Cohn, 2026.
6	126	0.610306866273	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	127	0.616047193210	Antoine Jay, 2026.
6	128	0.618872617056	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	129	0.620224367829	Henry Cohn, 2025.
6	130	0.622749533062	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	131	0.624452202888	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	132	0.624694337870	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	133	0.626090430089	Antoine Jay, 2026.
6	134	0.627762731707	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	135	0.629447717737	Antoine Jay, 2026.
6	136	0.630749416149	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	137	0.631575173435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	138	0.633669770336	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	139	0.635852941496	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	140	0.636752821181	Antoine Jay, 2026.
6	141	0.636830011504	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	142	0.637378151040	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	143	0.638428796783	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	144	0.638598434948	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	145	0.639674399842	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	146	0.640469639839	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	147	0.641748038387	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	148	0.642736295513	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	149	0.644705619024	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	150	0.644904835601	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	151	0.644919433277	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	152	0.645073960373	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	153	0.645210956961	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	154	0.645661944093	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	155	0.646192045530	Antoine Jay, 2026.
6	156	0.647251806639	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	157	0.648607476968	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	158	0.649821257599	Antoine Jay, 2026.
6	159	0.650461345030	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	160	0.650866730014	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	161	0.651395674836	Antoine Jay, 2026.
6	162	0.651869454855	Antoine Jay, 2026.
6	163	0.652307561259	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	164	0.653028628063	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	165	0.653531275605	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	166	0.653972556245	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	167	0.655327277538	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	168	0.656419753699	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	169	0.658674020111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	170	0.660039796784	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	171	0.661216162738	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	172	0.662523168284	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	173	0.663595611062	Antoine Jay, 2026.
6	174	0.663910790633	Antoine Jay, 2026.
6	175	0.664423776344	Antoine Jay, 2026.
6	176	0.664655289830	Antoine Jay, 2026.
6	177	0.667248188847	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	178	0.668347200084	Antoine Jay, 2026.
6	179	0.669353780760	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	180	0.670193100921	Antoine Jay, 2026.
6	181	0.670435765875	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	182	0.671572335619	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	183	0.672123467486	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	184	0.672423934627	Antoine Jay, 2026.
6	185	0.673138325950	WolfFrogs, 2026.
6	186	0.673827638855	Antoine Jay, 2026.
6	187	0.674109703209	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	188	0.674695081992	Arhan Canli, 2026.
6	189	0.674814958648	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	190	0.674912548875	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	191	0.674914031863	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	192	0.674959810623	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	193	0.674971493431	Antoine Jay, 2026.
6	194	0.675977230691	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	195	0.675982483231	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	196	0.676000059853	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	197	0.676139784165	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	198	0.676255980506	Antoine Jay, 2026.
6	199	0.677240718061	Antoine Jay, 2026.
6	200	0.679468174757	Antoine Jay, 2026.
6	201	0.681454928946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	202	0.681973854192	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	203	0.682701893528	Antoine Jay, 2026.
6	204	0.684008396939	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	205	0.684949098050	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	206	0.685714605963	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	207	0.686362737907	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	208	0.687185627750	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	209	0.687876625759	Antoine Jay, 2026.
6	210	0.688519839782	Antoine Jay, 2026.
6	211	0.689173397234	Antoine Jay, 2026.
6	212	0.689755479547	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	213	0.689977050006	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	214	0.690421520629	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	215	0.691011081446	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	216	0.691472408860	Antoine Jay, 2026.
6	217	0.692100456953	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	218	0.693060343689	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	219	0.693408930195	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	220	0.694029014563	Antoine Jay, 2026.
6	221	0.694336878946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	222	0.694750308013	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	223	0.695344854705	Antoine Jay, 2026.
6	224	0.695842585723	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	225	0.695866030090	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	226	0.696030700811	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	227	0.696834443942	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	228	0.697147091343	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	229	0.697678057483	Antoine Jay, 2026.
6	230	0.698237904688	WolfFrogs, 2026.
6	231	0.698260569308	Antoine Jay, 2026.
6	232	0.698603053103	Antoine Jay, 2026.
6	233	0.699497731090	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	234	0.699913239980	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	243	0.7	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $10 x - 7$
6	244	0.702537542448	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	245	0.702672200221	Arhan Canli, 2026.
6	246	0.703102701988	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	247	0.703287570521	Antoine Jay, 2026.
6	248	0.703299253606	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
6	249	0.703518144610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	250	0.703830702694	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	251	0.703943163251	Antoine Jay, 2026.
6	252	0.704020745924	Antoine Jay, 2026.
6	253	0.704155539127	Antoine Jay, 2026.
6	254	0.704586804672	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	255	0.704715705496	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	256	0.704929499027	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	257	0.705350637779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	258	0.705825097762	Antoine Jay, 2026.
6	259	0.706348039265	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	260	0.707048162858	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	261	0.707830163349	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	262	0.708324049489	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	263	0.708911219352	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	264	0.709495868359	Antoine Jay, 2026.
6	265	0.710452246796	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	266	0.711283932571	Antoine Jay, 2026.
6	267	0.711971525677	Antoine Jay, 2026.
6	268	0.712787199947	Antoine Jay, 2026.
6	269	0.713424493237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	270	0.714094595168	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	271	0.714540135464	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	272	0.714831282150	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	273	0.716191352399	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	274	0.716982971491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	275	0.717946707650	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	276	0.718571685080	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	277	0.719093214548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	278	0.719862177159	Antoine Jay, 2026.
6	279	0.720497788804	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	280	0.720903551890	Antoine Jay, 2026.
6	281	0.721058774151	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	282	0.721629762453	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	283	0.722101793118	Antoine Jay, 2026.
6	284	0.722651497789	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	285	0.723268654005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	286	0.723334202630	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	287	0.723525667473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	288	0.723643340710	Antoine Jay, 2026.
6	289	0.724833672242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	290	0.725270556420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	291	0.725842284682	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	292	0.726180888995	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	293	0.726691621923	Antoine Jay, 2026.
6	294	0.727143598821	Antoine Jay, 2026.
6	295	0.727654977774	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	296	0.728186899473	Antoine Jay, 2026.
6	297	0.728471064050	Antoine Jay, 2026.
6	298	0.728960565357	Antoine Jay, 2026.
6	299	0.729552255389	Antoine Jay, 2026.
6	300	0.730001196044	Antoine Jay, 2026.
6	301	0.730592684104	Antoine Jay, 2026.
6	302	0.730858679154	Antoine Jay, 2026.
6	303	0.731363023332	Antoine Jay, 2026.
6	304	0.732007831009	Antoine Jay, 2026.
6	305	0.732468645026	Antoine Jay, 2026.
6	306	0.733242268353	Antoine Jay, 2026.
6	307	0.733624399291	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	308	0.733823478181	Antoine Jay, 2026.
6	309	0.734174669919	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	313	0.734184550198	Antoine Jay, 2026.
6	314	0.734364474812	Antoine Jay, 2026.
6	315	0.734407551384	Antoine Jay, 2026.
6	317	0.734963186458	Antoine Jay, 2026.
6	321	0.734991928201	Antoine Jay, 2026.
6	323	0.734994517848	Antoine Jay, 2026.
6	324	0.735091229356	Antoine Jay, 2026.
6	325	0.736301255836	Antoine Jay, 2026.
6	326	0.737251558725	Antoine Jay, 2026.
6	327	0.738169232866	Antoine Jay, 2026.
6	328	0.738828011509	Antoine Jay, 2026.
6	329	0.739132360988	Antoine Jay, 2026.
6	330	0.739647888674	Antoine Jay, 2026.
6	331	0.740262938002	Antoine Jay, 2026.
6	332	0.740806185948	Antoine Jay, 2026.
6	333	0.741154930151	Antoine Jay, 2026.
6	334	0.741496145347	Antoine Jay, 2026.
6	335	0.741940132132	Antoine Jay, 2026.
6	336	0.742238695686	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	337	0.742298827463	Arhan Canli, 2026.
6	338	0.742634661211	Antoine Jay, 2026.
6	339	0.743004914036	Antoine Jay, 2026.
6	340	0.743323703615	Antoine Jay, 2026.
6	341	0.743329214847	Antoine Jay, 2026.
6	342	0.743817924989	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	343	0.743995719715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	344	0.744395245204	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	345	0.744756203998	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	346	0.745191046164	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	347	0.745371510584	Antoine Jay, 2026.
6	348	0.745679867439	Christopher Smolen, 2026.
6	349	0.746213670532	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	350	0.746715928722	Antoine Jay, 2026.
6	351	0.747205569230	Antoine Jay, 2026.
6	352	0.747412546226	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	353	0.747893912943	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	354	0.748328774265	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	355	0.748782560784	Antoine Jay, 2026.
6	356	0.748928984716	Antoine Jay, 2026.
6	357	0.749467312700	Antoine Jay, 2026.
6	358	0.749887184013	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	359	0.750094952746	Arhan Canli, 2026.
6	360	0.750626052538	Antoine Jay, 2026.
6	361	0.750915700887	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	362	0.751272998926	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	363	0.751653558570	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	364	0.751931704440	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	365	0.752239954321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	366	0.752461797163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	367	0.753080047901	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	368	0.753224373386	Antoine Jay, 2026.
6	369	0.753554276304	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	370	0.753761371071	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	371	0.754134032258	Antoine Jay, 2026.
6	372	0.754532215374	Antoine Jay, 2026.
6	373	0.754675211338	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	374	0.755031454246	Antoine Jay, 2026.
6	375	0.755234337778	Antoine Jay, 2026.
6	376	0.755708382548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	377	0.756099249601	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	378	0.756263564336	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	379	0.756717448737	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	380	0.757009750044	Antoine Jay, 2026.
6	381	0.757135693315	Antoine Jay, 2026.
6	382	0.757353025994	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	383	0.757429123509	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	384	0.758013309209	Antoine Jay, 2026.
6	385	0.758168610548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	386	0.758634656889	Antoine Jay, 2026.
6	387	0.758912681209	Antoine Jay, 2026.
6	388	0.759185810221	Antoine Jay, 2026.
6	389	0.759378595246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	390	0.759643489826	Antoine Jay, 2026.
6	391	0.759792311921	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	392	0.760122594926	Antoine Jay, 2026.
6	393	0.760403100944	Antoine Jay, 2026.
6	394	0.760639350964	Antoine Jay, 2026.
6	395	0.760850400810	Antoine Jay, 2026.
6	396	0.761151964083	Antoine Jay, 2026.
6	397	0.761340845349	Antoine Jay, 2026.
6	398	0.761786544496	Antoine Jay, 2026.
6	399	0.761868799038	Antoine Jay, 2026.
6	400	0.762866231327	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	401	0.763152944920	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	402	0.763554362453	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	403	0.763622301719	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	404	0.763966961114	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	405	0.764274247981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	406	0.764457441833	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	407	0.764619393785	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	408	0.764934518470	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	409	0.765266483321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	410	0.765440068363	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	411	0.765665824682	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	412	0.765920392496	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	413	0.766009449797	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	414	0.766333650246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	415	0.766582573714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	416	0.766895217494	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	417	0.767075634933	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	418	0.767392122022	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	419	0.767623829363	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	420	0.767793596500	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	421	0.768007380881	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	422	0.768253994114	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	423	0.768503869702	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	424	0.768718639128	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	425	0.768929934229	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	426	0.769117200561	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	427	0.769357197436	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	428	0.769612874281	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	429	0.769802858185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	430	0.770029651946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	431	0.770257901289	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	432	0.770440405140	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	433	0.770667098803	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	434	0.770926953135	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	435	0.771055203553	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	436	0.771280142538	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	437	0.771484646979	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	438	0.771745266703	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	439	0.771966581378	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	440	0.772207948217	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	441	0.772229242444	Christopher Smolen, 2026.
6	442	0.772423504056	Christopher Smolen, 2026.
6	443	0.772788248460	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	444	0.772950652638	Antoine Jay, 2026.
6	445	0.773052053582	Christopher Smolen, 2026.
6	446	0.773409804779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	447	0.773564231323	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	448	0.773768254981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	449	0.774015394670	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	450	0.774247533089	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	451	0.774400576064	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	452	0.774587939699	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	453	0.774803243350	Antoine Jay, 2026.
6	454	0.774963328711	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	455	0.775162750965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	456	0.775345611014	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	457	0.775574849313	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	458	0.775857871861	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	459	0.775994191454	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	460	0.776187137044	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	461	0.776445476456	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	462	0.776512102015	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	463	0.776812795705	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	464	0.776821860993	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	465	0.777070928913	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	466	0.777326158510	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	467	0.777554247122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	468	0.777722689292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	469	0.777939897157	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	472	0.778061421378	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	473	0.778151528380	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	474	0.778159553720	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	475	0.778368992974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	476	0.778439394351	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	477	0.778458901810	Vadim Borisov, 2026.
6	478	0.778461652447	Vadim Borisov, 2026.
6	479	0.778483034469	Vadim Borisov, 2026.
6	480	0.778534324048	Vadim Borisov, 2026.
6	481	0.778855713371	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	482	0.779305709755	Vadim Borisov, 2026.
6	483	0.779333230930	Vadim Borisov, 2026.
6	484	0.779336453332	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	485	0.779545686971	Vadim Borisov, 2026.
6	486	0.779661603448	Vadim Borisov, 2026.
6	487	0.779866972746	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	488	0.779958136870	Vadim Borisov, 2026.
6	489	0.779958142417	Vadim Borisov, 2026.
6	490	0.780073303411	Vadim Borisov, 2026.
6	491	0.780191215744	Vadim Borisov, 2026.
6	492	0.780262656545	Vadim Borisov, 2026.
6	493	0.780304086240	Vadim Borisov, 2026.
6	494	0.780346525026	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	495	0.780358268927	Vadim Borisov, 2026.
6	496	0.780471562800	Vadim Borisov, 2026.
6	497	0.780496769539	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	498	0.780563718086	Vadim Borisov, 2026.
6	499	0.780627290803	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	500	0.780664060177	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	501	0.780718613665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	502	0.780805849263	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	512	0.780844799198	Antoine Jay, 2026.
6	513	0.781074716092	Antoine Jay, 2026.
6	515	0.781201374333	Antoine Jay, 2026.
6	516	0.781666315362	Antoine Jay, 2026.
6	517	0.781887501281	Antoine Jay, 2026.
6	518	0.782194223800	Antoine Jay, 2026.
6	519	0.782396180417	Antoine Jay, 2026.
6	520	0.782633741790	Antoine Jay, 2026.
6	525	0.785359708963	Antoine Jay, 2026.
6	526	0.785473753583	Antoine Jay, 2026.
6	527	0.785627207952	Antoine Jay, 2026.
6	528	0.785750716321	Antoine Jay, 2026.
6	529	0.785980598023	Antoine Jay, 2026.
6	530	0.786263833907	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	532	0.786662587989	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	533	0.786800940913	Christopher Smolen, 2026.
6	534	0.786809188672	Christopher Smolen, 2026.
6	535	0.786817163576	Pavlos Moros, 2026.
6	536	0.786840255474	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	537	0.786849432872	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	538	0.786860195792	Christopher Smolen, 2026.
6	539	0.786867260472	Christopher Smolen, 2026.
6	540	0.786875584565	Christopher Smolen, 2026.
6	541	0.786887548888	Pavlos Moros, 2026.
6	542	0.786894439044	Christopher Smolen, 2026.
6	543	0.786900814121	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	544	0.786906413328	Christopher Smolen, 2026.
6	545	0.786912755633	Pavlos Moros, 2026.
6	546	0.786940227870	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	547	0.786940301821	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	548	0.786942836454	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	549	0.786945300638	Antoine Jay, 2026.
6	550	0.786947165219	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	551	0.786954674684	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	552	0.786963721867	Vadim Borisov, 2026.
6	553	0.786966808555	Vadim Borisov, 2026.
6	554	0.786975667235	Vadim Borisov, 2026.
6	555	0.787007772544	Antoine Jay, 2026.
6	556	0.787014960031	Antoine Jay, 2026.
6	557	0.787044208628	Antoine Jay, 2026.
6	558	0.787072619879	Antoine Jay, 2026.
6	559	0.787708795864	Antoine Jay, 2026.
6	560	0.788287457423	Antoine Jay, 2026.
6	561	0.788623635310	Antoine Jay, 2026.
6	562	0.788803185722	Antoine Jay, 2026.
6	563	0.788908202544	Antoine Jay, 2026.
6	564	0.788980427154	Antoine Jay, 2026.
6	565	0.789032913638	Antoine Jay, 2026.
6	566	0.789639490235	Antoine Jay, 2026.
6	567	0.790176811718	Antoine Jay, 2026.
6	568	0.790380170509	Antoine Jay, 2026.
6	569	0.790496221910	Antoine Jay, 2026.
6	570	0.790705188614	Antoine Jay, 2026.
6	571	0.790729890400	Antoine Jay, 2026.
6	572	0.790801856896	Antoine Jay, 2026.
6	573	0.791412742194	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	574	0.791824282790	Antoine Jay, 2026.
6	575	0.792062102525	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	576	0.792263677429	Antoine Jay, 2026.
6	577	0.792771108142	Antoine Jay, 2026.
6	578	0.792957429941	Antoine Jay, 2026.
6	579	0.792999595650	Antoine Jay, 2026.
6	580	0.793048100459	Antoine Jay, 2026.
6	581	0.793297064543	Antoine Jay, 2026.
6	582	0.793378001931	Antoine Jay, 2026.
6	583	0.793426258407	Antoine Jay, 2026.
6	584	0.793644882860	Antoine Jay, 2026.
6	585	0.793826284134	Antoine Jay, 2026.
6	586	0.793925522236	Antoine Jay, 2026.
6	587	0.794011600462	Antoine Jay, 2026.
6	588	0.794184603098	Antoine Jay, 2026.
6	589	0.794304511664	Antoine Jay, 2026.
6	590	0.794400331325	Antoine Jay, 2026.
6	591	0.794611101774	Antoine Jay, 2026.
6	592	0.794704302763	Antoine Jay, 2026.
6	593	0.794862055973	Antoine Jay, 2026.
6	594	0.795063450319	Antoine Jay, 2026.
6	595	0.795149611344	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	598	0.795214049295	Antoine Jay, 2026.
6	599	0.795279530959	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	600	0.795384719249	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	601	0.795848156913	Antoine Jay, 2026.
6	602	0.795880464543	Antoine Jay, 2026.
6	603	0.795970632484	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	604	0.796174337381	Antoine Jay, 2026.
6	605	0.796337832833	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	606	0.796449949429	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	607	0.796600515435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	608	0.796942317012	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	609	0.796999788171	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	610	0.797068314880	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	611	0.797286251178	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	612	0.797488055700	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	613	0.797572416174	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	614	0.797748238330	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	615	0.797877500944	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	616	0.798059569781	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	617	0.798296779110	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	618	0.798447680787	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	619	0.798527819236	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	620	0.798611803397	Antoine Jay, 2026.
6	621	0.798771378224	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	622	0.798810307992	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	623	0.798986487424	Antoine Jay, 2026.
6	624	0.799166944761	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	625	0.799342533166	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	626	0.799541730863	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	627	0.799741192582	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	628	0.799917532763	Antoine Jay, 2026.
6	629	0.800126131330	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	630	0.800271549635	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	631	0.800503458250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	632	0.800684863346	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	633	0.800825798147	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	634	0.800935198945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	635	0.801155650665	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	636	0.801207874837	Antoine Jay, 2026.
6	637	0.801320933976	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	638	0.801422621667	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	639	0.801556122507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	640	0.801684874367	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	641	0.801812014545	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	642	0.801907880665	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	643	0.801933328311	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	644	0.802141430111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	645	0.802286471403	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	646	0.802419206060	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	647	0.802462764587	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	648	0.802608730554	Antoine Jay, 2026.
6	649	0.802691602545	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	650	0.802937826316	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	651	0.803075325564	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	652	0.803103409118	Antoine Jay, 2026.
6	653	0.803243624075	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	654	0.803424548185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	655	0.803554628605	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	656	0.803731069818	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	657	0.803924867735	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	658	0.804140793933	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	659	0.804305456827	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	660	0.804488413289	Antoine Jay, 2026.
6	661	0.804627302940	Antoine Jay, 2026.
6	662	0.804859069413	Antoine Jay, 2026.
6	663	0.805201360216	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	664	0.805415453265	Antoine Jay, 2026.
6	665	0.805596494041	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	666	0.805673355305	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	667	0.805998220397	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	668	0.806169811851	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	669	0.806176853508	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	670	0.806218047308	Antoine Jay, 2026.
6	671	0.806369873715	Antoine Jay, 2026.
6	672	0.806584872182	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	673	0.806677114689	Antoine Jay, 2026.
6	674	0.806879945008	Antoine Jay, 2026.
6	675	0.806996881635	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	676	0.807178308837	Antoine Jay, 2026.
6	677	0.807222968684	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	678	0.807554119396	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	679	0.807563387291	Antoine Jay, 2026.
6	680	0.807623665148	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	681	0.807800016066	Antoine Jay, 2026.
6	682	0.807994899448	Antoine Jay, 2026.
6	683	0.808205937649	Antoine Jay, 2026.
6	684	0.808506167153	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	685	0.808621337180	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	686	0.808816075617	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	687	0.808878964614	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	688	0.808938588478	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	689	0.809238639715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	690	0.809345517549	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	691	0.809581084450	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	692	0.809647402931	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	693	0.809771587562	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	694	0.809946896020	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	695	0.810080041843	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	696	0.810144829559	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	697	0.810290578538	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	698	0.810460665428	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	699	0.810605566367	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	700	0.810692101574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	701	0.810855676002	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	702	0.810954396287	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	703	0.811031139829	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	704	0.811195254369	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	705	0.811281791462	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	706	0.811438601177	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	707	0.811616983456	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	708	0.811723833998	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	709	0.811814242956	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	710	0.811921667767	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	711	0.812037245443	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	712	0.812140249791	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	713	0.812292091980	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	714	0.812406083565	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	715	0.812520138882	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	716	0.812604033058	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	717	0.812665555368	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	718	0.812915169639	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	719	0.813037847193	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	720	0.813107113323	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	721	0.813200160112	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	722	0.813357123592	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	723	0.813460767271	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	724	0.813554996938	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	725	0.813636298843	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	726	0.813714944420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	727	0.813893988664	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	728	0.814026933019	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	729	0.814151945656	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	730	0.814256062877	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	731	0.814346804431	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	732	0.814425012862	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	733	0.814566094123	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	734	0.814642072461	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	735	0.814767088012	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	736	0.814886148743	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	737	0.814974279756	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	738	0.814994882469	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	739	0.815245687094	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	740	0.815267427347	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	741	0.815405808854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	742	0.815528175063	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	743	0.815641997910	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	744	0.815716014680	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	745	0.815816611819	Antoine Jay, 2026.
6	746	0.815871921778	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	747	0.815981644465	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	748	0.816107200150	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	749	0.816261217481	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	750	0.816333187976	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	751	0.816452250979	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	752	0.816500866514	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	753	0.816643178118	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	754	0.816691919070	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	755	0.816822429611	Antoine Jay, 2026.
6	756	0.816918642045	Antoine Jay, 2026.
6	757	0.816943920479	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	758	0.817112809663	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	759	0.817260987330	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	760	0.817284682203	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	761	0.817413891809	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	762	0.817564590678	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	763	0.817574006116	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	764	0.817634509158	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	765	0.817768059736	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	766	0.817932086965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	767	0.817961350000	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	768	0.818111539852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	769	0.818176185237	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	770	0.818285157404	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	771	0.818396279044	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	772	0.818509964885	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	773	0.818573037800	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	774	0.818633055083	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	775	0.818761444861	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	776	0.818896252256	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	777	0.818977661018	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	778	0.819033318274	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	779	0.819142271142	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	780	0.819270918558	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	781	0.819321852578	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	782	0.819431586624	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	783	0.819557496732	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	784	0.819600898314	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	785	0.819661089635	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	786	0.819770893935	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	787	0.819858132646	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	788	0.819996683935	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	789	0.820051861919	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	790	0.820151224756	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	791	0.820228060507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	792	0.820381270645	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	793	0.820425511148	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	794	0.820472036263	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	795	0.820619729071	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	796	0.820673103374	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	797	0.820796364523	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	798	0.820842592969	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	799	0.820989534246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	800	0.821071062292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	801	0.821182301183	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	802	0.821257992670	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	803	0.821381077585	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	804	0.821429491689	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	805	0.821522417668	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	806	0.821642129090	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	807	0.821652424879	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	808	0.821771495894	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	809	0.821924383762	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	810	0.821965134515	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	811	0.822076629684	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	812	0.822144978550	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	813	0.822211273413	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	814	0.822309720257	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	815	0.822398194783	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	816	0.822434216075	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	817	0.822544183573	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	818	0.822693927779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	819	0.822756057753	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	820	0.822832632680	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	821	0.822904692390	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	822	0.823022629546	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	823	0.823082684445	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	824	0.823209093735	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	825	0.823245505148	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	826	0.823379494096	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	827	0.823451967845	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	828	0.823558334237	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	829	0.823646013974	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	830	0.823705072483	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	831	0.823839426208	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	832	0.823872846643	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	833	0.823946876121	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	834	0.824058367383	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	835	0.824127752701	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	836	0.824274120207	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	837	0.824295727068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	838	0.824405889222	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	839	0.824487551579	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	840	0.824518453310	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	841	0.824644721238	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	842	0.824717901241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	843	0.824833287748	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	844	0.824860500092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	845	0.824965037325	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	846	0.825084210816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	847	0.825091531758	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	848	0.825230465562	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	849	0.825333714496	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	850	0.825364057528	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	851	0.825474396749	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	852	0.825518791830	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	853	0.825626847835	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	854	0.825729134902	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	855	0.825833428340	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	856	0.825875293523	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	857	0.825941730353	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	858	0.826013581305	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	859	0.826114266375	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	860	0.826224994865	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	861	0.826312160230	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	862	0.826388189157	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	863	0.826484828487	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	864	0.826537238606	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	865	0.826647225251	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	866	0.826660742540	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	867	0.826786811923	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	868	0.826854346401	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	869	0.826951945251	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	870	0.826963222376	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	871	0.827120440576	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	872	0.827134400996	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	873	0.827240988854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	874	0.827356906786	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	875	0.827394065666	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	876	0.827501439343	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	877	0.827530172242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	878	0.827665288502	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	879	0.827808602149	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	880	0.827850915944	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	881	0.827923078847	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	882	0.827966221837	Pavlos Moros, 2026.
6	883	0.828008289641	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	884	0.828078675981	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	885	0.828202848068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	886	0.828255021731	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	887	0.828389104823	Pavlos Moros, 2026.
6	888	0.828436753574	Pavlos Moros, 2026.
6	889	0.828526651052	Pavlos Moros, 2026.
6	890	0.828578965951	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	891	0.828602895833	Pavlos Moros, 2026.
6	892	0.828665651392	Pavlos Moros, 2026.
6	893	0.828765347931	Pavlos Moros, 2026.
6	894	0.828846080283	Pavlos Moros, 2026.
6	895	0.828846667958	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	896	0.828930995912	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	897	0.828954552452	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	898	0.829055751840	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	899	0.829056306351	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	900	0.829101558627	Christopher Smolen, 2026.
6	901	0.829216244350	Christopher Smolen, 2026.
6	902	0.829319304572	Christopher Smolen, 2026.
6	903	0.829428657314	Christopher Smolen, 2026.
6	904	0.829513183070	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	905	0.829600624883	Christopher Smolen, 2026.
6	906	0.829647014502	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	907	0.829693870128	Antoine Jay, 2026.
6	908	0.829773742432	Pavlos Moros, 2026.
6	909	0.829861189564	Christopher Smolen, 2026.
6	910	0.829937459048	Vadim Borisov, 2026.
6	911	0.829945585160	Christopher Smolen, 2026.
6	912	0.830004405653	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	913	0.830065101160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	914	0.830150439044	Christopher Smolen, 2026.
6	918	0.830427350388	Vadim Borisov, 2026.
6	919	0.830427368725	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	920	0.830598514090	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	921	0.830617552878	Vadim Borisov, 2026.
6	922	0.830623853407	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	923	0.830652786818	Antoine Jay, 2026.
6	924	0.830743004519	Vadim Borisov, 2026.
6	925	0.830743012113	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	926	0.830839745021	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	927	0.831014992955	Vadim Borisov, 2026.
6	928	0.831019710861	Antoine Jay, 2026.
6	929	0.831165651447	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	930	0.831165707331	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	931	0.831165712574	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	932	0.831186535939	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	933	0.831204693147	Christopher Smolen, 2026.
6	934	0.831288430911	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	935	0.831317779941	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	936	0.831340839755	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	937	0.831400249854	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	938	0.831432871767	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	939	0.831656564642	Vadim Borisov, 2026.
6	940	0.831656566409	Vadim Borisov, 2026.
6	941	0.831656589134	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	942	0.831698377642	Christopher Smolen, 2026.
6	943	0.831768321462	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	944	0.831881718198	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	945	0.831883554184	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	946	0.831904297278	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	947	0.831949732974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	948	0.832008336599	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	949	0.832043794710	Vadim Borisov, 2026.
6	950	0.832053266971	Christopher Smolen, 2026.
6	951	0.832156990624	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	952	0.832190610957	Christopher Smolen, 2026.
6	953	0.832203721404	Christopher Smolen, 2026.
6	954	0.832220841159	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	955	0.832267960633	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	956	0.832306589339	Vadim Borisov, 2026.
6	957	0.832309292663	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	958	0.832320448543	Vadim Borisov, 2026.
6	959	0.832418262383	Christopher Smolen, 2026.
6	960	0.832463969254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	961	0.832480595660	Christopher Smolen, 2026.
6	962	0.832511692402	Christopher Smolen, 2026.
6	963	0.832562099166	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	964	0.832621895218	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	965	0.832694651301	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	966	0.832722635290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	967	0.832753760325	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	968	0.832816108395	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	969	0.832828411236	Vadim Borisov, 2026.
6	970	0.832828423962	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	971	0.832877043888	Vadim Borisov, 2026.
6	972	0.832877652000	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	973	0.832884544089	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	974	0.832900829202	Henry Cohn, 2026.
6	975	0.832990277717	Henry Cohn, 2026.
6	976	0.833001069441	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
6	990	0.833333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $6 x - 5$
6	1009	0.833333333334	Henry Cohn, 2026. $6 x - 5$
6	1010	0.837129847308	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1011	0.837186677658	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1012	0.837254463860	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1013	0.837291352850	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1014	0.837414963630	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1015	0.837470420730	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1016	0.837529178486	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1017	0.837594951247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1018	0.837648862292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1019	0.837700303923	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1020	0.837764989506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1021	0.837788722432	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1022	0.837818275188	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1023	0.837953401152	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
6	1024	0.838042424657	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	15	0.098701776273	P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911 . $175 x^{3} - 49 x^{2} - 7 x + 1$
7	16	0.113320879601	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. Minimal polynomial of degree 12
7	17	0.124841583816	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 48
7	18	0.126131983623	P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911 . $47 x^{2} + 2 x - 1$
7	19	0.156597385418	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $1280 x^{6} - 352 x^{4} - 48 x^{3} + 37 x^{2} + 3 x - 1$
7	20	0.169520847199	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $23 x^{2} + 2 x - 1$
7	21	0.181523960801	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7	22	0.182743997632	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $19 x^{2} + 2 x - 1$
7	23	0.182743997632	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $19 x^{2} + 2 x - 1$
7	24	0.182743997632	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $19 x^{2} + 2 x - 1$
7	25	0.214737233855	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $31 x^{2} - 2 x - 1$
7	26	0.231331430372	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7	27	0.240549382010	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	28	0.247356651208	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	29	0.248893779344	H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	30	0.249468282003	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	31	0.254502767515	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	32	0.265595699432	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	33	0.270023386002	Henry Cohn, 2024.
7	34	0.277696496789	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7	35	0.289773019868	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7	36	0.299959896814	Henry Cohn, 2023.
7	37	0.310451288111	Henry Cohn, 2026.
7	39	0.316279494687	Henry Cohn, 2023. $71 x^{2} + 6 x - 9$
7	40	0.323843153340	Henry Cohn, 2023.
7	41	0.325408592469	Henry Cohn, 2023. $32 x^{4} + 40 x^{3} - 23 x^{2} - 4 x + 2$
7	42	0.329083455200	Henry Cohn, 2025.
7	43	0.329665776133	Henry Cohn, 2023. Minimal polynomial of degree 10
7	44	0.332131779753	Henry Cohn, 2025. Minimal polynomial of degree 18
7	45	0.333226297127	Henry Cohn, 2026.
7	46	0.333312302683	Henry Cohn, 2026.
7	47	0.333332883018	Henry Cohn, 2026.
7	56*	0.333333333334	T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $3 x - 1$
7	57	0.389612708410	Henry Cohn, 2025.
7	58	0.393749423280	Henry Cohn, 2023.
7	59	0.403215732973	Antoine Jay, 2026.
7	60	0.407983464085	Henry Cohn, 2025.
7	61	0.412356098716	Henry Cohn, 2024.
7	62	0.414153717049	Antoine Jay, 2026.
7	63	0.415390831033	Henry Cohn, 2025.
7	64	0.418849672915	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	67	0.421258543571	Henry Cohn, 2024. $622 x^{3} - 771 x^{2} + 288 x - 31$
7	68	0.427531157020	Antoine Jay, 2026.
7	69	0.428294205644	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	70	0.428504478791	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	78	0.428571428572	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $7 x - 3$
7	79	0.452634554829	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	80	0.453887992064	Henry Cohn, 2024. Minimal polynomial of degree 20
7	81	0.458138645597	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	82	0.459673068887	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7	83	0.460413485151	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7	84	0.464981341724	Henry Cohn, 2026.
7	86	0.466580867327	Henry Cohn, 2025. Minimal polynomial of degree 24
7	87	0.469578821552	Henry Cohn, 2024.
7	88	0.471422440239	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. Minimal polynomial of degree 24
7	89	0.474245137129	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	90	0.475294477919	Henry Cohn, 2024.
7	91	0.477365257014	Henry Cohn, 2026.
7	92	0.480026527686	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	93	0.481457104911	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	94	0.482085551042	Antoine Jay, 2026.
7	95	0.482130625709	Henry Cohn, 2026.
7	96	0.482645252556	WolfFrogs, 2026.
7	97	0.486842071201	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7	98	0.489141129031	Henry Cohn, 2026.
7	99	0.493009411323	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7	100	0.494028376036	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	101	0.495013709792	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	102	0.495991491288	Antoine Jay, 2026.
7	103	0.496258128498	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	104	0.496955325144	Antoine Jay, 2026.
7	105	0.497885369812	Antoine Jay, 2026.
7	106	0.498391940490	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	107	0.498832400687	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	108	0.499405316212	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	109	0.499717714402	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	110	0.499849974639	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	111	0.499932087751	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	112	0.499972111374	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	113	0.499995039925	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	114	0.499996154536	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	116	0.499998956582	WolfFrogs, 2026.
7	118	0.499999170726	Arhan Canli, 2026.
7	126	0.5	A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060. $2 x - 1$
7	127	0.509952460664	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7	128	0.513834831907	Henry Cohn, 2026.
7	129	0.517664250674	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	130	0.518780653650	Henry Cohn, 2026.
7	133	0.519144098023	Antoine Jay, 2026.
7	135	0.519150233652	Henry Cohn, 2026.
7	136	0.519153914324	Henry Cohn, 2026.
7	137	0.519751518195	Henry Cohn, 2024.
7	138	0.527218738805	Henry Cohn, 2025.
7	139	0.529887702848	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	140	0.530991424267	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	141	0.530991424267	Antoine Jay, 2026.
7	142	0.531099948463	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	143	0.531315987861	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	144	0.531632269397	Henry Cohn, 2026.
7	145	0.532409979782	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	146	0.532826460410	Henry Cohn, 2026.
7	147	0.533407059487	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	148	0.533990718663	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	149	0.545143756917	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	150	0.545860431511	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	151	0.545860447604	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	152	0.545862514089	Henry Cohn, 2026.
7	154	0.546014546135	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $125 x^{9} + 2745 x^{8} + 492 x^{7} - 2092 x^{6} - 1090 x^{5} + 94 x^{4} + 284 x^{3} + 84 x^{2} - 3 x + 1$
7	155	0.546473120693	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	156	0.552231796943	Antoine Jay, 2026.
7	157	0.556018844774	Antoine Jay, 2026.
7	158	0.556023729871	Antoine Jay, 2026.
7	159	0.556652086588	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	160	0.558546515907	Antoine Jay, 2026.
7	161	0.558829148420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	162	0.559629485760	Henry Cohn, 2026.
7	163	0.561105723898	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	164	0.561391411974	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	167	0.561660415728	Antoine Jay, 2026.
7	168	0.561688600449	Henry Cohn, 2026. Minimal polynomial of degree 14
7	169	0.562559500091	Antoine Jay, 2026.
7	170	0.563543243883	Antoine Jay, 2026.
7	171	0.568285910825	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	172	0.569452222651	Antoine Jay, 2026.
7	173	0.569639238450	Arhan Canli, 2026.
7	174	0.569781795200	Henry Cohn, 2026.
7	176	0.569781851274	Henry Cohn, 2026.
7	177	0.570051314136	Arhan Canli, 2026.
7	178	0.570228182541	Arhan Canli, 2026.
7	180	0.570547900651	Henry Cohn, 2026.
7	181	0.573146186213	Antoine Jay, 2026. $1250 x^{8} - 725 x^{6} - 300 x^{4} - 38 x^{2} + 56$
7	182	0.577350269190	J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257–283, https://projecteuclid.org/euclid.em/1259158465. $3 x^{2} - 1$
7	183	0.586173768929	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	184	0.588182552503	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	200	0.590112298788	Henry Cohn, 2026. $19 x^{3} - 9 x^{2} - 3 x + 1$
7	201	0.594532548165	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	202	0.597686313216	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	203	0.600128337465	WolfFrogs, 2026.
7	204	0.601295600571	Arhan Canli, 2026.
7	205	0.602323919885	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	206	0.603051862435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	207	0.603762887635	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	208	0.606261907358	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	209	0.608036706858	Antoine Jay, 2026.
7	210	0.609447176471	WolfFrogs, 2026.
7	211	0.610334158251	WolfFrogs, 2026.
7	212	0.611946130573	Arhan Canli, 2026.
7	213	0.612666339789	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	214	0.613274598742	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	215	0.614263289089	Arhan Canli, 2026.
7	216	0.615145318474	Antoine Jay, 2026.
7	218	0.615558395315	Arhan Canli, 2026.
7	219	0.616171211557	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	220	0.616451724731	Antoine Jay, 2026.
7	221	0.617163694522	Antoine Jay, 2026.
7	222	0.618012390898	Arhan Canli, 2026.
7	223	0.618284197574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	224	0.619243319556	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	225	0.620191854122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	226	0.620889427903	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	227	0.621439811393	Antoine Jay, 2026.
7	228	0.622024230260	Arhan Canli, 2026.
7	229	0.622561631061	Antoine Jay, 2026.
7	230	0.622993876790	Antoine Jay, 2026.
7	231	0.623882858473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	232	0.624570556024	Henry Cohn, 2026.
7	233	0.625727779808	Antoine Jay, 2026.
7	234	0.626359207806	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	235	0.627077768940	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	236	0.628050135197	Antoine Jay, 2026.
7	237	0.628131254764	Antoine Jay, 2026.
7	238	0.628611885934	Antoine Jay, 2026.
7	239	0.629364200821	Antoine Jay, 2026.
7	240	0.630428718354	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	241	0.630891221156	Antoine Jay, 2026.
7	242	0.631186177913	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	243	0.631580976420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	245	0.631778693936	Antoine Jay, 2026.
7	246	0.632224280854	Antoine Jay, 2026.
7	247	0.632968634560	Antoine Jay, 2026.
7	248	0.633266711590	Antoine Jay, 2026.
7	249	0.633876057249	Antoine Jay, 2026.
7	250	0.634415867203	Antoine Jay, 2026.
7	251	0.635053851576	Antoine Jay, 2026.
7	252	0.635379252074	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	253	0.635644803694	Antoine Jay, 2026.
7	254	0.635754838476	Antoine Jay, 2026.
7	255	0.636304059783	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	256	0.636676560404	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	257	0.637091507336	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	258	0.637930699137	Antoine Jay, 2026.
7	259	0.638288180449	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	260	0.639089833203	Antoine Jay, 2026.
7	261	0.639465915604	Antoine Jay, 2026.
7	262	0.639832628239	Antoine Jay, 2026.
7	263	0.640295643827	Antoine Jay, 2026.
7	264	0.640801027795	Antoine Jay, 2026.
7	265	0.641155023975	Antoine Jay, 2026.
7	266	0.643687803365	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	267	0.643761014902	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	271	0.644120872095	Antoine Jay, 2026.
7	272	0.644790012804	Antoine Jay, 2026.
7	273	0.644895637610	Antoine Jay, 2026.
7	274	0.646175517168	Antoine Jay, 2026.
7	275	0.646964968453	Antoine Jay, 2026.
7	276	0.647123386608	Antoine Jay, 2026.
7	277	0.647672489959	Antoine Jay, 2026.
7	278	0.648140979120	Antoine Jay, 2026.
7	279	0.648732213539	Antoine Jay, 2026.
7	280	0.649489331123	Antoine Jay, 2026.
7	281	0.649718851223	Antoine Jay, 2026.
7	282	0.650142078253	Antoine Jay, 2026.
7	283	0.650748170168	Antoine Jay, 2026.
7	284	0.651344901983	Antoine Jay, 2026.
7	285	0.651498039493	Antoine Jay, 2026.
7	286	0.652086977371	Antoine Jay, 2026.
7	287	0.652346156144	Antoine Jay, 2026.
7	288	0.652721459444	Antoine Jay, 2026.
7	289	0.652943714635	Antoine Jay, 2026.
7	290	0.653288673755	Antoine Jay, 2026.
7	291	0.654468901079	Antoine Jay, 2026.
7	292	0.654634938996	Antoine Jay, 2026.
7	293	0.654855419158	Antoine Jay, 2026.
7	294	0.655295796272	Antoine Jay, 2026.
7	296	0.655635774062	Antoine Jay, 2026.
7	297	0.656075766601	Antoine Jay, 2026.
7	298	0.656587490507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	299	0.657090728606	Antoine Jay, 2026.
7	300	0.657826100085	Vadim Borisov, 2026.
7	301	0.657826134205	Antoine Jay, 2026.
7	302	0.658216750327	Antoine Jay, 2026.
7	303	0.658715797411	Antoine Jay, 2026.
7	304	0.659038256179	Antoine Jay, 2026.
7	306	0.659705318211	Antoine Jay, 2026.
7	307	0.660073046898	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
7	308	0.660592381030	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	309	0.660643264685	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	310	0.660669781815	Arhan Canli, 2026.
7	311	0.661014039051	WolfFrogs, 2026.
7	312	0.661577993559	Arhan Canli, 2026.
7	313	0.661907945780	Arhan Canli, 2026.
7	314	0.662230565911	Arhan Canli, 2026.
7	315	0.662416986720	Arhan Canli, 2026.
7	316	0.663252532119	Arhan Canli, 2026.
7	317	0.663576019938	Arhan Canli, 2026.
7	318	0.663794569192	Arhan Canli, 2026.
7	319	0.664145879861	Antoine Jay, 2026.
7	320	0.664199615726	Antoine Jay, 2026.
7	321	0.664752832524	Antoine Jay, 2026.
7	322	0.664892795059	Arhan Canli, 2026.
7	323	0.664998796049	Arhan Canli, 2026.
7	324	0.665072265371	WolfFrogs, 2026.
7	325	0.665470360375	Arhan Canli, 2026.
7	326	0.665513256459	Antoine Jay, 2026.
7	327	0.665675780744	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	328	0.665684209414	WolfFrogs, 2026.
7	329	0.665737853366	WolfFrogs, 2026.
7	330	0.665782435346	Vadim Borisov, 2026.
7	331	0.665782682691	Antoine Jay, 2026.
7	332	0.665951399591	Antoine Jay, 2026.
7	333	0.666009092842	WolfFrogs, 2026.
7	334	0.666148340822	Christopher Smolen, 2026.
7	335	0.666203113851	WolfFrogs, 2026.
7	336	0.666666222154	Vadim Borisov, 2026.
7	337	0.666666227468	Antoine Jay, 2026.
7	358	0.666666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 2$
7	359	0.668169153059	WolfFrogs, 2026.
7	360	0.668706906376	WolfFrogs, 2026.
7	361	0.668937174268	Antoine Jay, 2026.
7	362	0.668965354362	Henry Cohn, 2026.
7	364	0.668971516703	Antoine Jay, 2026.
7	365	0.670467152674	Antoine Jay, 2026.
7	366	0.670923693486	Arhan Canli, 2026.
7	367	0.671084097317	Antoine Jay, 2026.
7	368	0.671586876700	Antoine Jay, 2026.
7	369	0.671829787739	Antoine Jay, 2026.
7	370	0.672135805879	Antoine Jay, 2026.
7	371	0.672555027738	Antoine Jay, 2026.
7	372	0.673507128878	Antoine Jay, 2026.
7	373	0.673779632822	Antoine Jay, 2026.
7	374	0.673857129010	Antoine Jay, 2026.
7	375	0.674093217128	Antoine Jay, 2026.
7	376	0.674332426331	Antoine Jay, 2026.
7	377	0.674541801131	Antoine Jay, 2026.
7	378	0.674776517556	Antoine Jay, 2026.
7	379	0.675004160239	Antoine Jay, 2026.
7	380	0.675368079332	Antoine Jay, 2026.
7	381	0.675633572057	Antoine Jay, 2026.
7	382	0.675923934478	Antoine Jay, 2026.
7	383	0.676302941347	Antoine Jay, 2026.
7	384	0.676436787067	Antoine Jay, 2026.
7	385	0.676680374220	Antoine Jay, 2026.
7	386	0.676938432216	Antoine Jay, 2026.
7	387	0.677132909131	Antoine Jay, 2026.
7	388	0.677327458258	Antoine Jay, 2026.
7	389	0.677545591825	Antoine Jay, 2026.
7	390	0.677890255494	Antoine Jay, 2026.
7	391	0.678032924803	Antoine Jay, 2026.
7	392	0.678149175355	Antoine Jay, 2026.
7	393	0.678377570158	Arhan Canli, 2026.
7	394	0.678828792738	Antoine Jay, 2026.
7	395	0.679193677214	Arhan Canli, 2026.
7	396	0.679739235767	Antoine Jay, 2026.
7	397	0.679966035442	Christopher Smolen, 2026.
7	398	0.680331853255	Arhan Canli, 2026.
7	399	0.680373521377	WolfFrogs, 2026.
7	400	0.680517571661	Christopher Smolen, 2026.
7	401	0.680728002834	Arhan Canli, 2026.
7	402	0.680786878514	Arhan Canli, 2026.
7	403	0.681085306212	Arhan Canli, 2026.
7	404	0.681327740992	Arhan Canli, 2026.
7	405	0.681562567161	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	406	0.681708358203	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	407	0.681906056086	Arhan Canli, 2026.
7	408	0.681998263953	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	409	0.682138872009	Arhan Canli, 2026.
7	410	0.682233823410	Antoine Jay, 2026.
7	411	0.682336530111	Antoine Jay, 2026.
7	412	0.682447451976	Antoine Jay, 2026.
7	413	0.682567248525	Antoine Jay, 2026.
7	414	0.682676666761	Antoine Jay, 2026.
7	415	0.683063818346	Antoine Jay, 2026.
7	416	0.683358540374	Antoine Jay, 2026.
7	417	0.684332524225	Antoine Jay, 2026.
7	418	0.684462745320	Antoine Jay, 2026.
7	419	0.684656891595	Antoine Jay, 2026.
7	420	0.684893070354	Antoine Jay, 2026.
7	421	0.685689604389	Antoine Jay, 2026.
7	422	0.686119368175	Antoine Jay, 2026.
7	423	0.686438477353	Antoine Jay, 2026.
7	424	0.686630054150	Antoine Jay, 2026.
7	425	0.687319559944	Antoine Jay, 2026.
7	426	0.687540879068	Antoine Jay, 2026.
7	427	0.688418015059	Henry Cohn, 2026.
7	428	0.689122619730	Antoine Jay, 2026.
7	429	0.689748526664	Antoine Jay, 2026.
7	430	0.690379757119	Antoine Jay, 2026.
7	431	0.690761353179	Antoine Jay, 2026.
7	432	0.691410077455	Antoine Jay, 2026.
7	433	0.691858303308	Christopher Smolen, 2026.
7	434	0.692096437972	Antoine Jay, 2026.
7	435	0.692280231777	Antoine Jay, 2026.
7	436	0.692694442865	Antoine Jay, 2026.
7	437	0.693230078226	Antoine Jay, 2026.
7	438	0.693557245515	Antoine Jay, 2026.
7	439	0.694014133560	Antoine Jay, 2026.
7	440	0.694381453679	Antoine Jay, 2026.
7	441	0.694900043692	Antoine Jay, 2026.
7	442	0.695181908302	Antoine Jay, 2026.
7	443	0.695489632094	Antoine Jay, 2026.
7	445	0.696032448661	Antoine Jay, 2026.
7	446	0.696574620743	Antoine Jay, 2026.
7	447	0.697104265387	Antoine Jay, 2026.
7	448	0.697183416001	Henry Cohn, 2026.
7	449	0.697538024407	Antoine Jay, 2026.
7	450	0.697896694931	Antoine Jay, 2026.
7	451	0.698123259730	Antoine Jay, 2026.
7	452	0.698555637390	Antoine Jay, 2026.
7	453	0.698980407400	Antoine Jay, 2026.
7	454	0.699191518132	Antoine Jay, 2026.
7	455	0.699441285078	Antoine Jay, 2026.
7	456	0.700055139542	Antoine Jay, 2026.
7	457	0.700267003468	Antoine Jay, 2026.
7	462	0.700496799415	Antoine Jay, 2026.
7	463	0.700615392503	Antoine Jay, 2026.
7	464	0.700689959911	Arhan Canli, 2026.
7	465	0.700911401529	Antoine Jay, 2026.
7	468	0.700930131160	Antoine Jay, 2026.
7	470	0.701563343617	Antoine Jay, 2026.
7	471	0.702030232491	Antoine Jay, 2026.
7	472	0.702222620549	Antoine Jay, 2026.
7	473	0.702324293004	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	474	0.702350087803	Antoine Jay, 2026.
7	475	0.702429227996	Antoine Jay, 2026.
7	476	0.702452230194	Vadim Borisov, 2026.
7	477	0.702452373684	Antoine Jay, 2026.
7	478	0.702621843018	Antoine Jay, 2026.
7	479	0.702630360435	Antoine Jay, 2026.
7	480	0.702805770382	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
7	481	0.702983201213	Antoine Jay, 2026.
7	482	0.703239205712	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
7	483	0.703553929342	Antoine Jay, 2026.
7	484	0.703619423408	Antoine Jay, 2026.
7	485	0.703656502581	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	486	0.703665951818	Christopher Smolen, 2026.
7	487	0.703707496065	Antoine Jay, 2026.
7	488	0.703779035538	Antoine Jay, 2026.
7	490	0.703801208337	Antoine Jay, 2026.
7	491	0.704146873689	Vadim Borisov, 2026.
7	492	0.704178142253	Antoine Jay, 2026.
7	493	0.704672426429	Henry Cohn, 2026.
7	494	0.705007241771	Antoine Jay, 2026.
7	495	0.705482276421	Antoine Jay, 2026.
7	496	0.706019938169	Antoine Jay, 2026.
7	497	0.706742283417	Antoine Jay, 2026.
7	498	0.707387711636	Antoine Jay, 2026.
7	499	0.709082760946	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	500	0.709219991894	Christopher Smolen, 2026.
7	501	0.709287910519	Antoine Jay, 2026.
7	502	0.709513942287	Arhan Canli, 2026.
7	503	0.709823937484	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	504	0.709863546823	Vadim Borisov, 2026.
7	505	0.709919838493	Vadim Borisov, 2026.
7	506	0.709986481628	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	507	0.709994190700	Christopher Smolen, 2026.
7	508	0.710744030551	Arhan Canli, 2026.
7	509	0.710836309273	Antoine Jay, 2026.
7	510	0.711043499812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	511	0.711045129551	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	512	0.711046738151	Christopher Smolen, 2026.
7	513	0.711126854334	Antoine Jay, 2026.
7	514	0.711303979345	Christopher Smolen, 2026.
7	515	0.711633950312	Vadim Borisov, 2026.
7	516	0.711634224585	Vadim Borisov, 2026.
7	517	0.711634247156	Antoine Jay, 2026.
7	518	0.712046029805	Vadim Borisov, 2026.
7	519	0.712089546792	Vadim Borisov, 2026.
7	520	0.712103937895	Christopher Smolen, 2026.
7	521	0.712145428167	Vadim Borisov, 2026.
7	522	0.712145429249	Antoine Jay, 2026.
7	523	0.712550163572	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	524	0.712570106442	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	525	0.712602304753	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	526	0.712956046951	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	527	0.712995682024	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	528	0.713061884933	Christopher Smolen, 2026.
7	529	0.713129041936	Christopher Smolen, 2026.
7	530	0.713281373631	Christopher Smolen, 2026.
7	531	0.713325845148	Christopher Smolen, 2026.
7	532	0.713380333265	Christopher Smolen, 2026.
7	533	0.713420342424	Christopher Smolen, 2026.
7	534	0.713431667725	Christopher Smolen, 2026.
7	535	0.713456351107	Christopher Smolen, 2026.
7	536	0.713479889183	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	537	0.713729969766	Vadim Borisov, 2026.
7	538	0.713731108249	Christopher Smolen, 2026.
7	539	0.713769515080	Christopher Smolen, 2026.
7	540	0.713830907081	Christopher Smolen, 2026.
7	541	0.713859421143	Vadim Borisov, 2026.
7	542	0.713859460712	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	543	0.713940934545	Christopher Smolen, 2026.
7	544	0.714012355358	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	545	0.714033660632	Vadim Borisov, 2026.
7	546	0.714039407452	Christopher Smolen, 2026.
7	547	0.714049066029	Christopher Smolen, 2026.
7	548	0.714080994976	Vadim Borisov, 2026.
7	549	0.714081006211	Christopher Smolen, 2026.
7	550	0.714135163786	Christopher Smolen, 2026.
7	551	0.714145017057	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	632	0.714285714286	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 5$
7	633	0.718297547507	Antoine Jay, 2026.
7	634	0.720000324950	Christopher Smolen, 2026.
7	635	0.721178122386	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	636	0.722117607812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	637	0.722880036919	Christopher Smolen, 2026.
7	638	0.723655454508	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	639	0.724333108957	Antoine Jay, 2026.
7	640	0.724989550022	Antoine Jay, 2026.
7	641	0.725503573961	Antoine Jay, 2026.
7	642	0.726049803543	Christopher Smolen, 2026.
7	643	0.726401613030	Antoine Jay, 2026.
7	644	0.726738816647	Antoine Jay, 2026.
7	645	0.727041221531	Antoine Jay, 2026.
7	646	0.727302059152	Christopher Smolen, 2026.
7	649	0.727457373928	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	650	0.728170557953	Antoine Jay, 2026.
7	651	0.728411895015	Antoine Jay, 2026.
7	652	0.729494834022	Antoine Jay, 2026.
7	653	0.729544493259	Antoine Jay, 2026.
7	654	0.729728465294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	655	0.729930872535	Antoine Jay, 2026.
7	656	0.730552168056	Christopher Smolen, 2026.
7	657	0.730761943477	Antoine Jay, 2026.
7	658	0.730961181141	Christopher Smolen, 2026.
7	659	0.731012193191	Henry Cohn, 2026.
7	660	0.731461143330	Antoine Jay, 2026.
7	662	0.731724797272	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	663	0.732053750318	Antoine Jay, 2026.
7	664	0.732431489161	Antoine Jay, 2026.
7	665	0.732735699641	Antoine Jay, 2026.
7	666	0.733018166654	Antoine Jay, 2026.
7	667	0.733468340467	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	668	0.733620990199	Antoine Jay, 2026.
7	669	0.733946916420	Antoine Jay, 2026.
7	670	0.734170302897	Antoine Jay, 2026.
7	671	0.734263857472	Antoine Jay, 2026.
7	672	0.734595763300	Antoine Jay, 2026.
7	673	0.734999579022	Antoine Jay, 2026.
7	674	0.735113503944	Antoine Jay, 2026.
7	675	0.735324899847	Antoine Jay, 2026.
7	676	0.735569166015	Antoine Jay, 2026.
7	677	0.735823405398	Antoine Jay, 2026.
7	678	0.736072446053	Antoine Jay, 2026.
7	679	0.736271837999	Antoine Jay, 2026.
7	680	0.736571855263	Antoine Jay, 2026.
7	681	0.736834765349	Antoine Jay, 2026.
7	682	0.737073826809	Antoine Jay, 2026.
7	683	0.737345336714	Antoine Jay, 2026.
7	684	0.737422588592	Antoine Jay, 2026.
7	685	0.737751646914	Antoine Jay, 2026.
7	686	0.737901802869	Vadim Borisov, 2026.
7	687	0.737903692982	Antoine Jay, 2026.
7	688	0.737915962403	Vadim Borisov, 2026.
7	689	0.737916478771	Antoine Jay, 2026.
7	690	0.737999335019	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	691	0.738394876853	Vadim Borisov, 2026.
7	692	0.738394917956	Vadim Borisov, 2026.
7	693	0.738395045023	Vadim Borisov, 2026.
7	694	0.738395126661	Vadim Borisov, 2026.
7	695	0.738395127118	Vadim Borisov, 2026.
7	696	0.738395134923	Vadim Borisov, 2026.
7	697	0.738395165408	Vadim Borisov, 2026.
7	698	0.738395187226	Christopher Smolen, 2026.
7	699	0.738442712222	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	700	0.738653994774	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	701	0.739034864597	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	702	0.739244344341	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	703	0.739269500797	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	704	0.739341527981	Vadim Borisov, 2026.
7	705	0.739341530900	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	706	0.739343710226	Vadim Borisov, 2026.
7	707	0.739351490849	Henry Cohn, 2026.
7	708	0.739530861627	Vadim Borisov, 2026.
7	716	0.739530875607	Antoine Jay, 2026.
7	717	0.740143033262	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	718	0.740147954490	Vadim Borisov, 2026.
7	719	0.740703152403	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	720	0.741205868249	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	721	0.741498568672	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	722	0.741498895297	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	723	0.741499301122	Vadim Borisov, 2026.
7	724	0.741499416461	Vadim Borisov, 2026.
7	725	0.741499988721	Vadim Borisov, 2026.
7	726	0.741500462944	Vadim Borisov, 2026.
7	727	0.741500869779	Vadim Borisov, 2026.
7	728	0.741501503442	Vadim Borisov, 2026.
7	729	0.741616292252	Vadim Borisov, 2026.
7	730	0.741616366339	Vadim Borisov, 2026.
7	731	0.741616435012	Vadim Borisov, 2026.
7	733	0.741619636967	Vadim Borisov, 2026.
7	734	0.741620281058	Vadim Borisov, 2026.
7	735	0.741713896286	Vadim Borisov, 2026.
7	736	0.741714418932	Vadim Borisov, 2026.
7	737	0.741715313972	Vadim Borisov, 2026.
7	739	0.741716004153	Vadim Borisov, 2026.
7	740	0.741716370568	Vadim Borisov, 2026.
7	742	0.741722033023	Vadim Borisov, 2026.
7	743	0.741722460537	Vadim Borisov, 2026.
7	744	0.742342578882	Vadim Borisov, 2026.
7	746	0.742487105408	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	747	0.742711624930	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	748	0.743057433395	Vadim Borisov, 2026.
7	749	0.743057441430	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	750	0.743585558057	Christopher Smolen, 2026.
7	792	0.744904412220	Henry Cohn, 2026.
7	793	0.745228241383	Vadim Borisov, 2026.
7	794	0.745727567092	Vadim Borisov, 2026.
7	795	0.747181731750	Vadim Borisov, 2026.
7	796	0.747236359572	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	797	0.747537310095	Vadim Borisov, 2026.
7	798	0.747950686583	Vadim Borisov, 2026.
7	882	0.75	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4 x - 3$
7	883	0.755753466654	Christopher Smolen, 2026.
7	884	0.756979583320	Vadim Borisov, 2026.
7	885	0.757725392198	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	886	0.757912358088	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	887	0.758215445288	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	888	0.758305280060	Vadim Borisov, 2026.
7	889	0.758499202673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	890	0.758574722277	Antoine Jay, 2026.
7	891	0.758647362507	Vadim Borisov, 2026.
7	892	0.758854041113	Vadim Borisov, 2026.
7	893	0.759075424667	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	894	0.759434342514	Vadim Borisov, 2026.
7	895	0.759681895174	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	896	0.759705329831	Vadim Borisov, 2026.
7	897	0.760125152088	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	898	0.760212734793	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	899	0.760245837416	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	900	0.760347612537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	901	0.760553755027	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	902	0.760581853256	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	903	0.760752431022	Vadim Borisov, 2026.
7	904	0.760928389445	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	905	0.760993996091	Vadim Borisov, 2026.
7	906	0.760995159898	Vadim Borisov, 2026.
7	907	0.761098810421	Vadim Borisov, 2026.
7	908	0.761098915026	Vadim Borisov, 2026.
7	909	0.762409655625	Antoine Jay, 2026.
7	910	0.762423848135	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	911	0.762436792734	Vadim Borisov, 2026.
7	912	0.762526072788	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	913	0.762554283556	Antoine Jay, 2026.
7	914	0.762643610036	Vadim Borisov, 2026.
7	915	0.762708230199	Vadim Borisov, 2026.
7	916	0.762801243301	Vadim Borisov, 2026.
7	917	0.762801258583	Vadim Borisov, 2026.
7	918	0.762938043304	Christopher Smolen, 2026.
7	919	0.762954157984	Antoine Jay, 2026.
7	920	0.763220735220	Antoine Jay, 2026.
7	921	0.763279598096	Antoine Jay, 2026.
7	922	0.763311774035	Vadim Borisov, 2026.
7	923	0.763413688963	Vadim Borisov, 2026.
7	924	0.763413719612	Christopher Smolen, 2026.
7	925	0.764026973880	Antoine Jay, 2026.
7	926	0.764151710747	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	927	0.764270182030	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	928	0.764295868873	Vadim Borisov, 2026.
7	929	0.764295920230	Vadim Borisov, 2026.
7	931	0.764354560625	Vadim Borisov, 2026.
7	932	0.764651884776	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	933	0.764754387647	Vadim Borisov, 2026.
7	934	0.765705024161	Vadim Borisov, 2026.
7	936	0.766038510505	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	937	0.766114677976	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	939	0.766136629469	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	940	0.766207734936	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	941	0.766241820667	Vadim Borisov, 2026.
7	942	0.766377630817	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	943	0.766411053165	Vadim Borisov, 2026.
7	944	0.766803803979	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	945	0.766934776556	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	946	0.766989672925	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	947	0.767000130581	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	948	0.767287833401	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	949	0.767356666549	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	953	0.767573795715	Vadim Borisov, 2026.
7	954	0.767894804333	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	956	0.767980766937	Vadim Borisov, 2026.
7	957	0.768364000223	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	958	0.768444139394	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	959	0.768536091356	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	961	0.768538676522	Vadim Borisov, 2026.
7	962	0.768540324784	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	963	0.768717098931	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	964	0.769003705013	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	965	0.769116075978	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	966	0.769348592418	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	967	0.769360711865	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	968	0.769424889764	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	969	0.769454229278	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	970	0.769523205381	Vadim Borisov, 2026.
7	971	0.769525768331	Vadim Borisov, 2026.
7	972	0.769895765307	Vadim Borisov, 2026.
7	973	0.769999259879	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	974	0.770041720539	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	975	0.770118858626	Vadim Borisov, 2026.
7	976	0.770120653128	Christopher Smolen, 2026.
7	977	0.770383485518	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	978	0.770384814310	Vadim Borisov, 2026.
7	979	0.770503446698	Vadim Borisov, 2026.
7	980	0.770785939387	Vadim Borisov, 2026.
7	981	0.770788165283	Vadim Borisov, 2026.
7	982	0.771359263699	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	983	0.771615596385	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	984	0.771976187980	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	986	0.772395343132	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	987	0.772827580580	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	988	0.773128727739	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	989	0.773169759380	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	990	0.773205778072	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	991	0.773228286663	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	992	0.773482692079	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	993	0.773546557323	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	994	0.774100154467	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	996	0.774220955905	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	998	0.774522748552	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	999	0.774552419689	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1001	0.774902058369	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1002	0.774941388750	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1005	0.775378648458	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1006	0.775676170073	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1008	0.775723682850	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1009	0.775788968543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1010	0.775987397991	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1011	0.776032507651	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1012	0.776095570192	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1013	0.776255680650	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1014	0.776383127287	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1015	0.776404924011	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
7	1016	0.776437117827	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1017	0.776560597981	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1018	0.776695494643	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1019	0.776705434795	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1021	0.776780113316	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1022	0.776935152541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1023	0.776997761682	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
7	1024	0.777057460364	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	17	0.087733463324	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $288 x^{3} - 64 x^{2} - 8 x + 1$
8	18	0.099469572709	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
8	19	0.111409975027	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. Minimal polynomial of degree 29
8	20	0.119496866688	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $224 x^{3} + 60 x^{2} - 2 x - 1$
8	21	0.130601937482	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $28 x^{2} + 4 x - 1$
8	22	0.130601937482	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $28 x^{2} + 4 x - 1$
8	23	0.157169941990	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. Minimal polynomial of degree 68
8	24	0.157692144940	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434. $4 x^{4} - 4 x^{3} - 27 x^{2} - 2 x + 1$
8	25	0.164334174126	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 18
8	26	0.172652095036	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 40
8	27	0.179856457059	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 32
8	28	0.181158420022	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $36 x^{4} + 24 x^{3} - 36 x^{2} + 1$
8	29	0.187922490077	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8	30	0.203916279404	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8	31	0.219706528517	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8	32	0.227325452024	H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $95 x^{2} - 4 x - 4$
8	33	0.227325452024	Henry Cohn, 2023. $95 x^{2} - 4 x - 4$
8	34	0.233864616950	Henry Cohn, 2023. $26887680 x^{6} + 11003904 x^{5} - 444096 x^{4} - 594432 x^{3} - 55800 x^{2} - 480 x - 1$
8	35	0.236461100794	Henry Cohn, 2023. $4 x^{4} + 8 x^{3} - 20 x^{2} + 1$
8	38	0.239920745566	Henry Cohn, 2023. $1088 x^{4} - 80 x^{2} + 1$
8	39	0.243600150512	Henry Cohn, 2023. $1183744 x^{8} + 122880 x^{7} - 575488 x^{6} - 138240 x^{5} + 53632 x^{4} + 14976 x^{3} - 1568 x^{2} - 720 x + 81$
8	40	0.265121155593	Henry Cohn, 2025.
8	41	0.269588854450	Henry Cohn, 2025.
8	42	0.276791074187	Henry Cohn, 2023.
8	43	0.285155668748	Henry Cohn, 2025.
8	44	0.288883348745	Henry Cohn, 2026.
8	45	0.293504048474	Henry Cohn, 2025.
8	46	0.298271343353	Henry Cohn, 2025.
8	47	0.301070997037	Henry Cohn, 2025.
8	48	0.306282125496	Antoine Jay, 2026.
8	49	0.310389147843	Antoine Jay, 2026.
8	50	0.314033492890	Henry Cohn, 2026.
8	51	0.316443462389	Henry Cohn, 2026.
8	52	0.317147531407	Henry Cohn, 2025.
8	53	0.323010527708	Henry Cohn, 2025.
8	54	0.326002020004	Henry Cohn, 2025.
8	55	0.328647326389	Henry Cohn, 2025.
8	56	0.330635803908	Henry Cohn, 2024.
8	57	0.332150812596	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	58	0.332676598414	Henry Cohn, 2025.
8	59	0.333047458957	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	60	0.333151357502	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	61	0.333209980467	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	62	0.333256273907	Henry Cohn, 2025.
8	63	0.333327460019	Henry Cohn, 2025.
8	64	0.333333333334	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $3 x - 1$
8	65	0.340292894900	Henry Cohn, 2025.
8	66	0.348587110939	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	67	0.350755730045	Henry Cohn, 2025.
8	68	0.352461904199	Henry Cohn, 2025.
8	71	0.353553390594	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $8 x^{2} - 1$
8	72	0.357142857143	J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645. $14 x - 5$
8	73	0.374351529308	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	74	0.375030122030	Henry Cohn, 2025.
8	75	0.380094852183	Antoine Jay, 2026.
8	76	0.383280469013	Henry Cohn, 2023.
8	77	0.386305789989	Henry Cohn, 2025.
8	78	0.387847284160	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	79	0.394981375552	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	80	0.396538111934	Antoine Jay, 2026.
8	83	0.4	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. $5 x - 2$
8	84	0.401846838467	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	85	0.404581540848	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	86	0.405334578003	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	87	0.409316951820	Antoine Jay, 2026.
8	88	0.414496555473	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	89	0.418879541456	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	90	0.420094879237	WolfFrogs, 2026.
8	91	0.422012113619	Antoine Jay, 2026.
8	92	0.422534257743	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	93	0.423439618648	Henry Cohn, 2026.
8	94	0.425228129624	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	95	0.425941370243	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	96	0.426574471726	Antoine Jay, 2026.
8	97	0.427496184451	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	98	0.428017627035	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	99	0.428528982794	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	100	0.428556416307	Henry Cohn, 2026.
8	101	0.428570622361	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8	114	0.428571428572	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 3$
8	115	0.447549129183	Antoine Jay, 2026.
8	116	0.448006550764	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	117	0.451120240325	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	118	0.455245746618	Henry Cohn, 2026.
8	119	0.458816566687	Arhan Canli, 2026.
8	120	0.459145126780	Arhan Canli, 2026.
8	121	0.460382918560	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	122	0.461371601821	Antoine Jay, 2026.
8	123	0.461840931837	Antoine Jay, 2026.
8	124	0.462008783202	Antoine Jay, 2026.
8	125	0.462338089318	Henry Cohn, 2026.
8	126	0.462515578819	Arhan Canli, 2026.
8	136	0.462585942982	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $68 x^{2} - 12 x - 9$
8	137	0.466198512763	Antoine Jay, 2026.
8	138	0.467414917187	Henry Cohn, 2026.
8	139	0.468626675290	Antoine Jay, 2026.
8	140	0.470739427918	Arhan Canli, 2026.
8	141	0.472435490732	Antoine Jay, 2026.
8	142	0.475908546178	Antoine Jay, 2026.
8	143	0.476461010968	Henry Cohn, 2026.
8	144	0.480908914999	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	145	0.481521469834	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	146	0.482399773434	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	147	0.484209448415	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	148	0.484245716110	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	149	0.486767184379	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	150	0.487648230980	Antoine Jay, 2026.
8	151	0.487887508881	Antoine Jay, 2026.
8	152	0.489724705162	Antoine Jay, 2026.
8	153	0.490234991382	Antoine Jay, 2026.
8	154	0.491215963917	Antoine Jay, 2026.
8	155	0.491623402860	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	156	0.491893127124	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	157	0.491894252940	Antoine Jay, 2026.
8	158	0.492271275301	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	159	0.493760091273	Antoine Jay, 2026.
8	160	0.494564898334	Antoine Jay, 2026.
8	161	0.495153169130	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	162	0.495522495063	Arhan Canli, 2026.
8	163	0.495955193965	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	164	0.496214575647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	165	0.496460499905	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	166	0.496544477279	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	167	0.497664822236	Antoine Jay, 2026.
8	168	0.497868996290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	169	0.498128393575	Arhan Canli, 2026.
8	170	0.498357159483	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	171	0.498524508761	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	172	0.498771778705	Antoine Jay, 2026.
8	173	0.499105256774	Antoine Jay, 2026.
8	174	0.499223817331	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	176	0.499453831360	Antoine Jay, 2026.
8	177	0.499697127938	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	178	0.499766168860	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	179	0.499813915649	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	180	0.499908532950	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	181	0.499916999850	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	182	0.499933245344	Antoine Jay, 2026.
8	183	0.499963528269	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	184	0.499982953032	Arhan Canli, 2026.
8	185	0.499990000854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	186	0.499993235395	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	187	0.499998008149	Christopher Smolen, 2026.
8	189	0.499999552096	Henry Cohn, 2026.
8	190	0.499999999195	Antoine Jay, 2026.
8	240*	0.5	A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8. $2 x - 1$
8	241	0.539498331391	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	242	0.543974310785	Henry Cohn, 2026.
8	243	0.547175986802	Antoine Jay, 2026.
8	244	0.549283805935	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	245	0.551383290811	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	246	0.552666772638	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	247	0.553380715777	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	248	0.554776566902	Antoine Jay, 2026.
8	249	0.557438797449	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	250	0.558859739958	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	251	0.560701675879	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	252	0.560729052434	Christopher Smolen, 2026.
8	253	0.560729053839	Arhan Canli, 2026.
8	254	0.560737725137	Vadim Borisov, 2026.
8	255	0.560737730131	Arhan Canli, 2026.
8	256	0.564484384386	Antoine Jay, 2026.
8	257	0.564818410964	Arhan Canli, 2026.
8	258	0.566489387013	Antoine Jay, 2026.
8	259	0.566839080582	Antoine Jay, 2026.
8	260	0.567249036669	Antoine Jay, 2026.
8	261	0.567682648979	Antoine Jay, 2026.
8	263	0.567756277849	Antoine Jay, 2026.
8	264	0.568290010880	Antoine Jay, 2026.
8	265	0.568803202553	Antoine Jay, 2026.
8	266	0.569804194898	Antoine Jay, 2026.
8	267	0.570187870356	Antoine Jay, 2026.
8	268	0.570751352353	Antoine Jay, 2026.
8	269	0.571527676670	Antoine Jay, 2026.
8	270	0.572158522952	Antoine Jay, 2026.
8	271	0.572919605078	Antoine Jay, 2026.
8	272	0.573552936236	Antoine Jay, 2026.
8	273	0.574551603666	Antoine Jay, 2026.
8	274	0.575634049566	Vadim Borisov, 2026.
8	275	0.575634050725	Arhan Canli, 2026.
8	276	0.576355037527	Antoine Jay, 2026.
8	285	0.577069495831	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	286	0.577244417894	Henry Cohn, 2026.
8	287	0.578063056176	Christopher Smolen, 2026.
8	288	0.578133513088	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	289	0.578729323949	Henry Cohn, 2026.
8	290	0.579469739594	Antoine Jay, 2026.
8	291	0.580564759738	Antoine Jay, 2026.
8	292	0.580921020516	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	293	0.581960380242	Antoine Jay, 2026.
8	294	0.583062827889	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	295	0.584468273991	Antoine Jay, 2026.
8	296	0.585051761322	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	297	0.585701757052	Antoine Jay, 2026.
8	298	0.586012649688	Vadim Borisov, 2026.
8	299	0.586013567336	Vadim Borisov, 2026.
8	300	0.586015921431	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	301	0.586019086073	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	302	0.586019094591	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	303	0.586019264900	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	304	0.586019294083	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	305	0.586019301410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	306	0.586019334774	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	307	0.586019375431	Vadim Borisov, 2026.
8	308	0.586019452027	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	309	0.586031719097	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	310	0.586042114414	Vadim Borisov, 2026.
8	311	0.586042196137	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	312	0.586045966169	Vadim Borisov, 2026.
8	313	0.586045979773	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	316	0.586046598039	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	317	0.586065758543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	318	0.586081635463	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	319	0.586090913838	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	321	0.586117396853	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	324	0.586181180100	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	332	0.586201033835	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. Minimal polynomial of degree 8
8	333	0.587750058926	Antoine Jay, 2026.
8	334	0.592276912366	Antoine Jay, 2026.
8	335	0.594091250683	Antoine Jay, 2026.
8	336	0.594990373996	Antoine Jay, 2026.
8	337	0.596683329460	Henry Cohn, 2026.
8	338	0.597338460895	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	339	0.597567805782	Antoine Jay, 2026.
8	340	0.598040162722	Vadim Borisov, 2026.
8	343	0.598229711333	Antoine Jay, 2026.
8	344	0.598606759649	Antoine Jay, 2026.
8	345	0.599243873684	Antoine Jay, 2026.
8	346	0.599838568056	Christopher Smolen, 2026.
8	347	0.600522495730	Antoine Jay, 2026.
8	348	0.602022939357	Vadim Borisov, 2026.
8	349	0.602573933959	Antoine Jay, 2026.
8	350	0.603155495076	Antoine Jay, 2026.
8	351	0.603785177614	Antoine Jay, 2026.
8	352	0.604000959770	Vadim Borisov, 2026.
8	353	0.604000962529	Christopher Smolen, 2026.
8	354	0.604380902526	Henry Cohn, 2026.
8	355	0.604678407617	Arhan Canli, 2026.
8	356	0.605163953643	Antoine Jay, 2026.
8	357	0.605359310604	Christopher Smolen, 2026.
8	358	0.605440460971	Christopher Smolen, 2026.
8	359	0.606856763681	Antoine Jay, 2026.
8	360	0.606950812844	Christopher Smolen, 2026.
8	361	0.607270330957	Antoine Jay, 2026.
8	362	0.607935818529	Antoine Jay, 2026.
8	363	0.609412057740	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	364	0.609623239851	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	365	0.609798003561	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	366	0.610155653715	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	367	0.610574492723	Antoine Jay, 2026.
8	368	0.611122956334	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	370	0.611574464884	Antoine Jay, 2026.
8	371	0.611961505563	Antoine Jay, 2026.
8	372	0.612284202232	Antoine Jay, 2026.
8	373	0.613536926805	Antoine Jay, 2026.
8	374	0.614813127052	Christopher Smolen, 2026.
8	375	0.616209331887	Antoine Jay, 2026.
8	376	0.616762070471	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	377	0.617429362079	Antoine Jay, 2026.
8	378	0.617470233543	Antoine Jay, 2026.
8	379	0.618230442382	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	380	0.618253881874	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	381	0.618738576218	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	382	0.619301816486	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	383	0.619581794759	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	384	0.619950643740	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	385	0.620517487163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	386	0.621043610473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	387	0.621566781504	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	388	0.621941117548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	389	0.622506097974	Antoine Jay, 2026.
8	390	0.623039029212	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	391	0.623479672770	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	392	0.623825151444	Antoine Jay, 2026.
8	393	0.624130748536	Antoine Jay, 2026.
8	394	0.624422564957	Antoine Jay, 2026.
8	395	0.625006363927	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	396	0.625351446106	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	397	0.625782629245	Arhan Canli, 2026.
8	398	0.626057129501	Antoine Jay, 2026.
8	399	0.626442105756	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	400	0.626774641079	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	401	0.627009670976	Antoine Jay, 2026.
8	402	0.627600786656	Antoine Jay, 2026.
8	403	0.628037351506	Antoine Jay, 2026.
8	404	0.628527286200	Antoine Jay, 2026.
8	405	0.628797988295	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	406	0.629274498338	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	407	0.629593936904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	408	0.629935510796	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	409	0.630319773176	Antoine Jay, 2026.
8	410	0.630479149133	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	411	0.630665367219	Antoine Jay, 2026.
8	412	0.630994525154	Antoine Jay, 2026.
8	413	0.631190198468	Antoine Jay, 2026.
8	414	0.631535495650	Antoine Jay, 2026.
8	415	0.631727415918	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	416	0.632058973439	Antoine Jay, 2026.
8	417	0.632379174754	Antoine Jay, 2026.
8	418	0.632725619608	Antoine Jay, 2026.
8	419	0.633108108139	Antoine Jay, 2026.
8	420	0.633244391233	Antoine Jay, 2026.
8	421	0.633509587191	Antoine Jay, 2026.
8	422	0.633722823936	Antoine Jay, 2026.
8	423	0.633836669871	Antoine Jay, 2026.
8	424	0.634053632816	Antoine Jay, 2026.
8	425	0.634256039005	Antoine Jay, 2026.
8	426	0.634419509119	Antoine Jay, 2026.
8	427	0.634809643967	Antoine Jay, 2026.
8	428	0.634884227236	Antoine Jay, 2026.
8	429	0.635250564616	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
8	430	0.635466453618	Antoine Jay, 2026.
8	431	0.635769390354	Antoine Jay, 2026.
8	432	0.636808633186	Arhan Canli, 2026.
8	433	0.637083856258	Arhan Canli, 2026.
8	435	0.637330339660	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	436	0.637467933743	Christopher Smolen, 2026.
8	438	0.637913335785	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	439	0.637991374733	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	440	0.638046123703	Vadim Borisov, 2026.
8	441	0.638089755005	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	442	0.638118964366	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	443	0.638185305519	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	444	0.638190735088	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	445	0.638245901122	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	446	0.638269482943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	447	0.638297421010	Christopher Smolen, 2026.
8	448	0.638640489436	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	449	0.638774192031	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	450	0.638990200585	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	451	0.639049700405	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	452	0.639075869089	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	453	0.639179069229	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	454	0.639187836828	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	455	0.639250340772	Vadim Borisov, 2026.
8	456	0.639963569677	Arhan Canli, 2026.
8	457	0.640271802905	Vadim Borisov, 2026.
8	458	0.640623143911	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	459	0.640641459056	Christopher Smolen, 2026.
8	460	0.640700049216	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	461	0.640784511478	Christopher Smolen, 2026.
8	462	0.641494129349	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	463	0.641570768771	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	464	0.641628043281	Vadim Borisov, 2026.
8	465	0.641799049208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	466	0.641949262120	Christopher Smolen, 2026.
8	467	0.642685542202	Christopher Smolen, 2026.
8	468	0.642922730840	Christopher Smolen, 2026.
8	469	0.643117946134	Christopher Smolen, 2026.
8	470	0.643280178875	Christopher Smolen, 2026.
8	471	0.643434159932	Christopher Smolen, 2026.
8	472	0.643630165352	Christopher Smolen, 2026.
8	473	0.643692546338	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	474	0.643830573405	Christopher Smolen, 2026.
8	475	0.643911105875	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	476	0.643913276959	Vadim Borisov, 2026.
8	478	0.644135228517	Vadim Borisov, 2026.
8	479	0.644441177792	Christopher Smolen, 2026.
8	480	0.645219051508	Christopher Smolen, 2026.
8	481	0.645328657686	Christopher Smolen, 2026.
8	482	0.645543322179	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	483	0.645580764202	Christopher Smolen, 2026.
8	485	0.646054319200	Antoine Jay, 2026.
8	486	0.646622588377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	487	0.646720252874	Christopher Smolen, 2026.
8	488	0.647006863545	Antoine Jay, 2026.
8	489	0.647076222984	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	490	0.647720462698	Christopher Smolen, 2026.
8	491	0.647787789635	Antoine Jay, 2026.
8	492	0.647982905234	Vadim Borisov, 2026.
8	493	0.647982937872	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	494	0.648556184328	Antoine Jay, 2026.
8	495	0.648982408534	Christopher Smolen, 2026.
8	496	0.649011250987	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	497	0.649037667807	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	498	0.649062631756	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	499	0.649092893869	Christopher Smolen, 2026.
8	500	0.649141303020	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	501	0.649398797989	Antoine Jay, 2026.
8	502	0.649630187043	Antoine Jay, 2026.
8	503	0.649819504261	Christopher Smolen, 2026.
8	504	0.650329335809	Christopher Smolen, 2026.
8	505	0.650399991932	Christopher Smolen, 2026.
8	507	0.650493021014	Antoine Jay, 2026.
8	508	0.650561319408	Christopher Smolen, 2026.
8	509	0.650693284096	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	510	0.650717986183	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	511	0.650737266749	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	512	0.651623887475	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	513	0.651679258299	Christopher Smolen, 2026.
8	514	0.651986205732	Antoine Jay, 2026.
8	515	0.652417217679	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	516	0.652509609537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	517	0.652557914923	Antoine Jay, 2026.
8	518	0.652842202439	Antoine Jay, 2026.
8	519	0.653023813845	Antoine Jay, 2026.
8	520	0.653276562825	Vadim Borisov, 2026.
8	521	0.653276567790	Christopher Smolen, 2026.
8	522	0.653354781955	Antoine Jay, 2026.
8	523	0.653765124151	Antoine Jay, 2026.
8	524	0.653942974234	Antoine Jay, 2026.
8	525	0.654181870782	Christopher Smolen, 2026.
8	526	0.654395364566	Christopher Smolen, 2026.
8	527	0.654610463827	Vadim Borisov, 2026.
8	528	0.654701067155	Christopher Smolen, 2026.
8	529	0.655015633193	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	530	0.655233352604	Christopher Smolen, 2026.
8	531	0.655714019345	Christopher Smolen, 2026.
8	532	0.655742049438	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	533	0.655938149151	Christopher Smolen, 2026.
8	534	0.656154669294	Christopher Smolen, 2026.
8	535	0.656434923787	Christopher Smolen, 2026.
8	536	0.656701550865	Christopher Smolen, 2026.
8	537	0.656911198249	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	538	0.657092427742	Christopher Smolen, 2026.
8	539	0.657505906117	Christopher Smolen, 2026.
8	540	0.657684331932	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	541	0.657784529141	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	542	0.658020201164	Christopher Smolen, 2026.
8	543	0.658309294624	Christopher Smolen, 2026.
8	544	0.658635082302	Christopher Smolen, 2026.
8	545	0.658859417323	Christopher Smolen, 2026.
8	546	0.658991333604	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	547	0.659327240495	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	548	0.659529681174	Christopher Smolen, 2026.
8	549	0.659608890542	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	550	0.659624104091	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	551	0.659962321245	Christopher Smolen, 2026.
8	552	0.660486969375	Christopher Smolen, 2026.
8	553	0.660618277699	Christopher Smolen, 2026.
8	554	0.660756363204	Christopher Smolen, 2026.
8	555	0.660856453106	Christopher Smolen, 2026.
8	556	0.661108461536	Christopher Smolen, 2026.
8	557	0.661254269177	Christopher Smolen, 2026.
8	558	0.661399284942	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	559	0.661522781500	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	560	0.661527213633	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	561	0.661532537845	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	562	0.661609684597	Vadim Borisov, 2026.
8	563	0.661609754037	Vadim Borisov, 2026.
8	564	0.661609813393	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	565	0.661970097922	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	566	0.662025626330	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	567	0.662592547554	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	568	0.662651846679	Vadim Borisov, 2026.
8	569	0.662835874924	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	570	0.662851927515	Vadim Borisov, 2026.
8	571	0.662860352172	Antoine Jay, 2026.
8	573	0.663029900343	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	574	0.663126920657	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	575	0.663224028912	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	576	0.663312464912	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	577	0.663374082226	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	578	0.663442763046	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	579	0.663471103393	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	580	0.663489994977	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	581	0.663490033313	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	582	0.663962371643	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	583	0.663981301151	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	584	0.664007232421	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	585	0.664045849880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	587	0.664402835470	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	588	0.664402929431	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	589	0.665059246107	Vadim Borisov, 2026.
8	590	0.665060684908	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	591	0.665067074507	Vadim Borisov, 2026.
8	592	0.665067077711	Vadim Borisov, 2026.
8	594	0.665067077712	Vadim Borisov, 2026.
8	595	0.665067090087	Christopher Smolen, 2026.
8	596	0.665194629121	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	597	0.665259707197	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	598	0.665266293055	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	599	0.665294553072	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	600	0.665316382544	Vadim Borisov, 2026.
8	601	0.665316384060	Vadim Borisov, 2026.
8	602	0.665316405925	Vadim Borisov, 2026.
8	603	0.665316407123	Vadim Borisov, 2026.
8	604	0.665316409611	Vadim Borisov, 2026.
8	605	0.665316411370	Christopher Smolen, 2026.
8	606	0.665346262631	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	607	0.665355688255	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	608	0.665421875731	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	609	0.665435270917	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	610	0.665443591099	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	612	0.665519015208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	613	0.665534094579	Vadim Borisov, 2026.
8	614	0.665534480741	Vadim Borisov, 2026.
8	615	0.665534496433	Christopher Smolen, 2026.
8	616	0.665638507632	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	617	0.665645572998	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	618	0.665690287543	Vadim Borisov, 2026.
8	619	0.665691106470	Vadim Borisov, 2026.
8	620	0.665736769681	Vadim Borisov, 2026.
8	621	0.665738104289	Vadim Borisov, 2026.
8	622	0.665776890706	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	624	0.665780152796	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	625	0.665783252995	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	627	0.665786557873	Vadim Borisov, 2026.
8	628	0.665786630680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	629	0.665853599126	Vadim Borisov, 2026.
8	630	0.665854108547	Vadim Borisov, 2026.
8	631	0.665854994074	Vadim Borisov, 2026.
8	632	0.665855350765	Vadim Borisov, 2026.
8	633	0.665855629966	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	634	0.666069828167	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	635	0.666103203318	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	636	0.666114743880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	637	0.666116012333	Vadim Borisov, 2026.
8	638	0.666122240263	Vadim Borisov, 2026.
8	639	0.666122250774	Vadim Borisov, 2026.
8	640	0.666122435863	Vadim Borisov, 2026.
8	641	0.666122480445	Vadim Borisov, 2026.
8	642	0.666123448088	Vadim Borisov, 2026.
8	643	0.666123501951	Vadim Borisov, 2026.
8	644	0.666228016888	Vadim Borisov, 2026.
8	645	0.666228039582	Vadim Borisov, 2026.
8	646	0.666229620314	Vadim Borisov, 2026.
8	648	0.666229621131	Vadim Borisov, 2026.
8	651	0.666229621328	Vadim Borisov, 2026.
8	652	0.666229621357	Vadim Borisov, 2026.
8	653	0.666229621765	Vadim Borisov, 2026.
8	654	0.666238123809	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	656	0.666526421134	Vadim Borisov, 2026.
8	657	0.666526422687	Vadim Borisov, 2026.
8	658	0.666526436252	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	659	0.666593347898	Christopher Smolen, 2026.
8	660	0.666731543805	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	661	0.666995144805	Vadim Borisov, 2026.
8	662	0.666995148180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	663	0.667873171293	Christopher Smolen, 2026.
8	664	0.668084676255	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	665	0.668298241063	Christopher Smolen, 2026.
8	666	0.668603491169	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	667	0.668688312287	Christopher Smolen, 2026.
8	668	0.668745495302	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	669	0.668759145098	Christopher Smolen, 2026.
8	670	0.669027204560	Christopher Smolen, 2026.
8	671	0.669593442178	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	672	0.669882775059	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	673	0.670144806287	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	674	0.670495427554	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	675	0.670784206614	Christopher Smolen, 2026.
8	676	0.671121084948	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	677	0.671547431775	Christopher Smolen, 2026.
8	678	0.671758891498	Christopher Smolen, 2026.
8	679	0.673146557538	Christopher Smolen, 2026.
8	680	0.673409014619	Christopher Smolen, 2026.
8	681	0.673440497783	Christopher Smolen, 2026.
8	682	0.673471379992	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	683	0.673482526261	Christopher Smolen, 2026.
8	684	0.673537402078	Christopher Smolen, 2026.
8	685	0.674072052242	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	686	0.674211831528	Christopher Smolen, 2026.
8	687	0.674549523085	Christopher Smolen, 2026.
8	688	0.674937721392	Christopher Smolen, 2026.
8	689	0.675169181624	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	690	0.675521706158	Christopher Smolen, 2026.
8	691	0.676025026550	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	692	0.676435064628	Christopher Smolen, 2026.
8	693	0.676907611319	Christopher Smolen, 2026.
8	694	0.677235705837	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	695	0.677449037953	Christopher Smolen, 2026.
8	696	0.677680837333	Christopher Smolen, 2026.
8	697	0.677809216465	Christopher Smolen, 2026.
8	698	0.678216198412	Christopher Smolen, 2026.
8	699	0.678432768876	Vadim Borisov, 2026.
8	700	0.678434728539	Antoine Jay, 2026.
8	701	0.678811737942	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	702	0.678823804095	Antoine Jay, 2026.
8	703	0.679313455048	Antoine Jay, 2026.
8	704	0.679776142062	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	705	0.679807907969	Antoine Jay, 2026.
8	706	0.680360236136	Vadim Borisov, 2026.
8	707	0.680366083300	Antoine Jay, 2026.
8	708	0.680602169848	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	709	0.680917409716	Christopher Smolen, 2026.
8	710	0.681397796503	Christopher Smolen, 2026.
8	711	0.681569070425	Christopher Smolen, 2026.
8	712	0.681660793992	Antoine Jay, 2026.
8	713	0.682062164517	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	715	0.682275865588	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	716	0.682401791695	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	717	0.682652801499	Antoine Jay, 2026.
8	718	0.682923290349	Antoine Jay, 2026.
8	719	0.683535343615	Christopher Smolen, 2026.
8	720	0.683724852272	Christopher Smolen, 2026.
8	721	0.683931939379	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	722	0.684082030535	Christopher Smolen, 2026.
8	723	0.684265710874	Antoine Jay, 2026.
8	724	0.684506285731	Vadim Borisov, 2026.
8	725	0.684507090204	Antoine Jay, 2026.
8	726	0.685032183379	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	727	0.685216273295	Christopher Smolen, 2026.
8	728	0.685493254716	Christopher Smolen, 2026.
8	729	0.685548102644	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	730	0.686121909144	Christopher Smolen, 2026.
8	732	0.686218981399	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	733	0.686219063547	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	734	0.686251254120	Christopher Smolen, 2026.
8	735	0.686572783975	Antoine Jay, 2026.
8	736	0.687497384044	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	737	0.687549945199	Christopher Smolen, 2026.
8	738	0.687682776363	Christopher Smolen, 2026.
8	739	0.687766512931	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	740	0.687920470931	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	741	0.688123065684	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	742	0.688248110710	Christopher Smolen, 2026.
8	743	0.688271750064	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	744	0.688503151963	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	745	0.688524681742	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	746	0.688878863929	Christopher Smolen, 2026.
8	747	0.688930403314	Christopher Smolen, 2026.
8	749	0.688950348565	Vadim Borisov, 2026.
8	750	0.688950364665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	751	0.689459339366	Christopher Smolen, 2026.
8	752	0.689646253130	Vadim Borisov, 2026.
8	753	0.689646256259	Vadim Borisov, 2026.
8	754	0.689646275349	Vadim Borisov, 2026.
8	755	0.689646439926	Vadim Borisov, 2026.
8	756	0.689646441420	Vadim Borisov, 2026.
8	757	0.689874820251	Vadim Borisov, 2026.
8	758	0.689874836760	Vadim Borisov, 2026.
8	759	0.689874837478	Vadim Borisov, 2026.
8	760	0.689874837624	Vadim Borisov, 2026.
8	761	0.689874837781	Vadim Borisov, 2026.
8	762	0.690157950887	Vadim Borisov, 2026.
8	763	0.690166818294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	764	0.690260738837	Vadim Borisov, 2026.
8	765	0.690725857070	Vadim Borisov, 2026.
8	768	0.690855769597	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	769	0.691262065909	Vadim Borisov, 2026.
8	770	0.691262080478	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	771	0.691495179765	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	772	0.691499690258	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	773	0.691518197085	Vadim Borisov, 2026.
8	774	0.691522097771	Vadim Borisov, 2026.
8	775	0.691522105746	Christopher Smolen, 2026.
8	776	0.691755159212	Vadim Borisov, 2026.
8	777	0.692355368126	Vadim Borisov, 2026.
8	778	0.692449410430	Vadim Borisov, 2026.
8	779	0.692454527419	Christopher Smolen, 2026.
8	780	0.692475065786	Vadim Borisov, 2026.
8	781	0.692475134675	Vadim Borisov, 2026.
8	782	0.692475152338	Vadim Borisov, 2026.
8	783	0.692475162587	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	784	0.692778373706	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	786	0.693042492824	Vadim Borisov, 2026.
8	787	0.693042523237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	788	0.693525144010	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	789	0.693544169681	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	790	0.693563813738	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	791	0.693597947952	Christopher Smolen, 2026.
8	792	0.694200510719	Christopher Smolen, 2026.
8	793	0.694321469037	Vadim Borisov, 2026.
8	794	0.694323810368	Vadim Borisov, 2026.
8	795	0.694324516587	Vadim Borisov, 2026.
8	796	0.694326887144	Vadim Borisov, 2026.
8	797	0.694326897378	Vadim Borisov, 2026.
8	798	0.694327005518	Vadim Borisov, 2026.
8	799	0.694684954386	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	800	0.695059775483	Christopher Smolen, 2026.
8	801	0.695303197569	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	802	0.695497949394	Vadim Borisov, 2026.
8	803	0.695497949707	Vadim Borisov, 2026.
8	804	0.695497957455	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	806	0.695957069268	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	807	0.696001496922	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	808	0.696013913714	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	809	0.696029733529	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	810	0.696057729329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	811	0.696305050606	Vadim Borisov, 2026.
8	812	0.696305057403	Christopher Smolen, 2026.
8	813	0.696811226553	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	814	0.697112701952	Vadim Borisov, 2026.
8	815	0.697112806836	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	819	0.697379739060	Vadim Borisov, 2026.
8	820	0.697379753462	Christopher Smolen, 2026.
8	821	0.697663155155	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	822	0.697824733337	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	823	0.697843291360	Vadim Borisov, 2026.
8	824	0.697844441755	Vadim Borisov, 2026.
8	825	0.697844930845	Vadim Borisov, 2026.
8	826	0.697845162036	Vadim Borisov, 2026.
8	827	0.697845162161	Vadim Borisov, 2026.
8	828	0.697845171445	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	829	0.698601276275	Christopher Smolen, 2026.
8	830	0.698635912177	Vadim Borisov, 2026.
8	831	0.698635912899	Vadim Borisov, 2026.
8	832	0.698635913003	Vadim Borisov, 2026.
8	833	0.698850162080	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	834	0.698864356569	Vadim Borisov, 2026.
8	835	0.698865017902	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	836	0.699306446995	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	837	0.699334504829	Christopher Smolen, 2026.
8	838	0.699611080317	Christopher Smolen, 2026.
8	839	0.699629591419	Christopher Smolen, 2026.
8	840	0.699984775268	Christopher Smolen, 2026.
8	841	0.700205705914	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	842	0.700225645875	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	843	0.700228271431	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	844	0.700241093469	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	845	0.700242077156	Vadim Borisov, 2026.
8	846	0.700270281390	Christopher Smolen, 2026.
8	847	0.700533648165	Vadim Borisov, 2026.
8	848	0.700535168708	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	849	0.700623744401	Vadim Borisov, 2026.
8	850	0.700623747548	Christopher Smolen, 2026.
8	851	0.701038857863	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	852	0.701043744422	Christopher Smolen, 2026.
8	853	0.701510128570	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	854	0.701521708807	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	856	0.701835164019	Vadim Borisov, 2026.
8	857	0.701835625589	Vadim Borisov, 2026.
8	858	0.701835628225	Vadim Borisov, 2026.
8	859	0.701835638539	Vadim Borisov, 2026.
8	860	0.701835643057	Vadim Borisov, 2026.
8	861	0.701835644986	Vadim Borisov, 2026.
8	862	0.701835671886	Vadim Borisov, 2026.
8	863	0.701835680968	Christopher Smolen, 2026.
8	864	0.702088529735	Vadim Borisov, 2026.
8	865	0.702088543853	Vadim Borisov, 2026.
8	866	0.702088633340	Vadim Borisov, 2026.
8	867	0.702093252991	Vadim Borisov, 2026.
8	868	0.702093261338	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	869	0.702304523188	Vadim Borisov, 2026.
8	870	0.702304526860	Christopher Smolen, 2026.
8	871	0.702324341877	Vadim Borisov, 2026.
8	872	0.702473212895	Vadim Borisov, 2026.
8	873	0.702552506105	Christopher Smolen, 2026.
8	876	0.703343709504	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	877	0.703430888550	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	879	0.704248377817	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	880	0.704282956914	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	881	0.704286713962	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	882	0.704290610369	Christopher Smolen, 2026.
8	884	0.704472160912	Vadim Borisov, 2026.
8	885	0.704472166089	Christopher Smolen, 2026.
8	887	0.704955234832	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	888	0.704960484401	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	889	0.704962813218	Christopher Smolen, 2026.
8	890	0.705017005225	Vadim Borisov, 2026.
8	891	0.705305870131	Vadim Borisov, 2026.
8	892	0.705306109754	Vadim Borisov, 2026.
8	893	0.705414814315	Vadim Borisov, 2026.
8	894	0.705429854944	Vadim Borisov, 2026.
8	895	0.705443986360	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	896	0.705475598111	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	897	0.705489749195	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	898	0.705500771458	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	899	0.705516265086	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	900	0.705520455237	Vadim Borisov, 2026.
8	901	0.705522442348	Vadim Borisov, 2026.
8	902	0.705522490814	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	903	0.705682169493	Vadim Borisov, 2026.
8	904	0.705689747836	Vadim Borisov, 2026.
8	905	0.705696296350	Vadim Borisov, 2026.
8	906	0.705914114008	Vadim Borisov, 2026.
8	909	0.706380219673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	910	0.706399734949	Christopher Smolen, 2026.
8	911	0.706419521877	Vadim Borisov, 2026.
8	912	0.706431515626	Vadim Borisov, 2026.
8	913	0.706452550889	Vadim Borisov, 2026.
8	914	0.706501596981	Vadim Borisov, 2026.
8	915	0.706832233249	Vadim Borisov, 2026.
8	916	0.706848985399	Vadim Borisov, 2026.
8	917	0.706858045728	Vadim Borisov, 2026.
8	918	0.706968535694	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	919	0.707003003069	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	920	0.707005444458	Vadim Borisov, 2026.
8	921	0.707006538235	Vadim Borisov, 2026.
8	922	0.707006553758	Pavlos Moros, 2026.
8	923	0.707404335731	Vadim Borisov, 2026.
8	924	0.707404343013	Christopher Smolen, 2026.
8	925	0.707529231734	Vadim Borisov, 2026.
8	926	0.707533859492	Vadim Borisov, 2026.
8	927	0.707628181446	Vadim Borisov, 2026.
8	928	0.707823744719	Vadim Borisov, 2026.
8	929	0.707830150672	Vadim Borisov, 2026.
8	930	0.707831407350	Vadim Borisov, 2026.
8	931	0.707831411956	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	932	0.707995545006	Vadim Borisov, 2026.
8	933	0.708009420230	Vadim Borisov, 2026.
8	934	0.708010580542	Vadim Borisov, 2026.
8	935	0.708282367190	Vadim Borisov, 2026.
8	936	0.708296066856	Vadim Borisov, 2026.
8	937	0.708298372717	Vadim Borisov, 2026.
8	938	0.708306503981	Vadim Borisov, 2026.
8	939	0.708728874225	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	940	0.708736072068	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	941	0.708888970766	Vadim Borisov, 2026.
8	942	0.708889209495	Vadim Borisov, 2026.
8	943	0.708913156092	Vadim Borisov, 2026.
8	944	0.708913162809	Christopher Smolen, 2026.
8	945	0.709014653197	Vadim Borisov, 2026.
8	946	0.709084442673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	947	0.709105197749	Vadim Borisov, 2026.
8	948	0.709426042900	Vadim Borisov, 2026.
8	949	0.709445943346	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	950	0.709447666678	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	951	0.709451371151	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	952	0.709500284569	Vadim Borisov, 2026.
8	953	0.709505939764	Vadim Borisov, 2026.
8	954	0.709509417323	Vadim Borisov, 2026.
8	955	0.709838525307	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	956	0.709843336187	Vadim Borisov, 2026.
8	957	0.709843349277	Vadim Borisov, 2026.
8	958	0.709843361054	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	959	0.710127666574	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	960	0.710141274807	Vadim Borisov, 2026.
8	961	0.710152903772	Vadim Borisov, 2026.
8	962	0.710431188904	Vadim Borisov, 2026.
8	963	0.710431210203	Vadim Borisov, 2026.
8	964	0.710431263460	Vadim Borisov, 2026.
8	965	0.710438866461	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	966	0.710672507045	Vadim Borisov, 2026.
8	967	0.710673775085	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	968	0.710675927117	Vadim Borisov, 2026.
8	969	0.710676523150	Vadim Borisov, 2026.
8	970	0.710676537942	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	971	0.710860441056	Vadim Borisov, 2026.
8	972	0.711398699031	Vadim Borisov, 2026.
8	973	0.711409068184	Vadim Borisov, 2026.
8	974	0.711415133594	Vadim Borisov, 2026.
8	975	0.711415181217	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	976	0.711423941715	Vadim Borisov, 2026.
8	977	0.711428811224	Christopher Smolen, 2026.
8	978	0.711457723929	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	979	0.711777836742	Vadim Borisov, 2026.
8	980	0.711777838901	Vadim Borisov, 2026.
8	981	0.711777839842	Vadim Borisov, 2026.
8	982	0.711777839863	Vadim Borisov, 2026.
8	983	0.711777853087	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	984	0.711946926408	Henry Cohn, 2026.
8	985	0.712097353525	Vadim Borisov, 2026.
8	986	0.712097437535	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	987	0.712102805596	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	988	0.712111254707	Henry Cohn, 2026.
8	989	0.712543948811	Vadim Borisov, 2026.
8	990	0.712744268765	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	991	0.712744345666	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	992	0.712773351126	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	993	0.712774058943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	996	0.712776404760	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	998	0.712776563458	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	999	0.712776767812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1000	0.713091866209	Vadim Borisov, 2026.
8	1003	0.713108265641	Vadim Borisov, 2026.
8	1004	0.713108265899	Vadim Borisov, 2026.
8	1005	0.713208276954	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1006	0.713208719783	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1007	0.713213035701	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1008	0.713237900268	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1009	0.713238602288	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1010	0.713245692197	Vadim Borisov, 2026.
8	1011	0.713246128388	Vadim Borisov, 2026.
8	1012	0.713246160225	Vadim Borisov, 2026.
8	1014	0.713246286293	Vadim Borisov, 2026.
8	1015	0.713246368361	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1016	0.713367883880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1017	0.713381720046	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1018	0.713382381143	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1019	0.713398721032	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1020	0.713403461619	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1021	0.713405072657	Vadim Borisov, 2026.
8	1022	0.713405219854	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1023	0.713407908230	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
8	1024	0.713409854554	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	19	0.079067151218	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $441 x^{3} - 81 x^{2} - 9 x + 1$
9	20	0.087067958322	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $63 x^{2} + 6 x - 1$
9	21	0.087067958322	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $63 x^{2} + 6 x - 1$
9	22	0.109015375240	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $662 x^{4} + 23 x^{3} - 67 x^{2} - 3 x + 1$
9	23	0.114272369686	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 16
9	24	0.127138702332	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	25	0.135451570712	H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	26	0.146662063556	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	27	0.149913487586	H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	28	0.150185176423	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	29	0.150221104823	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $31 x^{2} + 2 x - 1$
9	30	0.150221104823	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $31 x^{2} + 2 x - 1$
9	31	0.150221104823	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $31 x^{2} + 2 x - 1$
9	32	0.150221104823	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $31 x^{2} + 2 x - 1$
9	33	0.180525091271	Henry Cohn, 2023.
9	34	0.183408724272	Henry Cohn, 2023.
9	35	0.195176120873	Henry Cohn, 2024.
9	36	0.199856614456	Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
9	37	0.213781170696	Henry Cohn, 2025.
9	38	0.216954638443	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. Minimal polynomial of degree 25
9	39	0.222837046412	Henry Cohn, 2023.
9	40	0.225659998291	Henry Cohn, 2025.
9	42	0.226907255686	Henry Cohn, 2025. $190336 x^{6} + 377632 x^{5} - 322153 x^{4} - 82188 x^{3} + 48762 x^{2} - 972 x - 729$
9	43	0.231201190091	Henry Cohn, 2023.
9	44	0.233554527157	Henry Cohn, 2025. Minimal polynomial of degree 12
9	45	0.238126842799	Antoine Jay, 2026.
9	47	0.238172399483	Henry Cohn, 2023. $335 x^{2} - 42 x - 9$
9	48	0.254741665820	Henry Cohn, 2025.
9	50	0.256477368938	Henry Cohn, 2026. $23 x^{2} - 2 x - 1$
9	51	0.266033138128	Henry Cohn, 2026.
9	52	0.267191024627	Henry Cohn, 2023. $71 x^{2} - 4 x - 4$
9	53	0.269834758170	Henry Cohn, 2023. Minimal polynomial of degree 12
9	54	0.271671378177	Henry Cohn, 2025.
9	56	0.272133267170	Henry Cohn, 2025. Minimal polynomial of degree 16
9	57	0.282916244589	Henry Cohn, 2026.
9	58	0.288070633971	Henry Cohn, 2026.
9	59	0.293417195891	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	60	0.294882506582	Henry Cohn, 2026.
9	61	0.297699008547	Henry Cohn, 2026.
9	62	0.299403415604	Henry Cohn, 2026.
9	63	0.302685227391	Henry Cohn, 2025.
9	64	0.306653313780	Henry Cohn, 2023.
9	65	0.310452472771	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	66	0.312985380433	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	67	0.317743893678	Antoine Jay, 2026.
9	68	0.320443109443	Antoine Jay, 2026.
9	69	0.323069726165	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	70	0.324965150908	Antoine Jay, 2026.
9	71	0.328557229113	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	73	0.328655902767	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	74	0.328659593981	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	75	0.328681603186	Luke Granto, 2026.
9	76	0.329078250903	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
9	77	0.329568132165	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
9	78	0.330101895521	Henry Cohn, 2025.
9	79	0.330918543665	Henry Cohn, 2024.
9	80	0.332702480388	Henry Cohn, 2026.
9	96	0.333333333334	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $3 x - 1$
9	97	0.370544871674	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	98	0.372095090703	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	101	0.375074698542	Henry Cohn, 2025. $3191 x^{4} + 68 x^{3} - 350 x^{2} - 44 x - 1$
9	102	0.378388662601	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9	103	0.378848187681	Antoine Jay, 2026.
9	104	0.378871017908	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	105	0.391186576796	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9	106	0.394927888776	Antoine Jay, 2026.
9	107	0.397603950591	Antoine Jay, 2026.
9	108	0.398682392141	Arhan Canli, 2026.
9	109	0.401754598812	Antoine Jay, 2026.
9	110	0.404779227936	Antoine Jay, 2026.
9	111	0.405584207795	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	112	0.407568931890	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	113	0.408811682611	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	114	0.408819333860	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	116	0.410522833572	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
9	117	0.411581888580	Antoine Jay, 2026.
9	118	0.412636571764	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	119	0.413789580597	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	120	0.415205142822	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	121	0.416594609435	Arhan Canli, 2026.
9	122	0.417512612802	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	123	0.418356132922	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	124	0.419394190201	Antoine Jay, 2026.
9	126	0.419821271705	Antoine Jay, 2026. $11 x^{2} - 7 x + 1$
9	127	0.419965080683	Antoine Jay, 2026.
9	128	0.421421412796	Antoine Jay, 2026.
9	129	0.422312266938	Antoine Jay, 2026.
9	130	0.422315460779	Henry Cohn, 2026.
9	131	0.422454555952	Arhan Canli, 2026.
9	132	0.425587732894	Antoine Jay, 2026.
9	133	0.426733257695	Antoine Jay, 2026.
9	134	0.427514427929	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	135	0.428457405987	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	146	0.428571428572	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $7 x - 3$
9	147	0.436766252768	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	148	0.438918713662	Antoine Jay, 2026.
9	149	0.440849213224	Antoine Jay, 2026.
9	166	0.444444444445	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $9 x - 4$
9	167	0.452966673042	Antoine Jay, 2026.
9	168	0.453507863161	Arhan Canli, 2026.
9	172	0.454545454546	Antoine Jay, 2026. $11 x - 5$
9	173	0.454589124395	Arhan Canli, 2026.
9	174	0.455060433172	Arhan Canli, 2026.
9	175	0.459062585317	Antoine Jay, 2026.
9	176	0.461182575345	Arhan Canli, 2026.
9	177	0.461445028075	Antoine Jay, 2026.
9	178	0.461813080770	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	179	0.462011320848	Arhan Canli, 2026.
9	180	0.462343498571	Arhan Canli, 2026.
9	181	0.462474011934	Arhan Canli, 2026.
9	182	0.462523840723	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	183	0.462573710456	Antoine Jay, 2026.
9	184	0.464694263290	Antoine Jay, 2026.
9	185	0.467101682559	Antoine Jay, 2026.
9	186	0.469750463226	Antoine Jay, 2026.
9	187	0.471163913396	Arhan Canli, 2026.
9	188	0.471569139874	Antoine Jay, 2026.
9	189	0.473519352101	Antoine Jay, 2026.
9	210	0.475156558223	Henry Cohn, 2026. $103 x^{2} - 30 x - 9$
9	211	0.478969377503	Arhan Canli, 2026.
9	212	0.481269171015	Antoine Jay, 2026.
9	213	0.483346952707	Arhan Canli, 2026.
9	214	0.484779093518	Christopher Smolen, 2026.
9	215	0.485362507721	Arhan Canli, 2026.
9	216	0.485914600621	Henry Cohn, 2026.
9	217	0.486662821488	Henry Cohn, 2026.
9	218	0.487621120361	Antoine Jay, 2026.
9	219	0.490589373508	Arhan Canli, 2026.
9	220	0.492383125492	Christopher Smolen, 2026.
9	221	0.492897656164	Antoine Jay, 2026.
9	222	0.494560521638	Arhan Canli, 2026.
9	223	0.494717729895	Antoine Jay, 2026.
9	224	0.495303188575	Antoine Jay, 2026.
9	225	0.496768186005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	226	0.497248609751	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	227	0.497329907714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	228	0.497668059493	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	229	0.497822050259	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	230	0.497884306494	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	231	0.498030322873	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	232	0.498190384169	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	233	0.498493759279	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	234	0.498547983778	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	235	0.498866488005	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	236	0.498935409826	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	237	0.499000324016	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	238	0.499094909724	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	239	0.499157479241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	240	0.499281280424	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	241	0.499390148971	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	242	0.499392591329	Arhan Canli, 2026.
9	243	0.499530108333	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	244	0.499566262550	Christopher Smolen, 2026.
9	245	0.499688902150	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	246	0.499742620019	Antoine Jay, 2026.
9	247	0.499777637952	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	248	0.499798413234	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	249	0.499826016730	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	250	0.499892509880	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	251	0.499899082992	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	252	0.499901611940	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	253	0.499922723941	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	254	0.499934392862	Vadim Borisov, 2026.
9	255	0.499934526076	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	256	0.499938045365	Henry Cohn, 2026.
9	257	0.499938213322	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	258	0.499947959597	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	259	0.499970693213	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	260	0.499975558808	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	261	0.499979962357	Vadim Borisov, 2026.
9	262	0.499979964741	Henry Cohn, 2026.
9	263	0.499982046131	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	265	0.499984234546	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	266	0.499988751859	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	267	0.499990321255	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	268	0.499991646816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	269	0.499992141918	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	270	0.499992265213	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	271	0.499992413282	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	272	0.499992538484	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	274	0.499994077513	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	275	0.499998619132	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	276	0.499998638848	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	277	0.499999276410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	278	0.499999999944	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	279	0.499999999945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	306	0.5	J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937. $2 x - 1$
9	307	0.516998733609	Arhan Canli, 2026.
9	308	0.518883500173	Antoine Jay, 2026.
9	309	0.520113189100	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	310	0.520131186110	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	311	0.521061165935	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	312	0.521138622793	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	313	0.521604167389	Arhan Canli, 2026.
9	314	0.522364305746	Arhan Canli, 2026.
9	315	0.522936969509	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	330	0.523809523810	Henry Cohn and Ilmari Vahteristo (independently), 2026. $21 x - 11$
9	331	0.528370945601	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	332	0.529992384264	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	333	0.532251422791	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	334	0.534202121452	Antoine Jay, 2026.
9	335	0.535442302756	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	336	0.536054419347	Arhan Canli, 2026.
9	337	0.536096812266	Arhan Canli, 2026.
9	338	0.536421637383	Arhan Canli, 2026.
9	339	0.536746247680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	340	0.536981702073	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	341	0.536991409302	Christopher Smolen, 2026.
9	342	0.538471078282	Arhan Canli, 2026.
9	343	0.538568169262	Antoine Jay, 2026.
9	344	0.539815559814	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	345	0.539898077989	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	346	0.541048605859	Arhan Canli, 2026.
9	347	0.541582641311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	348	0.541902199468	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	349	0.542397699647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	350	0.542448425847	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	351	0.542582494960	Arhan Canli, 2026.
9	352	0.542634904659	Vadim Borisov, 2026.
9	353	0.542635734147	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	354	0.543723749384	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	355	0.543726717854	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	356	0.543738833352	Vadim Borisov, 2026.
9	357	0.543738838580	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	358	0.544089283564	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	359	0.544997581138	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	361	0.545053362208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	362	0.545095095129	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	363	0.545150076749	Arhan Canli, 2026.
9	364	0.546402689428	Christopher Smolen, 2026.
9	482	0.546918160679	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x^{2} - 2 x - 1$
9	483	0.555131082959	Christopher Smolen, 2026.
9	484	0.556740572411	Christopher Smolen, 2026.
9	485	0.562156167319	Christopher Smolen, 2026.
9	486	0.565393409851	Christopher Smolen, 2026.
9	487	0.567592308099	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	488	0.569243462794	Christopher Smolen, 2026.
9	489	0.570780508844	Christopher Smolen, 2026.
9	490	0.572421257451	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	491	0.574074345687	Christopher Smolen, 2026.
9	492	0.574927688547	Christopher Smolen, 2026.
9	493	0.576320523998	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	494	0.576747670098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	495	0.578745880248	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	496	0.580065422782	Christopher Smolen, 2026.
9	497	0.580560916050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	498	0.581324246164	Christopher Smolen, 2026.
9	499	0.582980126505	Christopher Smolen, 2026.
9	500	0.583853808980	Christopher Smolen, 2026.
9	501	0.584635905469	Christopher Smolen, 2026.
9	502	0.585601045874	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	503	0.585791710340	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	504	0.585794473247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	505	0.585809731255	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	506	0.585831045016	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	507	0.585836845057	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	508	0.585846360172	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	509	0.585871704212	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	510	0.585873725647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	511	0.585879120023	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	512	0.585890273696	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	513	0.585903442309	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	514	0.585910086578	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	515	0.585912707852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	516	0.585915569474	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	517	0.585915629883	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	518	0.585917737662	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	519	0.585952208146	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	520	0.585952996988	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	521	0.585953783311	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	522	0.585955555903	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	523	0.585956608129	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	527	0.585994501812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	528	0.585999209151	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	529	0.586396034650	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	530	0.586651287786	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	531	0.587042905017	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	532	0.587161302985	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	533	0.587300838363	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	534	0.587402231045	Vadim Borisov, 2026.
9	535	0.587402672293	Vadim Borisov, 2026.
9	536	0.587402757227	Christopher Smolen, 2026.
9	537	0.593752762902	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	538	0.594982127800	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	539	0.595253712823	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	540	0.595782813425	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	541	0.596344124440	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	542	0.596457244628	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	543	0.597052860380	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	610	0.6	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 3$
9	612	0.6	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $5 x - 3$
9	613	0.605088099623	Christopher Smolen, 2026.
9	614	0.605480107752	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	615	0.606010404989	Vadim Borisov, 2026.
9	616	0.606264941239	Vadim Borisov, 2026.
9	617	0.607955693059	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	618	0.608312251756	Christopher Smolen, 2026.
9	619	0.608390413630	Vadim Borisov, 2026.
9	620	0.608390440658	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	621	0.609172888776	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	622	0.609768428619	Vadim Borisov, 2026.
9	623	0.610534888498	Vadim Borisov, 2026.
9	624	0.610806384286	Vadim Borisov, 2026.
9	625	0.610851116286	Vadim Borisov, 2026.
9	626	0.611168134638	Vadim Borisov, 2026.
9	627	0.611478164264	Vadim Borisov, 2026.
9	628	0.611716031609	Vadim Borisov, 2026.
9	629	0.611869845483	Vadim Borisov, 2026.
9	630	0.611998895969	Vadim Borisov, 2026.
9	631	0.612208765659	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	632	0.612499476668	Vadim Borisov, 2026.
9	633	0.612606559982	Vadim Borisov, 2026.
9	634	0.612968413088	Vadim Borisov, 2026.
9	635	0.613115206511	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	636	0.613491435150	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	637	0.613679183643	Vadim Borisov, 2026.
9	638	0.613679183819	Vadim Borisov, 2026.
9	639	0.614085140156	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	640	0.614088561101	Vadim Borisov, 2026.
9	641	0.614088562153	Vadim Borisov, 2026.
9	642	0.614672035377	Vadim Borisov, 2026.
9	643	0.614873419734	Vadim Borisov, 2026.
9	644	0.614981707954	Vadim Borisov, 2026.
9	645	0.615280901119	Vadim Borisov, 2026.
9	646	0.615591836549	Vadim Borisov, 2026.
9	647	0.615713861363	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	648	0.615913829355	Vadim Borisov, 2026.
9	649	0.615971902809	Vadim Borisov, 2026.
9	650	0.616557980927	Vadim Borisov, 2026.
9	651	0.616647282542	Vadim Borisov, 2026.
9	722	0.618033988750	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $x^{2} + x - 1$
9	723	0.624150346220	Christopher Smolen, 2026.
9	724	0.626178657850	Vadim Borisov, 2026.
9	725	0.626634773647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	726	0.627498706543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	727	0.627819502882	Vadim Borisov, 2026.
9	728	0.629587376071	Vadim Borisov, 2026.
9	729	0.629677164527	Vadim Borisov, 2026.
9	730	0.629802805105	Vadim Borisov, 2026.
9	731	0.629803127661	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	732	0.630082847048	Vadim Borisov, 2026.
9	733	0.630226639009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	734	0.630322722056	Vadim Borisov, 2026.
9	735	0.632829481925	Vadim Borisov, 2026.
9	736	0.632927103294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	737	0.633028091549	Vadim Borisov, 2026.
9	739	0.633596767314	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	740	0.633644067920	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	741	0.633788139569	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	742	0.633810127577	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	743	0.633824790269	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	744	0.633913457838	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	745	0.633936557165	Vadim Borisov, 2026.
9	746	0.633937952493	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	748	0.633949447153	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	749	0.633953579683	Vadim Borisov, 2026.
9	750	0.633981194819	Vadim Borisov, 2026.
9	751	0.633999492325	Vadim Borisov, 2026.
9	752	0.633999618400	Vadim Borisov, 2026.
9	753	0.634314737881	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	754	0.634349791437	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	755	0.634349836561	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	756	0.634379219830	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	757	0.634379240053	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	758	0.634512088063	Christopher Smolen, 2026.
9	759	0.634848358653	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	760	0.634906820177	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	761	0.634907765364	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	762	0.634945126996	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	765	0.635974976127	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	767	0.636694707849	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	768	0.636750856249	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	769	0.636756472306	Vadim Borisov, 2026.
9	771	0.636756472439	Vadim Borisov, 2026.
9	772	0.636756571932	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	773	0.636887462362	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	774	0.636976580396	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	775	0.637257595592	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	777	0.637970291258	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	778	0.640080870843	Vadim Borisov, 2026.
9	779	0.640104612682	Vadim Borisov, 2026.
9	782	0.640215676368	Vadim Borisov, 2026.
9	783	0.640626760182	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	784	0.640775165540	Vadim Borisov, 2026.
9	785	0.641395080984	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	787	0.641459485252	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	791	0.641583259435	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	792	0.641625138774	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	793	0.641695690257	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	796	0.641708573425	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	797	0.641754771515	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	798	0.641795814822	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	799	0.641842237199	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	800	0.641872539502	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	801	0.641911467105	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	802	0.641992832685	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	803	0.641995165722	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	804	0.642078349425	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	809	0.642098877234	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	810	0.642161058083	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	811	0.642163596803	Vadim Borisov, 2026.
9	812	0.642332336889	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	813	0.642440522613	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	814	0.642466017433	Vadim Borisov, 2026.
9	815	0.642480098647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	816	0.642481857424	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	817	0.642589136541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	818	0.642620529315	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	819	0.644609574384	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	820	0.644716743420	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	821	0.644863808535	Vadim Borisov, 2026.
9	822	0.645250601229	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	824	0.645315603258	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	826	0.645390757520	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	827	0.645413774348	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	828	0.645549492619	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	830	0.645601954399	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	832	0.645838014091	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	834	0.646142577435	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	837	0.646169871737	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	838	0.646884451814	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	842	0.647209556440	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	846	0.647272004310	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	849	0.647392577798	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	850	0.647443307328	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	851	0.647515997718	Vadim Borisov, 2026.
9	852	0.647523534779	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	853	0.647529757944	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	856	0.647564353463	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	857	0.647593569990	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	859	0.647609499635	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	860	0.647657530475	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	861	0.647682014056	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	862	0.647813931439	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	863	0.648067121613	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	864	0.648147755560	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	865	0.648212959057	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	866	0.648251377676	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	867	0.648257225015	Vadim Borisov, 2026.
9	868	0.648453650359	Vadim Borisov, 2026.
9	869	0.648454801630	Vadim Borisov, 2026.
9	870	0.648458144446	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	871	0.648607661933	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	872	0.648615975799	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	873	0.648793834367	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	874	0.648864200025	Vadim Borisov, 2026.
9	875	0.648865584148	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	878	0.648958410424	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	879	0.648988998603	Vadim Borisov, 2026.
9	880	0.648992009128	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	881	0.649141117150	Vadim Borisov, 2026.
9	882	0.649149021052	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	883	0.649346960413	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	884	0.649350808218	Vadim Borisov, 2026.
9	885	0.649354621586	Vadim Borisov, 2026.
9	886	0.649354643692	Vadim Borisov, 2026.
9	887	0.649354826178	Vadim Borisov, 2026.
9	888	0.649355053962	Vadim Borisov, 2026.
9	889	0.649355155500	Vadim Borisov, 2026.
9	890	0.649420622982	Vadim Borisov, 2026.
9	891	0.649420881311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	892	0.649448688749	Vadim Borisov, 2026.
9	893	0.649497769172	Vadim Borisov, 2026.
9	894	0.649816168601	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
9	895	0.649881302977	Vadim Borisov, 2026.
9	896	0.649908740466	Vadim Borisov, 2026.
9	897	0.661562289808	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	898	0.661568360058	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	899	0.661728563180	Henry Cohn, 2026.
9	900	0.661743995751	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	901	0.661974040053	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	902	0.662004358975	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	903	0.662053385469	Henry Cohn, 2026.
9	904	0.662183171626	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	905	0.662275543178	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	906	0.662391753063	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	907	0.662402323288	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	908	0.662583967344	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	909	0.662678023302	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	910	0.662793802367	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	911	0.662876070626	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	912	0.662925413517	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	913	0.663068852408	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	914	0.663188307929	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	915	0.663241591472	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	916	0.663369297068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	917	0.663388419505	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	918	0.663512179338	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	919	0.663660999420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
9	962	0.663713900134	Kevin Li, 2026. $23 x^{6} - 6 x^{5} + 5 x^{4} - 4 x^{3} - 3 x^{2} + 2 x - 1$
9	1008	0.666666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 2$
9	1024	0.666666666667	Subcode of a code of size 1056 from M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $3 x - 2$
10	21	0.072033139843	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $640 x^{3} - 100 x^{2} - 10 x + 1$
10	22	0.083956154719	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	23	0.086853938956	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	24	0.098710133500	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $613376 x^{8} - 228096 x^{7} + 40432 x^{6} + 16416 x^{5} - 8016 x^{4} - 216 x^{3} + 184 x^{2} - 1$
10	25	0.104476374556	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	26	0.104477652124	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	27	0.124212414191	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	28	0.128238684469	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $92 x^{2} - 4 x - 1$
10	29	0.130624314467	H. Cohn, Small spherical and projective codes, data set, updated 2026, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $144 x^{4} + 32 x^{3} - 4 x^{2} - 8 x + 1$
10	30	0.138418790027	H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10	31	0.144114939804	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 64
10	32	0.146959243017	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $279 x^{4} - 420 x^{3} + 102 x^{2} - 1$
10	33	0.150071241046	Henry Cohn, 2025.
10	34	0.150182194868	Henry Cohn, 2026.
10	35	0.157397110567	Henry Cohn, 2025.
10	36	0.164041833761	Henry Cohn, 2023.
10	40	0.166666666667	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $6 x - 1$
10	41	0.176776695297	Henry Cohn, 2023. $32 x^{2} - 1$
10	42	0.196163825125	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	43	0.205622503031	Henry Cohn, 2025.
10	44	0.209171113574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	45	0.210466062581	Antoine Jay, 2026.
10	46	0.210715021825	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10	47	0.210852566011	Antoine Jay, 2026.
10	50	0.210852996458	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $71 x^{2} + 4 x - 4$
10	51	0.216689708737	Henry Cohn, 2025.
10	52	0.230823073590	Henry Cohn, 2026.
10	57	0.231237647788	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $36 x^{2} - 4 x - 1$
10	58	0.25	Henry Cohn, 2024. $4 x - 1$
10	59	0.252499828074	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. $40176 x^{6} + 4320 x^{5} - 10584 x^{4} - 168 x^{3} + 767 x^{2} - 8 x - 16$
10	60	0.252845078510	Henry Cohn, 2026.
10	61	0.255558009804	Henry Cohn, 2026.
10	62	0.257763357141	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10	63	0.257944905339	Henry Cohn, 2025. Minimal polynomial of degree 8
10	64	0.260533298510	Antoine Jay, 2026.
10	65	0.264797426966	Antoine Jay, 2026.
10	66	0.265168946762	Henry Cohn, 2025.
10	67	0.268064425530	Henry Cohn, 2025.
10	68	0.268886163790	Henry Cohn, 2026.
10	69	0.269687676191	Antoine Jay, 2026.
10	70	0.271728058742	Henry Cohn, 2026.
10	71	0.271905044079	Henry Cohn, 2026.
10	72	0.274447908374	Henry Cohn, 2026.
10	73	0.275987133320	Henry Cohn, 2025.
10	74	0.279604372359	Henry Cohn, 2026.
10	75	0.283455182208	Henry Cohn, 2026. Minimal polynomial of degree 8
10	76	0.284096667917	Henry Cohn, 2025.
10	77	0.284910960402	Henry Cohn, 2025.
10	78	0.289669889853	Antoine Jay, 2026.
10	79	0.295238257219	Antoine Jay, 2026.
10	80	0.299100985123	Antoine Jay, 2026.
10	81	0.301745610483	Henry Cohn, 2026.
10	82	0.304366085995	Antoine Jay, 2026.
10	83	0.307848155525	Antoine Jay, 2026.
10	84	0.310837057662	Henry Cohn, 2026.
10	85	0.315089504067	Antoine Jay, 2026.
10	86	0.316188311654	Antoine Jay, 2026.
10	87	0.317758303957	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	88	0.322766080727	Antoine Jay, 2026.
10	89	0.323143582443	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	90	0.323505160908	Antoine Jay, 2026.
10	91	0.324689223896	Antoine Jay, 2026.
10	92	0.325628340435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	93	0.328299445300	Antoine Jay, 2026.
10	94	0.328398279336	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	95	0.328398383008	Antoine Jay, 2026.
10	96	0.329803993465	Antoine Jay, 2026.
10	97	0.330219765464	Antoine Jay, 2026.
10	98	0.330420458580	Antoine Jay, 2026.
10	99	0.330618940334	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	100	0.330883770108	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	101	0.331142368088	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
10	102	0.331363824782	Antoine Jay, 2026.
10	103	0.333089994215	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	104	0.333109323347	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	105	0.333148058507	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
10	106	0.333168294471	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
10	107	0.333226936305	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	108	0.333278942046	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	109	0.335242068676	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	110	0.339290566040	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10	111	0.342116121270	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	112	0.344747256732	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	113	0.347102526263	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10	114	0.348279770876	Antoine Jay, 2026.
10	115	0.352502539478	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	116	0.353505255245	Antoine Jay, 2026.
10	117	0.358038919387	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	118	0.361446407779	Antoine Jay, 2026.
10	119	0.363467862179	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	120	0.364351581372	Antoine Jay, 2026.
10	121	0.364797944321	Antoine Jay, 2026.
10	122	0.365271206835	Antoine Jay, 2026.
10	125	0.365547986900	Antoine Jay, 2026. $1137312 x^{6} - 3083304 x^{5} + 3410228 x^{4} - 1698606 x^{3} + 305901 x^{2} + 22356 x - 9558$
10	126	0.365547986900	Henry Cohn, 2026. $1137312 x^{6} - 3083304 x^{5} + 3410228 x^{4} - 1698606 x^{3} + 305901 x^{2} + 22356 x - 9558$
10	127	0.366035053027	Henry Cohn, 2024.
10	128	0.367843283143	Antoine Jay, 2026.
10	129	0.370349178401	Antoine Jay, 2026.
10	130	0.371141231264	Antoine Jay, 2026.
10	131	0.371260106696	Antoine Jay, 2026.
10	132	0.371406638620	Antoine Jay, 2026.
10	133	0.384759603628	Antoine Jay, 2026.
10	134	0.388521611865	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	135	0.389923825120	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	136	0.391831286660	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	137	0.393925651981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	138	0.395330069318	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	139	0.395372280016	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	140	0.395804301526	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	141	0.395971804801	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	142	0.397677205052	Antoine Jay, 2026.
10	143	0.398049483549	Antoine Jay, 2026.
10	144	0.399344926322	Antoine Jay, 2026.
10	145	0.399756400880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	146	0.399778610726	Antoine Jay, 2026.
10	147	0.400097033068	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	148	0.400395362749	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	149	0.400551634334	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	150	0.400609668652	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	151	0.401079275174	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	152	0.401219650320	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	153	0.401233240790	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	154	0.401251981424	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	155	0.401353161400	Antoine Jay, 2026.
10	156	0.401577328424	Antoine Jay, 2026.
10	158	0.404395727365	Vadim Borisov, 2026.
10	159	0.404396151502	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	160	0.404491998797	Vadim Borisov, 2026.
10	164	0.404528881469	Antoine Jay, 2026.
10	165	0.405355045635	Christopher Smolen, 2026.
10	166	0.406288534163	Antoine Jay, 2026.
10	167	0.407851488983	Antoine Jay, 2026.
10	168	0.410356770027	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	169	0.410362321797	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	170	0.410912822209	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	171	0.410926667116	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	172	0.411156170422	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	173	0.411395711997	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	174	0.411482374360	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $9216 x^{6} - 9216 x^{5} - 9216 x^{4} + 7296 x^{3} - 992 x^{2} - 32 x + 1$
10	175	0.411732471727	Henry Cohn, 2026.
10	176	0.414247447961	Arhan Canli, 2026.
10	177	0.418783592622	Antoine Jay, 2026.
10	178	0.421695081072	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	179	0.423834056466	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	180	0.424022191838	Antoine Jay, 2026.
10	181	0.424299536291	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	182	0.424412918645	Antoine Jay, 2026.
10	183	0.424545403716	Antoine Jay, 2026.
10	184	0.425132348596	Antoine Jay, 2026.
10	185	0.425354315643	Antoine Jay, 2026.
10	186	0.425705045707	Arhan Canli, 2026.
10	187	0.426659806788	Antoine Jay, 2026.
10	188	0.427258027790	Antoine Jay, 2026.
10	189	0.427667817343	Arhan Canli, 2026.
10	194	0.428571428572	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 3$
10	195	0.438240194592	Antoine Jay, 2026.
10	196	0.439898943168	Vadim Borisov, 2026.
10	197	0.439899817767	Antoine Jay, 2026.
10	198	0.440587597527	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	199	0.440607373691	Vadim Borisov, 2026.
10	200	0.440607455328	Vadim Borisov, 2026.
10	201	0.440607509311	Arhan Canli, 2026.
10	202	0.441510498175	Vadim Borisov, 2026.
10	203	0.441510498958	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	205	0.441691379630	Henry Cohn, 2026.
10	206	0.442859555399	Arhan Canli, 2026.
10	212	0.442859607642	Henry Cohn, 2026.
10	213	0.443525528575	Arhan Canli, 2026.
10	214	0.446204624319	Arhan Canli, 2026.
10	215	0.447373814828	Arhan Canli, 2026.
10	216	0.448008566612	Christopher Smolen, 2026.
10	217	0.449229429718	Antoine Jay, 2026.
10	218	0.451824124875	Arhan Canli, 2026.
10	219	0.452627072060	Arhan Canli, 2026.
10	220	0.453149758904	Arhan Canli, 2026.
10	221	0.453270120444	Arhan Canli, 2026.
10	222	0.453446677796	Arhan Canli, 2026.
10	223	0.453615700017	Arhan Canli, 2026.
10	224	0.454217364857	Antoine Jay, 2026.
10	225	0.454254394734	Arhan Canli, 2026.
10	226	0.454436540322	Christopher Smolen, 2026.
10	227	0.454528906518	Antoine Jay, 2026.
10	228	0.454608334598	Arhan Canli, 2026.
10	229	0.454712753206	Arhan Canli, 2026.
10	230	0.455012149960	Antoine Jay, 2026.
10	231	0.455065648771	Antoine Jay, 2026.
10	232	0.455126996267	Antoine Jay, 2026.
10	233	0.455186742348	Arhan Canli, 2026.
10	240	0.455341801262	Henry Cohn, 2026. $18 x^{2} - 6 x - 1$
10	241	0.455994494527	Arhan Canli, 2026.
10	242	0.456033188739	Henry Cohn, 2026.
10	243	0.456199320396	Christopher Smolen, 2026.
10	244	0.456236677857	Arhan Canli, 2026.
10	245	0.457583601875	Arhan Canli, 2026.
10	246	0.458677526741	Arhan Canli, 2026.
10	247	0.462278779130	Henry Cohn, 2026.
10	248	0.463975675380	Antoine Jay, 2026.
10	249	0.464403229265	Arhan Canli, 2026.
10	250	0.464732416249	Arhan Canli, 2026.
10	251	0.465004516699	Arhan Canli, 2026.
10	252	0.465572082037	Arhan Canli, 2026.
10	253	0.466489269025	Antoine Jay, 2026.
10	254	0.467405791649	Antoine Jay, 2026.
10	255	0.469036460737	Arhan Canli, 2026.
10	256	0.470263138804	Arhan Canli, 2026.
10	257	0.470976870857	Christopher Smolen, 2026.
10	258	0.471922951289	Arhan Canli, 2026.
10	259	0.472977684937	Arhan Canli, 2026.
10	260	0.473951000248	Arhan Canli, 2026.
10	261	0.474786945752	Arhan Canli, 2026.
10	262	0.475657537944	Christopher Smolen, 2026.
10	263	0.475795839887	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	264	0.476137523732	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	265	0.476188016935	Vadim Borisov, 2026.
10	266	0.476191606451	Arhan Canli, 2026.
10	267	0.476400849282	Arhan Canli, 2026.
10	268	0.477185637708	Antoine Jay, 2026.
10	269	0.477452037999	Antoine Jay, 2026.
10	270	0.478173947907	Antoine Jay, 2026.
10	271	0.478514487957	Arhan Canli, 2026.
10	272	0.478902671592	Christopher Smolen, 2026.
10	273	0.479192786987	Christopher Smolen, 2026.
10	274	0.479824776701	Christopher Smolen, 2026.
10	275	0.480136212448	Antoine Jay, 2026.
10	276	0.480708124667	Antoine Jay, 2026.
10	277	0.481190313992	Arhan Canli, 2026.
10	278	0.481569617694	Antoine Jay, 2026.
10	279	0.482052878455	Antoine Jay, 2026.
10	280	0.482684021292	Antoine Jay, 2026.
10	281	0.483118720243	Antoine Jay, 2026.
10	282	0.483420542763	Christopher Smolen, 2026.
10	283	0.483461874586	Vadim Borisov, 2026.
10	284	0.483461876345	Christopher Smolen, 2026.
10	285	0.483656983869	Antoine Jay, 2026.
10	286	0.484116614277	Christopher Smolen, 2026.
10	287	0.484350682189	Antoine Jay, 2026.
10	288	0.484685560724	Christopher Smolen, 2026.
10	289	0.484835587314	Christopher Smolen, 2026.
10	290	0.484990551336	Christopher Smolen, 2026.
10	291	0.485249904082	Christopher Smolen, 2026.
10	292	0.485531919845	Christopher Smolen, 2026.
10	293	0.485802752983	Christopher Smolen, 2026.
10	294	0.486045554853	Christopher Smolen, 2026.
10	295	0.486396531465	Christopher Smolen, 2026.
10	296	0.486732042560	Christopher Smolen, 2026.
10	297	0.486926409346	Christopher Smolen, 2026.
10	298	0.487330711049	Antoine Jay, 2026.
10	299	0.487466549441	Antoine Jay, 2026.
10	300	0.487971738796	Christopher Smolen, 2026.
10	301	0.488324511582	Antoine Jay, 2026.
10	302	0.488852788224	Antoine Jay, 2026.
10	304	0.489424240885	Vadim Borisov, 2026.
10	305	0.489526980988	Arhan Canli, 2026.
10	306	0.489792096269	Vadim Borisov, 2026.
10	307	0.490204043113	Arhan Canli, 2026.
10	308	0.490250305127	Arhan Canli, 2026.
10	309	0.490350762682	Arhan Canli, 2026.
10	310	0.490538729803	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	311	0.490969883979	Arhan Canli, 2026.
10	312	0.490997562999	Christopher Smolen, 2026.
10	313	0.491167204712	Arhan Canli, 2026.
10	314	0.491264764427	Arhan Canli, 2026.
10	315	0.491410646684	Arhan Canli, 2026.
10	316	0.491643582790	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	317	0.491674545256	Christopher Smolen, 2026.
10	318	0.492026634657	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	319	0.492083129698	Antoine Jay, 2026.
10	320	0.492271143780	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	321	0.492936229846	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	322	0.492969782476	Antoine Jay, 2026.
10	323	0.493076746689	Arhan Canli, 2026.
10	324	0.493304489471	Arhan Canli, 2026.
10	325	0.493889201149	Christopher Smolen, 2026.
10	326	0.494165484264	Vadim Borisov, 2026.
10	327	0.494165521578	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	328	0.494304277865	Christopher Smolen, 2026.
10	329	0.494912863385	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	330	0.495034973636	Arhan Canli, 2026.
10	331	0.495263497004	Antoine Jay, 2026.
10	332	0.495362702784	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	333	0.495397029799	Vadim Borisov, 2026.
10	334	0.495525839848	Antoine Jay, 2026.
10	335	0.495562158587	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	336	0.495848393588	Antoine Jay, 2026.
10	337	0.496689165124	Christopher Smolen, 2026.
10	338	0.496756067885	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	339	0.496808734905	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	340	0.496899785859	Vadim Borisov, 2026.
10	341	0.496902936229	Vadim Borisov, 2026.
10	342	0.496985715381	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	343	0.497094778389	Christopher Smolen, 2026.
10	344	0.497230912595	Christopher Smolen, 2026.
10	345	0.497355992097	Antoine Jay, 2026.
10	346	0.497714891470	Antoine Jay, 2026.
10	347	0.497788288350	Christopher Smolen, 2026.
10	348	0.497865244837	Christopher Smolen, 2026.
10	349	0.497895906448	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	350	0.497983639140	Christopher Smolen, 2026.
10	351	0.498063391427	Antoine Jay, 2026.
10	352	0.498221016294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	353	0.498228525767	Vadim Borisov, 2026.
10	354	0.498234656744	Christopher Smolen, 2026.
10	355	0.498329999344	Arhan Canli, 2026.
10	356	0.498355446906	Christopher Smolen, 2026.
10	357	0.498438741994	Christopher Smolen, 2026.
10	358	0.498493207876	Christopher Smolen, 2026.
10	359	0.498521155086	Arhan Canli, 2026.
10	360	0.498608138013	Christopher Smolen, 2026.
10	361	0.498769678595	Christopher Smolen, 2026.
10	362	0.498872888059	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	363	0.498899163815	Christopher Smolen, 2026.
10	364	0.498914158892	Christopher Smolen, 2026.
10	365	0.498936320272	Christopher Smolen, 2026.
10	366	0.498957529515	Christopher Smolen, 2026.
10	367	0.498969558379	Christopher Smolen, 2026.
10	368	0.499047955104	Christopher Smolen, 2026.
10	369	0.499062385861	Christopher Smolen, 2026.
10	370	0.499192583279	Christopher Smolen, 2026.
10	371	0.499252640314	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	372	0.499391339333	Christopher Smolen, 2026.
10	373	0.499437514986	Christopher Smolen, 2026.
10	374	0.499452356550	Christopher Smolen, 2026.
10	375	0.499511655927	Christopher Smolen, 2026.
10	376	0.499553642792	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	377	0.499687998825	Christopher Smolen, 2026.
10	378	0.499820676722	Christopher Smolen, 2026.
10	379	0.499857816192	Christopher Smolen, 2026.
10	380	0.499866499927	Christopher Smolen, 2026.
10	381	0.499906550584	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	382	0.499907157134	Christopher Smolen, 2026.
10	383	0.499923757652	Christopher Smolen, 2026.
10	384	0.499932543540	Christopher Smolen, 2026.
10	385	0.499942741253	Christopher Smolen, 2026.
10	386	0.499974231834	Christopher Smolen, 2026.
10	387	0.499978355731	Christopher Smolen, 2026.
10	500	0.5	J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3. $2 x - 1$
10	510	0.5	M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002. $2 x - 1$
10	511	0.526390788653	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	512	0.529226751109	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	513	0.530791842239	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	514	0.532342169412	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	515	0.533873838507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	516	0.535309707239	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	517	0.536566180419	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	518	0.538008600875	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	519	0.539314326209	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	520	0.540212519018	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	521	0.541110873643	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	522	0.541747519623	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	523	0.542893796886	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	524	0.543530156280	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	525	0.544404804597	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	526	0.545088071398	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	527	0.545811198686	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	528	0.546336417769	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	529	0.547268524813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	530	0.547807074620	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	531	0.548352755990	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	532	0.548900249813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	533	0.549455481946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	534	0.550070144415	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	535	0.550553114220	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	536	0.551146534165	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	537	0.551469049981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	538	0.552005402249	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	539	0.552091158183	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	540	0.552665940570	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	541	0.553040247497	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	542	0.553225083058	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	543	0.553671540834	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	544	0.553867027124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	545	0.554442150335	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	546	0.554653922841	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	547	0.555339420427	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
10	596	0.555555555556	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 5$
10	608	0.555555555556	Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 5$
10	609	0.560716409718	Vadim Borisov, 2026.
10	610	0.560729583256	Christopher Smolen, 2026.
10	611	0.560750461267	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	612	0.560785827126	Vadim Borisov, 2026.
10	613	0.560785840971	Vadim Borisov, 2026.
10	614	0.560785871515	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	615	0.561395427240	Christopher Smolen, 2026.
10	616	0.562281297715	Vadim Borisov, 2026.
10	740	0.564577451054	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $92 x^{2} - 36 x - 9$
10	771	0.564577451054	Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $92 x^{2} - 36 x - 9$
10	772	0.564579250102	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	773	0.569690922975	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	774	0.570126264444	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	775	0.570337579719	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	776	0.570742609825	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	777	0.571007490242	Vadim Borisov, 2026.
10	778	0.571599146532	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	779	0.571760553716	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	780	0.572053994551	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	781	0.572443429050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	782	0.572570049865	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	783	0.573458190083	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	784	0.573508781751	Vadim Borisov, 2026.
10	785	0.573703944063	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	786	0.575855556620	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	787	0.575950001664	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	788	0.575987911254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	789	0.576878823379	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	790	0.577887365211	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	791	0.578161828076	Christopher Smolen, 2026.
10	792	0.578327460502	Vadim Borisov, 2026.
10	793	0.578327560537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	794	0.579172305459	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	795	0.579385994474	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	796	0.580106414217	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	797	0.580536182453	Vadim Borisov, 2026.
10	798	0.580620043270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	799	0.581819079943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	800	0.581950392247	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	801	0.582157716377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	802	0.583081634299	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	803	0.583362891569	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	804	0.583559579866	Christopher Smolen, 2026.
10	805	0.583798652199	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	806	0.584221112361	Vadim Borisov, 2026.
10	807	0.584222962525	Vadim Borisov, 2026.
10	808	0.584223081481	Christopher Smolen, 2026.
10	809	0.584762653966	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	810	0.585257752588	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	811	0.585300556194	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	812	0.585398563795	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	813	0.585459809724	Christopher Smolen, 2026.
10	814	0.585582484236	Christopher Smolen, 2026.
10	815	0.585648005098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	816	0.585766111102	Christopher Smolen, 2026.
10	870	0.585786437627	Kevin Li, 2026. $x^{2} - 4 x + 2$
10	903	0.585786437627	Henry Cohn, 2026. $x^{2} - 4 x + 2$
10	904	0.587122113827	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	905	0.587516233230	Vadim Borisov, 2026.
10	906	0.587521098998	Vadim Borisov, 2026.
10	907	0.587692419296	Vadim Borisov, 2026.
10	908	0.588030706686	Vadim Borisov, 2026.
10	909	0.588516672897	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	910	0.588688786812	Vadim Borisov, 2026.
10	911	0.588969062737	Vadim Borisov, 2026.
10	912	0.588998977310	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	913	0.589209920306	Vadim Borisov, 2026.
10	914	0.589302267088	Vadim Borisov, 2026.
10	915	0.589339005615	Vadim Borisov, 2026.
10	916	0.589339073513	Vadim Borisov, 2026.
10	917	0.589402637204	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	918	0.589435172164	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	919	0.589667407779	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	920	0.589703442189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	921	0.589896080294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	922	0.589942229094	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	923	0.590130219348	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	924	0.590200694224	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	925	0.590282520761	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	926	0.590364042375	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	928	0.590411791990	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	929	0.590804750561	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	930	0.590838307259	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	931	0.590978567096	Vadim Borisov, 2026.
10	932	0.590984188925	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	933	0.591080357661	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	934	0.591084213260	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	935	0.591213568388	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	936	0.591227986287	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	937	0.591300453285	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	938	0.591306629001	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	939	0.591384643767	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	940	0.591390818472	Vadim Borisov, 2026.
10	941	0.591478801379	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	942	0.591552453041	Vadim Borisov, 2026.
10	943	0.591561972511	Vadim Borisov, 2026.
10	944	0.591561975569	Vadim Borisov, 2026.
10	945	0.591561994080	Vadim Borisov, 2026.
10	946	0.591676329897	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	947	0.591676510023	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	948	0.591676515543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	949	0.591774162172	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
10	950	0.593185707432	Vadim Borisov, 2026.
10	951	0.593618337771	Vadim Borisov, 2026.
10	952	0.593835271609	Vadim Borisov, 2026.
10	953	0.594102638851	Vadim Borisov, 2026.
10	954	0.594223196793	Christopher Smolen, 2026.
10	955	0.594471298322	Vadim Borisov, 2026.
10	968	0.598871257965	Kevin Li, 2026. $41 x^{4} + 12 x^{3} - 18 x^{2} - 4 x + 1$
10	1024	0.6	Subcode of a code of size 1190 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 3$
11	23	0.066201272532	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $891 x^{3} - 121 x^{2} - 11 x + 1$
11	24	0.077294525867	H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 26
11	25	0.083618757829	H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11	26	0.090957106782	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11	27	0.096579767338	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11	28	0.102062072616	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $96 x^{2} - 1$
11	29	0.108541175054	H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial of degree 32
11	30	0.111111111112	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $9 x - 1$
11	31	0.116882716629	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $1880159 x^{4} + 662980 x^{3} + 23850 x^{2} - 9500 x - 625$
11	32	0.127120178791	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11	33	0.130869404972	Henry Cohn, 2023. $4276703 x^{4} + 1417464 x^{3} - 4824 x^{2} - 23328 x - 1296$
11	35	0.134804262191	Henry Cohn, 2023. $379 x^{2} - 14 x - 5$
11	36	0.135617659465	Henry Cohn, 2023. $34679 x^{4} + 11944 x^{3} + 264 x^{2} - 224 x - 16$
11	37	0.141119306055	Henry Cohn, 2023.
11	40	0.142857142858	H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $7 x - 1$
11	41	0.151608920662	Henry Cohn, 2023. $215 x^{2} - 26 x - 1$
11	42	0.152689377129	Henry Cohn, 2023. $441 x^{4} + 84 x^{3} - 66 x^{2} + 1$
11	43	0.154540745580	Henry Cohn, 2024.
11	44	0.164387348702	Henry Cohn, 2023.
11	45	0.167764862361	Henry Cohn, 2023.
11	46	0.173024920814	Henry Cohn, 2023.
11	47	0.193134292608	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	48	0.198507362836	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	49	0.200478577594	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	50	0.201682182708	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
11	51	0.204957387535	Henry Cohn, 2023. Minimal polynomial of degree 12
11	52	0.207163129386	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	53	0.209178537882	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	54	0.210356284337	Antoine Jay, 2026.
11	55	0.211676319336	Antoine Jay, 2026.
11	56	0.214633932920	Antoine Jay, 2026.
11	61	0.214737233855	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $31 x^{2} - 2 x - 1$
11	68	0.231819094924	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $79 x^{2} - 14 x - 1$
11	69	0.241565014044	Henry Cohn, 2025. Minimal polynomial of degree 16
11	70	0.244726315701	Henry Cohn, 2026. $263 x^{8} - 408 x^{7} + 27724 x^{6} - 10136 x^{5} - 11182 x^{4} + 5880 x^{3} - 932 x^{2} + 56 x - 1$
11	71	0.251063071270	Henry Cohn, 2026.
11	72	0.252505460067	Luke Granto, 2026.
11	73	0.252809003477	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	74	0.253814485528	Henry Cohn, 2026.
11	75	0.255492795341	Antoine Jay, 2026.
11	76	0.255729128120	Antoine Jay, 2026.
11	77	0.258886418676	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	78	0.259645753634	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	79	0.260230531928	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	80	0.261163095118	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11	81	0.261593527993	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11	82	0.263018342364	Antoine Olivier, 2026.
11	83	0.263833259782	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11	84	0.265001083146	Henry Cohn, 2026.
11	85	0.266119803599	Antoine Jay, 2026.
11	90	0.267191024627	Henry Cohn, 2026. $71 x^{2} - 4 x - 4$
11	91	0.273036326608	Henry Cohn, 2026.
11	92	0.280231597465	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	93	0.281331655261	Henry Cohn, 2026.
11	94	0.282309473524	Henry Cohn, 2026.
11	95	0.283341061081	Antoine Jay, 2026.
11	96	0.284656615290	Antoine Jay, 2026.
11	97	0.285667906221	Antoine Jay, 2026.
11	98	0.287338503170	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11	99	0.288535692949	Antoine Jay, 2026.
11	100	0.299763934480	Antoine Jay, 2026.
11	101	0.302822234654	Antoine Jay, 2026.
11	102	0.304425499261	Antoine Jay, 2026.
11	103	0.304540282949	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	104	0.304774622973	Antoine Jay, 2026.
11	105	0.305250484672	Henry Cohn, 2026.
11	106	0.306417420784	Henry Cohn, 2026.
11	107	0.309832969299	Henry Cohn, 2026.
11	108	0.313206839612	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11	109	0.319003125079	Antoine Jay, 2026.
11	110	0.321179598662	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	111	0.322192544229	Arhan Canli, 2026.
11	112	0.322257808620	Arhan Canli, 2026.
11	113	0.322493378151	Antoine Jay, 2026.
11	114	0.322691441984	Arhan Canli, 2026.
11	115	0.322904447309	Arhan Canli, 2026.
11	116	0.323595103174	Antoine Jay, 2026.
11	117	0.324275550293	Antoine Jay, 2026.
11	118	0.324624058219	Antoine Jay, 2026.
11	119	0.324905922020	Antoine Jay, 2026.
11	120	0.325028575040	Antoine Jay, 2026.
11	121	0.325463854372	Antoine Jay, 2026.
11	122	0.325931334499	Antoine Jay, 2026.
11	123	0.327037788617	Antoine Jay, 2026.
11	124	0.327848562883	Antoine Jay, 2026.
11	125	0.328078744834	Antoine Jay, 2026.
11	126	0.331455431898	Antoine Jay, 2026.
11	127	0.332142102590	Antoine Jay, 2026.
11	128	0.332166503541	Arhan Canli, 2026.
11	129	0.332282468190	Antoine Jay, 2026.
11	130	0.332374521039	Antoine Jay, 2026.
11	131	0.332556317289	Antoine Jay, 2026.
11	132	0.333102701122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	136	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
11	156	0.333333333334	M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002. $3 x - 1$
11	157	0.360197440733	Antoine Jay, 2026.
11	158	0.363455231410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	159	0.366462928122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	160	0.369327437577	Antoine Jay, 2026.
11	161	0.371018284341	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	162	0.371543533119	Antoine Jay, 2026.
11	163	0.374234763346	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	166	0.375	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $8 x - 3$
11	167	0.380491995217	Vadim Borisov, 2026.
11	168	0.380604655257	Vadim Borisov, 2026.
11	169	0.380770975935	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	170	0.380890135885	Vadim Borisov, 2026.
11	171	0.380955001683	Christopher Smolen, 2026.
11	172	0.387517047379	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	173	0.387900466619	Antoine Jay, 2026.
11	174	0.389918913044	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	175	0.389978948476	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	176	0.390002696432	Antoine Jay, 2026.
11	177	0.390586852971	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	178	0.391471389777	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	180	0.391575479369	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
11	182	0.391846615013	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	183	0.392207717075	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	184	0.392209462012	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	185	0.393901804287	Antoine Jay, 2026.
11	186	0.394604270711	Antoine Jay, 2026.
11	187	0.395325573915	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	188	0.395366529175	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	189	0.395374693689	Antoine Jay, 2026.
11	190	0.395889540597	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	191	0.395932931287	Arhan Canli, 2026.
11	192	0.396249890713	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	193	0.396290902807	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	194	0.396318236410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	195	0.396954528619	Vadim Borisov, 2026.
11	196	0.396959811413	Arhan Canli, 2026.
11	197	0.397258209194	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	198	0.397653489446	Antoine Jay, 2026.
11	199	0.397997843261	Antoine Jay, 2026.
11	200	0.398042605880	Antoine Jay, 2026.
11	201	0.398575443508	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	202	0.399143524260	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	203	0.399743629360	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	204	0.400308204110	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	205	0.400575416411	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	206	0.401653680251	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	207	0.402094738575	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	208	0.404393262012	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	209	0.405390054495	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	210	0.405609872100	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	211	0.405610414758	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	212	0.406010594803	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	213	0.406192123357	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	214	0.407740589104	Antoine Jay, 2026.
11	215	0.409891112491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	216	0.410877688272	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	217	0.411687079085	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	218	0.412120687575	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	219	0.412283759118	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	220	0.412311500303	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	221	0.413518416386	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	222	0.414241603265	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	223	0.414641559769	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	224	0.415048312425	Antoine Jay, 2026.
11	225	0.416114434105	Antoine Jay, 2026.
11	226	0.418425000815	Antoine Jay, 2026.
11	227	0.418956170415	Antoine Jay, 2026.
11	228	0.419910924104	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	229	0.422539921563	Antoine Jay, 2026.
11	230	0.423202550439	Antoine Jay, 2026.
11	231	0.424746747885	Antoine Jay, 2026.
11	232	0.425297112275	Antoine Jay, 2026.
11	233	0.425705815026	Antoine Jay, 2026.
11	234	0.425966110169	Antoine Jay, 2026.
11	235	0.426491111360	Antoine Jay, 2026.
11	236	0.426884106087	Antoine Jay, 2026.
11	237	0.427200182937	Arhan Canli, 2026.
11	238	0.427522975004	Antoine Jay, 2026.
11	239	0.427738735631	Arhan Canli, 2026.
11	240	0.427978522034	Arhan Canli, 2026.
11	241	0.428329998034	Arhan Canli, 2026.
11	242	0.428490026433	Arhan Canli, 2026.
11	243	0.428967131503	Arhan Canli, 2026.
11	244	0.429342786436	Antoine Jay, 2026.
11	245	0.429540867075	Antoine Jay, 2026.
11	246	0.429608118254	Antoine Jay, 2026.
11	247	0.430150886337	Antoine Jay, 2026.
11	248	0.430845950132	Arhan Canli, 2026.
11	249	0.430857864339	Antoine Jay, 2026.
11	250	0.431881873143	Antoine Jay, 2026.
11	251	0.433060218160	Antoine Jay, 2026.
11	252	0.433957561418	Arhan Canli, 2026.
11	253	0.435431849728	Arhan Canli, 2026.
11	254	0.435599176150	Christopher Smolen, 2026.
11	256	0.436406329525	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	257	0.436422980364	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	258	0.436532825744	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	259	0.436716777508	Vadim Borisov, 2026.
11	260	0.436717567141	Vadim Borisov, 2026.
11	261	0.437037936058	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	263	0.437094023179	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	264	0.437208845752	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	265	0.437705550877	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	266	0.437925397406	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	267	0.438166606435	Vadim Borisov, 2026.
11	268	0.438291360494	Christopher Smolen, 2026.
11	269	0.438473121567	Christopher Smolen, 2026.
11	270	0.438907162745	Christopher Smolen, 2026.
11	271	0.439265100937	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	272	0.439689888372	Vadim Borisov, 2026.
11	273	0.439721164015	Arhan Canli, 2026.
11	274	0.440130428495	Christopher Smolen, 2026.
11	275	0.440511073283	Arhan Canli, 2026.
11	276	0.440566692112	Christopher Smolen, 2026.
11	277	0.441099849761	Arhan Canli, 2026.
11	278	0.441351175749	Christopher Smolen, 2026.
11	279	0.441566022795	Christopher Smolen, 2026.
11	280	0.441718930232	Christopher Smolen, 2026.
11	281	0.442402044794	Christopher Smolen, 2026.
11	282	0.442664824516	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	283	0.442746590432	Arhan Canli, 2026.
11	284	0.443020346098	Arhan Canli, 2026.
11	285	0.443551692316	Arhan Canli, 2026.
11	286	0.443937253441	Antoine Jay, 2026.
11	287	0.444166020938	Arhan Canli, 2026.
11	288	0.444412834715	Antoine Jay, 2026.
11	289	0.444740550599	Christopher Smolen, 2026.
11	290	0.445387377760	Christopher Smolen, 2026.
11	291	0.445575787184	Henry Cohn, 2026.
11	292	0.445925212566	Christopher Smolen, 2026.
11	293	0.446796016455	Christopher Smolen, 2026.
11	294	0.447606131349	Arhan Canli, 2026.
11	295	0.448956006087	Christopher Smolen, 2026.
11	296	0.449962346238	Christopher Smolen, 2026.
11	297	0.450874517272	Christopher Smolen, 2026.
11	298	0.451302659355	Christopher Smolen, 2026.
11	299	0.453697767230	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	300	0.453789608035	Christopher Smolen, 2026.
11	301	0.455672641891	Christopher Smolen, 2026.
11	302	0.456163022741	Arhan Canli, 2026.
11	303	0.457358394335	Arhan Canli, 2026.
11	304	0.458711633652	Arhan Canli, 2026.
11	305	0.458838724717	Antoine Jay, 2026.
11	306	0.459469466356	Antoine Jay, 2026.
11	307	0.459827385295	Henry Cohn, 2026.
11	308	0.461074052115	Arhan Canli, 2026.
11	309	0.461147931588	Antoine Jay, 2026.
11	310	0.461809928321	Arhan Canli, 2026.
11	311	0.463454229266	Antoine Jay, 2026.
11	312	0.463785218942	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	313	0.463908683978	Vadim Borisov, 2026.
11	314	0.463929021688	Christopher Smolen, 2026.
11	315	0.464385383126	Christopher Smolen, 2026.
11	316	0.464997036157	Antoine Jay, 2026.
11	317	0.465291032362	Christopher Smolen, 2026.
11	318	0.465315124686	Antoine Jay, 2026.
11	319	0.466176028661	Antoine Jay, 2026.
11	320	0.466196425006	Christopher Smolen, 2026.
11	321	0.466777575789	Christopher Smolen, 2026.
11	322	0.466969816503	Arhan Canli, 2026.
11	323	0.467291639442	Antoine Jay, 2026.
11	324	0.467721411427	Antoine Jay, 2026.
11	325	0.468238857083	Antoine Jay, 2026.
11	326	0.468726855824	Antoine Jay, 2026.
11	327	0.469187446683	Arhan Canli, 2026.
11	328	0.469717127979	Arhan Canli, 2026.
11	329	0.470015291169	Christopher Smolen, 2026.
11	342	0.470588235295	Henry Cohn, 2026. $17 x - 8$
11	343	0.472339723589	Henry Cohn, 2026.
11	344	0.473457250643	Christopher Smolen, 2026.
11	345	0.474139949116	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	346	0.474551893654	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	347	0.474970594695	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	348	0.475274516494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	349	0.475373654814	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	350	0.475469925145	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	351	0.475502555224	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	352	0.475528154032	Vadim Borisov, 2026.
11	353	0.475528293083	Christopher Smolen, 2026.
11	354	0.476045991615	Antoine Jay, 2026.
11	355	0.476209191974	Christopher Smolen, 2026.
11	356	0.476474497961	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	357	0.476629086940	Vadim Borisov, 2026.
11	358	0.477815954432	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	359	0.477821887791	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	360	0.477846213532	Antoine Jay, 2026.
11	361	0.478176743481	Vadim Borisov, 2026.
11	362	0.478176850802	Christopher Smolen, 2026.
11	363	0.479047019377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	364	0.479146146404	Antoine Jay, 2026.
11	365	0.479206069935	Antoine Jay, 2026.
11	366	0.479276575882	Antoine Jay, 2026.
11	367	0.479430688698	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	368	0.479435886488	Vadim Borisov, 2026.
11	369	0.479435895590	Christopher Smolen, 2026.
11	370	0.479851831298	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	371	0.479924649928	Vadim Borisov, 2026.
11	372	0.479945581503	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	373	0.480471275976	Christopher Smolen, 2026.
11	374	0.480645936110	Christopher Smolen, 2026.
11	375	0.480988157941	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	376	0.481090453972	Vadim Borisov, 2026.
11	377	0.481428370575	Christopher Smolen, 2026.
11	378	0.481772386805	Christopher Smolen, 2026.
11	379	0.482240997769	Antoine Jay, 2026.
11	380	0.482321484554	Vadim Borisov, 2026.
11	381	0.482321488248	Vadim Borisov, 2026.
11	382	0.482321492294	Christopher Smolen, 2026.
11	383	0.483146356183	Christopher Smolen, 2026.
11	385	0.483527433591	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	386	0.483667859411	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	387	0.483683321864	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	388	0.483684928654	Vadim Borisov, 2026.
11	389	0.483685154790	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	390	0.483846686103	Christopher Smolen, 2026.
11	391	0.484412093884	Vadim Borisov, 2026.
11	392	0.484415903010	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	393	0.484430110766	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	394	0.484430404290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	395	0.484472283213	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	396	0.484505974385	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	397	0.484516428316	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	398	0.484546231757	Christopher Smolen, 2026.
11	400	0.485555363920	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	401	0.485633126858	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	402	0.485690190979	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	403	0.485859387072	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	404	0.485886902315	Christopher Smolen, 2026.
11	405	0.486064943583	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	406	0.486182848831	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	407	0.486252628683	Christopher Smolen, 2026.
11	408	0.486443080974	Christopher Smolen, 2026.
11	409	0.486503842736	Christopher Smolen, 2026.
11	410	0.486711196823	Christopher Smolen, 2026.
11	411	0.486971663527	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	412	0.488062654839	Christopher Smolen, 2026.
11	413	0.488445150125	Christopher Smolen, 2026.
11	414	0.488696607474	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	415	0.488767670488	Christopher Smolen, 2026.
11	416	0.489052635367	Christopher Smolen, 2026.
11	417	0.489125932084	Christopher Smolen, 2026.
11	418	0.489294048713	Christopher Smolen, 2026.
11	419	0.489363708305	Christopher Smolen, 2026.
11	420	0.489493081381	Christopher Smolen, 2026.
11	421	0.489597528719	Christopher Smolen, 2026.
11	422	0.489644081549	Vadim Borisov, 2026.
11	423	0.489836777576	Christopher Smolen, 2026.
11	424	0.489999371699	Christopher Smolen, 2026.
11	425	0.490105597591	Christopher Smolen, 2026.
11	426	0.490474152511	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	427	0.490512611271	Vadim Borisov, 2026.
11	428	0.490558181909	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	429	0.490634915530	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	430	0.491460367632	Vadim Borisov, 2026.
11	431	0.491465884212	Christopher Smolen, 2026.
11	432	0.491933934675	Christopher Smolen, 2026.
11	433	0.492097036806	Christopher Smolen, 2026.
11	434	0.492273978871	Christopher Smolen, 2026.
11	435	0.492334685720	Christopher Smolen, 2026.
11	436	0.492422211791	Vadim Borisov, 2026.
11	437	0.492480915469	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	438	0.492800946811	Christopher Smolen, 2026.
11	439	0.492839412502	Vadim Borisov, 2026.
11	440	0.492853836068	Vadim Borisov, 2026.
11	441	0.492875956006	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	442	0.493020720381	Vadim Borisov, 2026.
11	443	0.493028501282	Vadim Borisov, 2026.
11	444	0.493084233804	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	445	0.493278926141	Christopher Smolen, 2026.
11	446	0.493309572365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	447	0.493347730212	Christopher Smolen, 2026.
11	448	0.493366242378	Christopher Smolen, 2026.
11	449	0.493810881904	Vadim Borisov, 2026.
11	450	0.495169197237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	451	0.495172190050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	455	0.495213660642	Vadim Borisov, 2026.
11	456	0.495213662481	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	457	0.495425389092	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	458	0.496125347962	Christopher Smolen, 2026.
11	459	0.496345874866	Christopher Smolen, 2026.
11	460	0.496464549773	Vadim Borisov, 2026.
11	464	0.496464631074	Vadim Borisov, 2026.
11	465	0.496464639079	Vadim Borisov, 2026.
11	466	0.496464738109	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	470	0.496681603079	Vadim Borisov, 2026.
11	473	0.496681603621	Vadim Borisov, 2026.
11	474	0.496681603696	Vadim Borisov, 2026.
11	475	0.496681749242	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	476	0.496738536750	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	477	0.496738537561	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	482	0.496936936060	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	483	0.497123823152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	484	0.497161750923	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	485	0.499164330218	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	486	0.499173810421	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	487	0.499174960832	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	488	0.499179339208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	489	0.499182905280	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	490	0.499183464672	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	491	0.499184506742	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	492	0.499356969610	Vadim Borisov, 2026.
11	493	0.499358574026	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	494	0.499390339901	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	495	0.499391253796	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	496	0.499407235464	Vadim Borisov, 2026.
11	497	0.499408470060	Vadim Borisov, 2026.
11	498	0.499409156638	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	499	0.499435491187	Vadim Borisov, 2026.
11	500	0.499435549261	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	501	0.499444333250	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	502	0.499450169410	Christopher Smolen, 2026.
11	503	0.499471505632	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	504	0.499474761178	Christopher Smolen, 2026.
11	505	0.499560344028	Vadim Borisov, 2026.
11	506	0.499561903563	Christopher Smolen, 2026.
11	507	0.499562153480	Christopher Smolen, 2026.
11	508	0.499572369918	Vadim Borisov, 2026.
11	509	0.499578941440	Vadim Borisov, 2026.
11	510	0.499580613757	Christopher Smolen, 2026.
11	511	0.499585296394	Christopher Smolen, 2026.
11	512	0.499590145181	Vadim Borisov, 2026.
11	513	0.499591332607	Christopher Smolen, 2026.
11	514	0.499591465674	Vadim Borisov, 2026.
11	515	0.499593833188	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	516	0.499607146204	Vadim Borisov, 2026.
11	517	0.499610828369	Christopher Smolen, 2026.
11	518	0.499612296496	Vadim Borisov, 2026.
11	519	0.499618928595	Vadim Borisov, 2026.
11	520	0.499621096571	Vadim Borisov, 2026.
11	521	0.499624027949	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	522	0.499640526919	Christopher Smolen, 2026.
11	523	0.499640982044	Christopher Smolen, 2026.
11	524	0.499642626855	Vadim Borisov, 2026.
11	525	0.499643016997	Christopher Smolen, 2026.
11	526	0.499643442374	Christopher Smolen, 2026.
11	527	0.499643989722	Christopher Smolen, 2026.
11	528	0.499644492665	Christopher Smolen, 2026.
11	529	0.499644602511	Vadim Borisov, 2026.
11	530	0.499645595342	Vadim Borisov, 2026.
11	531	0.499647237689	Christopher Smolen, 2026.
11	532	0.499647383115	Vadim Borisov, 2026.
11	533	0.499650459645	Vadim Borisov, 2026.
11	534	0.499650977688	Christopher Smolen, 2026.
11	535	0.499651415749	Christopher Smolen, 2026.
11	536	0.499651860088	Vadim Borisov, 2026.
11	537	0.499652412120	Christopher Smolen, 2026.
11	538	0.499655322829	Vadim Borisov, 2026.
11	539	0.499655332624	Vadim Borisov, 2026.
11	540	0.499655339086	Vadim Borisov, 2026.
11	541	0.499655340102	Vadim Borisov, 2026.
11	542	0.499655344640	Vadim Borisov, 2026.
11	543	0.499655356763	Vadim Borisov, 2026.
11	544	0.499655544437	Christopher Smolen, 2026.
11	545	0.499656203187	Vadim Borisov, 2026.
11	546	0.499656446627	Christopher Smolen, 2026.
11	547	0.499657107851	Vadim Borisov, 2026.
11	549	0.499657166620	Vadim Borisov, 2026.
11	550	0.499658128118	Vadim Borisov, 2026.
11	551	0.499658300903	Vadim Borisov, 2026.
11	552	0.499658621620	Christopher Smolen, 2026.
11	553	0.499658709421	Vadim Borisov, 2026.
11	554	0.499658827334	Vadim Borisov, 2026.
11	555	0.499659056101	Christopher Smolen, 2026.
11	556	0.499659143867	Vadim Borisov, 2026.
11	557	0.499659184826	Vadim Borisov, 2026.
11	558	0.499659482245	Vadim Borisov, 2026.
11	559	0.499659624584	Vadim Borisov, 2026.
11	560	0.499659626282	Vadim Borisov, 2026.
11	564	0.499659643028	Vadim Borisov, 2026.
11	565	0.499659643628	Vadim Borisov, 2026.
11	566	0.499659643908	Vadim Borisov, 2026.
11	567	0.499660122013	Vadim Borisov, 2026.
11	568	0.499660198932	Christopher Smolen, 2026.
11	569	0.499660287059	Christopher Smolen, 2026.
11	570	0.499660411097	Vadim Borisov, 2026.
11	571	0.499660504593	Vadim Borisov, 2026.
11	572	0.499660574672	Vadim Borisov, 2026.
11	573	0.499660589844	Vadim Borisov, 2026.
11	574	0.499660590082	Vadim Borisov, 2026.
11	575	0.499660708373	Vadim Borisov, 2026.
11	576	0.499660915600	Vadim Borisov, 2026.
11	577	0.499661028882	Vadim Borisov, 2026.
11	578	0.499661118191	Christopher Smolen, 2026.
11	579	0.499662128465	Christopher Smolen, 2026.
11	580	0.499662885633	Vadim Borisov, 2026.
11	581	0.499662948257	Vadim Borisov, 2026.
11	582	0.499663469960	Vadim Borisov, 2026.
11	583	0.499663538330	Vadim Borisov, 2026.
11	584	0.499663811737	Christopher Smolen, 2026.
11	585	0.499664041985	Christopher Smolen, 2026.
11	586	0.499664073250	Christopher Smolen, 2026.
11	587	0.499664099161	Vadim Borisov, 2026.
11	589	0.499666072937	Vadim Borisov, 2026.
11	590	0.499666087387	Vadim Borisov, 2026.
11	591	0.499666304152	Christopher Smolen, 2026.
11	592	0.499668949797	Christopher Smolen, 2026.
11	593	0.499999985843	Christopher Smolen, 2026.
11	604	0.5	F. Bianchi, Y. Kwon, A. Pappu, and J. Zou, Harnessing the collective intelligence of AI agents in the wild for new discoveries, preprint, 2026, arXiv:2606.10402. $2 x - 1$
11	605	0.507413184507	Christopher Smolen, 2026.
11	606	0.508065825376	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	607	0.508541273904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	608	0.508829438760	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	609	0.509069881909	Christopher Smolen, 2026.
11	610	0.509551977262	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	611	0.509603781299	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	612	0.509708839475	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	613	0.509840968058	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	614	0.510303581774	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	615	0.510928748557	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	616	0.511122560303	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	617	0.511889368132	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	618	0.513408298563	Christopher Smolen, 2026.
11	619	0.513861441907	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	620	0.514033384198	Christopher Smolen, 2026.
11	621	0.514219792539	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	622	0.514294130580	Christopher Smolen, 2026.
11	623	0.515099544536	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	624	0.515382732138	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	625	0.515647140198	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	626	0.516014992788	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	627	0.516277098567	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	628	0.516911650397	Christopher Smolen, 2026.
11	629	0.517524503506	Christopher Smolen, 2026.
11	630	0.517863158701	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	631	0.518224674144	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	632	0.518567853365	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	633	0.518872119999	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	634	0.519534230430	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	635	0.519817484849	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	636	0.520425781348	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	637	0.520903322910	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	638	0.521125765803	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	639	0.521611716163	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	640	0.522139110644	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	641	0.522701283256	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	642	0.522900346210	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	643	0.523744021970	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	644	0.524069006124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	645	0.524518426324	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	646	0.524893981494	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	647	0.525217996054	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	648	0.525559588934	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	649	0.525567190493	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	650	0.525661139783	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	651	0.525700798225	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	652	0.525723786491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	653	0.525817650315	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	654	0.525906046626	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	655	0.526148490544	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	656	0.526325072251	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	657	0.526482827235	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	658	0.526589504774	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	659	0.526791058520	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	660	0.526902177410	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	661	0.526972284227	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	662	0.527047257742	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	663	0.527138857726	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	664	0.527226020483	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	665	0.527283407694	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	666	0.527704956501	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	667	0.527748892403	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	668	0.528029045945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	669	0.528207463542	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	670	0.528443600020	Christopher Smolen, 2026.
11	671	0.528734589746	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	672	0.528856859514	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	673	0.529260296662	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	674	0.529406305382	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	675	0.529544960915	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	676	0.529645748858	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	677	0.529757116000	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	678	0.529920319590	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	679	0.530044141613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	680	0.530070044323	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	681	0.530198061847	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	682	0.530411805364	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	683	0.530676208107	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	684	0.530773504207	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	685	0.530774069845	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	686	0.531175327713	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	687	0.531239879053	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	688	0.531314915121	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	689	0.532038767701	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	690	0.532737805980	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	691	0.532962752165	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	692	0.533712311242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	693	0.538656399915	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	694	0.538991959669	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	695	0.539416460832	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	696	0.539496346879	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	697	0.539954947249	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	698	0.540353882898	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	699	0.540646421959	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	700	0.540791584712	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	701	0.540855525815	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	702	0.540862221350	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	703	0.540981851225	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	704	0.541203830271	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	705	0.541229766172	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	706	0.541255810943	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	707	0.541271052012	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	708	0.541386027022	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	709	0.541431260795	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	710	0.541439446145	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	711	0.541443861560	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	712	0.541651939734	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	713	0.541688790862	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	714	0.541740403019	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	715	0.541853126681	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	716	0.542314305404	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	717	0.542392221456	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	718	0.542406385969	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	719	0.542450857794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	720	0.542571505243	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	721	0.542762548190	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	722	0.542944987473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	723	0.542978793099	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	724	0.543008409852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	725	0.543389456357	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	726	0.543540746098	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	727	0.543652841959	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	728	0.543803174122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	729	0.543830499379	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	730	0.543906423372	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	731	0.544841107604	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	732	0.544898479826	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	733	0.545311273427	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	734	0.545468235436	Vadim Borisov, 2026.
11	735	0.545468245284	Christopher Smolen, 2026.
11	736	0.546351006997	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	737	0.546621535430	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	738	0.546760720032	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
11	1002	0.546918160679	Kevin Li, 2026. $7 x^{2} - 2 x - 1$
11	1003	0.548554512227	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1004	0.555804495130	Henry Cohn, 2026.
11	1005	0.559538483492	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1006	0.560899004595	Vadim Borisov, 2026.
11	1007	0.561739743914	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1008	0.561920488398	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1009	0.562017152575	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1010	0.564200560005	Vadim Borisov, 2026.
11	1011	0.564582663111	Vadim Borisov, 2026.
11	1012	0.564719470136	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1013	0.566227156239	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1014	0.567361706609	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1015	0.568149020678	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1016	0.568838598999	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1017	0.569674748709	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1018	0.570559361101	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1020	0.571171616979	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1021	0.571171618054	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1022	0.572434306124	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
11	1024	0.572434321688	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	25	0.061281914575	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $1200 x^{3} - 144 x^{2} - 12 x + 1$
12	26	0.071428571429	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $14 x - 1$
12	27	0.074764926182	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12	28	0.082592206268	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12	29	0.084348009310	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $496 x^{4} + 92 x^{3} - 57 x^{2} - 8 x + 1$
12	30	0.089146601434	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $3856 x^{4} + 1456 x^{3} + 100 x^{2} - 12 x - 1$
12	31	0.098704091241	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $863 x^{2} + 6 x - 9$
12	32	0.098704091241	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $863 x^{2} + 6 x - 9$
12	34	0.112004618870	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $44 x^{2} + 4 x - 1$
12	35	0.119914058434	Henry Cohn, 2025.
12	36	0.121730661114	Henry Cohn, 2026.
12	37	0.121971459128	Henry Cohn, 2023. $359 x^{2} + 30 x - 9$
12	38	0.130785955647	Henry Cohn, 2026.
12	39	0.132497435001	Henry Cohn, 2023.
12	40	0.133638243588	Henry Cohn, 2023.
12	41	0.135922539556	Henry Cohn, 2023.
12	42	0.136597789057	Henry Cohn, 2023. $5296 x^{4} + 1248 x^{3} - 40 x^{2} - 24 x - 1$
12	43	0.139595542735	Henry Cohn, 2023. Minimal polynomial of degree 16
12	44	0.141964936980	Henry Cohn, 2023. $736256 x^{8} - 133120 x^{7} - 146176 x^{6} - 13824 x^{5} + 8368 x^{4} + 1568 x^{3} - 72 x^{2} - 24 x - 1$
12	45	0.149653254074	Henry Cohn, 2024.
12	46	0.150221879934	Henry Cohn, 2025.
12	50	0.150442862439	Henry Cohn, 2023. $956 x^{2} - 84 x - 9$
12	51	0.159810400056	Henry Cohn, 2023. $3600 x^{5} - 1080 x^{4} - 252 x^{3} + 36 x^{2} + 9 x - 1$
12	52	0.180095470186	Henry Cohn, 2025.
12	53	0.187323217985	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	54	0.189736045016	Antoine Jay, 2026.
12	55	0.193319221516	Antoine Jay, 2026.
12	60	0.193457871625	Henry Cohn, 2026. $3088 x^{4} - 1184 x^{3} - 120 x^{2} + 40 x + 1$
12	61	0.196565668411	Henry Cohn, 2026. Minimal polynomial of degree 12
12	62	0.197162933815	Henry Cohn, 2026. $24 x^{3} + 92 x^{2} - 14 x - 1$
12	63	0.207400372189	Antoine Jay, 2026.
12	64	0.210566554872	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12	65	0.214409160183	Henry Cohn, 2026.
12	66	0.214718112242	Antoine Olivier, 2026.
12	67	0.215314862828	Antoine Jay, 2026.
12	68	0.219978834878	Henry Cohn, 2026.
12	69	0.225092708566	Henry Cohn, 2026.
12	70	0.228364125667	Henry Cohn, 2026.
12	71	0.230206653866	Antoine Jay, 2026.
12	72	0.231096328878	Henry Cohn, 2026.
12	73	0.232328768771	Henry Cohn, 2026.
12	74	0.232756430709	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	78	0.233245773320	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $455568 x^{4} - 93824 x^{3} - 18708 x^{2} + 2448 x + 289$
12	79	0.241071142239	Antoine Jay, 2026.
12	80	0.243285310545	Antoine Jay, 2026.
12	81	0.243910094468	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12	90	0.244488618750	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. $29 x^{2} - 3 x - 1$
12	91	0.250930941988	Henry Cohn, 2026.
12	92	0.258276397340	Antoine Olivier, 2026.
12	93	0.258548478945	Antoine Jay, 2026.
12	94	0.258821811115	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	95	0.258907435640	Antoine Jay, 2026.
12	100	0.259843574332	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $167 x^{2} - 28 x - 4$
12	101	0.260004785660	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	102	0.267188139351	Antoine Jay, 2026.
12	103	0.268871884424	Arhan Canli, 2026.
12	104	0.271216741430	Arhan Canli, 2026.
12	106	0.271795861692	A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919. $9857 x^{4} - 1284 x^{3} - 378 x^{2} - 4 x + 1$
12	107	0.273389545228	Arhan Canli, 2026.
12	108	0.276742343471	Antoine Jay, 2026.
12	109	0.277251579211	Antoine Jay, 2026.
12	110	0.277818835253	Antoine Jay, 2026.
12	111	0.278673380268	Antoine Jay, 2026.
12	112	0.279410125474	Arhan Canli, 2026.
12	113	0.281946652762	Arhan Canli, 2026.
12	114	0.290350338240	Arhan Canli, 2026.
12	115	0.291519424715	Antoine Jay, 2026.
12	116	0.292118646643	Arhan Canli, 2026.
12	117	0.292825931080	Antoine Jay, 2026.
12	118	0.293549457622	Antoine Jay, 2026.
12	119	0.294441562714	Antoine Jay, 2026.
12	121	0.294708984703	Henry Cohn, 2026.
12	138	0.299119474480	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $49 x^{2} - 18 x + 1$
12	139	0.300637961639	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	140	0.307947500174	Antoine Jay, 2026.
12	141	0.310963297309	Antoine Jay, 2026.
12	142	0.317527068191	Antoine Jay, 2026.
12	143	0.317772919124	Antoine Jay, 2026.
12	144	0.317963092614	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	145	0.318260329457	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	146	0.318476035507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	147	0.318849581733	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	148	0.319694060759	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	149	0.320687471946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	150	0.322622969658	Antoine Jay, 2026.
12	151	0.324338709030	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	152	0.326095072979	Antoine Jay, 2026.
12	153	0.326509715022	Antoine Jay, 2026.
12	154	0.327732821508	Antoine Jay, 2026.
12	155	0.328339947058	Antoine Jay, 2026.
12	156	0.328528436930	Antoine Jay, 2026.
12	157	0.329207461444	Antoine Jay, 2026.
12	158	0.329441298800	Antoine Jay, 2026.
12	159	0.329602528000	Antoine Jay, 2026.
12	160	0.329797962540	Antoine Jay, 2026.
12	161	0.329897727579	Antoine Jay, 2026.
12	162	0.329991312203	Antoine Jay, 2026.
12	163	0.330656354956	Antoine Jay, 2026.
12	164	0.331261134476	Antoine Jay, 2026.
12	165	0.331415494102	Antoine Jay, 2026.
12	166	0.331797491509	Antoine Jay, 2026.
12	167	0.332153895455	Henry Cohn, 2026.
12	168	0.332482019903	Antoine Jay, 2026.
12	169	0.332713895660	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	170	0.332830733250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	171	0.332950075912	Antoine Jay, 2026.
12	172	0.332989693827	Antoine Jay, 2026.
12	173	0.333030966124	Antoine Jay, 2026.
12	174	0.333057570223	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	175	0.333096643877	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	176	0.333139737275	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	177	0.333140146607	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	178	0.333144100514	Christopher Smolen, 2026.
12	179	0.333333470507	Arhan Canli, 2026.
12	180	0.335268857602	Arhan Canli, 2026.
12	181	0.344130099215	Arhan Canli, 2026.
12	182	0.345527156300	Vadim Borisov, 2026.
12	183	0.345552228635	Henry Cohn, 2026.
12	184	0.348669590198	Arhan Canli, 2026.
12	185	0.348964201986	Christopher Smolen, 2026.
12	186	0.351891117772	Arhan Canli, 2026.
12	187	0.352415155894	Arhan Canli, 2026.
12	188	0.353528310263	Arhan Canli, 2026.
12	189	0.354668191491	Arhan Canli, 2026.
12	190	0.355745660293	Antoine Jay, 2026.
12	191	0.356085174184	Antoine Jay, 2026.
12	192	0.356522810908	Christopher Smolen, 2026.
12	193	0.357862431959	Antoine Jay, 2026.
12	194	0.360296802900	Christopher Smolen, 2026.
12	195	0.361701063121	Antoine Jay, 2026.
12	196	0.362299122138	Antoine Jay, 2026.
12	197	0.363059642807	Christopher Smolen, 2026.
12	198	0.364186303004	Antoine Jay, 2026.
12	199	0.365047857075	Antoine Jay, 2026.
12	200	0.365797047246	Antoine Jay, 2026.
12	201	0.367099356686	Antoine Jay, 2026.
12	202	0.367727770955	Antoine Jay, 2026.
12	203	0.369076752419	Antoine Jay, 2026.
12	204	0.369894963631	Antoine Jay, 2026.
12	205	0.370831165488	Antoine Jay, 2026.
12	206	0.372394404614	Antoine Jay, 2026.
12	207	0.373196169864	Arhan Canli, 2026.
12	208	0.374148704090	Arhan Canli, 2026.
12	210	0.375	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.12.12. The appendix lists the code size as 209, but the construction works just as well for 210. $8 x - 3$
12	211	0.376038746983	Arhan Canli, 2026.
12	212	0.377564210109	Arhan Canli, 2026.
12	213	0.377974062133	Arhan Canli, 2026.
12	214	0.378452957757	Christopher Smolen, 2026.
12	215	0.378690020499	Christopher Smolen, 2026.
12	216	0.379068197484	Christopher Smolen, 2026.
12	217	0.381183878200	Arhan Canli, 2026.
12	218	0.381999602744	Christopher Smolen, 2026.
12	219	0.382399065814	Christopher Smolen, 2026.
12	220	0.382673202938	Christopher Smolen, 2026.
12	221	0.383509271292	Christopher Smolen, 2026.
12	222	0.383960752052	Christopher Smolen, 2026.
12	223	0.384244521598	Arhan Canli, 2026.
12	224	0.384444059089	Arhan Canli, 2026.
12	225	0.384610145003	Arhan Canli, 2026.
12	226	0.384756962793	Christopher Smolen, 2026.
12	227	0.385699713776	Christopher Smolen, 2026.
12	228	0.386249042680	Arhan Canli, 2026.
12	229	0.386646344889	Arhan Canli, 2026.
12	230	0.387169729830	Arhan Canli, 2026.
12	231	0.387698853910	Arhan Canli, 2026.
12	232	0.389017597823	Christopher Smolen, 2026.
12	233	0.390786154791	Christopher Smolen, 2026.
12	234	0.390992495951	Christopher Smolen, 2026.
12	235	0.391126354980	Christopher Smolen, 2026.
12	236	0.391278949485	Antoine Jay, 2026.
12	237	0.391459944636	Christopher Smolen, 2026.
12	238	0.392096082371	Christopher Smolen, 2026.
12	239	0.392514197731	Arhan Canli, 2026.
12	240	0.392766118256	Arhan Canli, 2026.
12	241	0.392881828838	Antoine Jay, 2026.
12	242	0.395022688121	Christopher Smolen, 2026.
12	243	0.396563563687	Christopher Smolen, 2026.
12	244	0.398228657979	Christopher Smolen, 2026.
12	245	0.398642271085	Christopher Smolen, 2026.
12	246	0.398806474205	Christopher Smolen, 2026.
12	247	0.398968698288	Christopher Smolen, 2026.
12	248	0.399113353625	Christopher Smolen, 2026.
12	288	0.4	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
12	290	0.4	Henry Cohn, 2026. $5 x - 2$
12	291	0.401553680753	Henry Cohn, 2026.
12	292	0.405513213901	Christopher Smolen, 2026.
12	293	0.408651409905	Christopher Smolen, 2026.
12	294	0.410469053543	Antoine Jay, 2026.
12	295	0.412242725686	Antoine Jay, 2026.
12	296	0.413719367618	Arhan Canli, 2026.
12	297	0.414697777536	Antoine Jay, 2026.
12	298	0.416838874760	Antoine Jay, 2026.
12	299	0.418218984370	Antoine Jay, 2026.
12	300	0.419668010003	Antoine Jay, 2026.
12	301	0.420502660930	Antoine Jay, 2026.
12	310	0.420718949140	Antoine Jay, 2026.
12	311	0.427673906537	Christopher Smolen, 2026.
12	314	0.427748179869	Vadim Borisov, 2026.
12	315	0.427794998224	Christopher Smolen, 2026.
12	316	0.427884680829	Christopher Smolen, 2026.
12	317	0.427906195785	Christopher Smolen, 2026.
12	318	0.427907993172	Vadim Borisov, 2026.
12	319	0.427930886815	Christopher Smolen, 2026.
12	321	0.427971002067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	322	0.427999645621	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	323	0.428024390826	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	324	0.428054087873	Vadim Borisov, 2026.
12	325	0.428054594655	Vadim Borisov, 2026.
12	326	0.428054755710	Christopher Smolen, 2026.
12	327	0.428083584609	Christopher Smolen, 2026.
12	328	0.428121370143	Christopher Smolen, 2026.
12	329	0.428157589204	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	330	0.428178333836	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	331	0.428203370711	Christopher Smolen, 2026.
12	332	0.428211133092	Vadim Borisov, 2026.
12	333	0.428216223900	Christopher Smolen, 2026.
12	334	0.428244766853	Vadim Borisov, 2026.
12	335	0.428244814075	Vadim Borisov, 2026.
12	336	0.428251371506	Christopher Smolen, 2026.
12	337	0.428308828794	Christopher Smolen, 2026.
12	346	0.428334994615	Arhan Canli, 2026.
12	347	0.428433879806	Christopher Smolen, 2026.
12	348	0.429372191579	Christopher Smolen, 2026.
12	349	0.430391296993	Christopher Smolen, 2026.
12	350	0.430719396353	Christopher Smolen, 2026.
12	351	0.430729612437	Christopher Smolen, 2026.
12	352	0.430893181279	Christopher Smolen, 2026.
12	353	0.431000514984	Christopher Smolen, 2026.
12	354	0.431034104104	Henry Cohn, 2026.
12	355	0.432414652007	Vadim Borisov, 2026.
12	356	0.432970117623	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	357	0.433481822368	Christopher Smolen, 2026.
12	358	0.434297738585	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	359	0.434748148476	Christopher Smolen, 2026.
12	360	0.436565539539	Antoine Jay, 2026.
12	361	0.436624449077	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	363	0.436942814730	Christopher Smolen, 2026.
12	364	0.437162182158	Antoine Jay, 2026.
12	365	0.440411891141	Antoine Jay, 2026.
12	366	0.440942977533	Christopher Smolen, 2026.
12	367	0.441157511632	Vadim Borisov, 2026.
12	368	0.441322206354	Christopher Smolen, 2026.
12	369	0.441778159104	Christopher Smolen, 2026.
12	370	0.441993505580	Christopher Smolen, 2026.
12	371	0.442216843155	Christopher Smolen, 2026.
12	372	0.442406317021	Christopher Smolen, 2026.
12	373	0.442437242477	Christopher Smolen, 2026.
12	374	0.442760569682	Christopher Smolen, 2026.
12	375	0.443091940379	Christopher Smolen, 2026.
12	408	0.444444444445	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $9 x - 4$
12	409	0.447146012106	Christopher Smolen, 2026.
12	410	0.447927217504	Christopher Smolen, 2026.
12	411	0.448614429727	Christopher Smolen, 2026.
12	412	0.449177206554	Christopher Smolen, 2026.
12	413	0.449570680377	Vadim Borisov, 2026.
12	414	0.449889314868	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	415	0.450174876458	Christopher Smolen, 2026.
12	416	0.450350610395	Christopher Smolen, 2026.
12	417	0.450647724042	Christopher Smolen, 2026.
12	418	0.450927514815	Christopher Smolen, 2026.
12	419	0.451165599154	Christopher Smolen, 2026.
12	420	0.451467838996	Christopher Smolen, 2026.
12	421	0.451743713523	Christopher Smolen, 2026.
12	422	0.452043966404	Christopher Smolen, 2026.
12	423	0.452511533432	Christopher Smolen, 2026.
12	424	0.452760473231	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	425	0.452830941446	Christopher Smolen, 2026.
12	426	0.458828260792	Christopher Smolen, 2026.
12	427	0.458840111009	Vadim Borisov, 2026.
12	428	0.459196691212	Vadim Borisov, 2026.
12	429	0.459326669634	Vadim Borisov, 2026.
12	430	0.460511062637	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	431	0.460542285495	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	432	0.460648554830	Christopher Smolen, 2026.
12	433	0.462233719555	Christopher Smolen, 2026.
12	434	0.462604976860	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	435	0.464549072078	Christopher Smolen, 2026.
12	436	0.464654960254	Christopher Smolen, 2026.
12	437	0.465589972932	Christopher Smolen, 2026.
12	438	0.465886485151	Vadim Borisov, 2026.
12	439	0.465886526914	Vadim Borisov, 2026.
12	440	0.465887124626	Christopher Smolen, 2026.
12	441	0.466272569883	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	442	0.466535858130	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	443	0.466542213624	Vadim Borisov, 2026.
12	444	0.466542628545	Christopher Smolen, 2026.
12	445	0.467044682246	Antoine Jay, 2026.
12	446	0.467209026067	Christopher Smolen, 2026.
12	447	0.467789696509	Christopher Smolen, 2026.
12	448	0.467957350398	Christopher Smolen, 2026.
12	449	0.468097182261	Antoine Jay, 2026.
12	451	0.468258551537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	452	0.468318200460	Christopher Smolen, 2026.
12	453	0.468843568619	Christopher Smolen, 2026.
12	454	0.468928852236	Christopher Smolen, 2026.
12	455	0.469054797868	Christopher Smolen, 2026.
12	456	0.469210144164	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	457	0.469574023121	Christopher Smolen, 2026.
12	458	0.469784988610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	459	0.469788927473	Christopher Smolen, 2026.
12	460	0.470249314822	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	461	0.470249686708	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	462	0.470344508767	Christopher Smolen, 2026.
12	463	0.470692979854	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	464	0.470710991572	Christopher Smolen, 2026.
12	465	0.471246656564	Christopher Smolen, 2026.
12	466	0.471612802208	Christopher Smolen, 2026.
12	467	0.471952879090	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	468	0.472039765110	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	469	0.472075926669	Christopher Smolen, 2026.
12	470	0.472535123071	Christopher Smolen, 2026.
12	471	0.472609243050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	472	0.472784662487	Christopher Smolen, 2026.
12	473	0.472812274567	Christopher Smolen, 2026.
12	474	0.472898819252	Christopher Smolen, 2026.
12	475	0.472994269021	Christopher Smolen, 2026.
12	476	0.473048924237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	477	0.473213619449	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	478	0.473498842321	Christopher Smolen, 2026.
12	479	0.473614591887	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	480	0.473726064160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	481	0.473956805219	Christopher Smolen, 2026.
12	482	0.474194881673	Vadim Borisov, 2026.
12	483	0.474194885065	Christopher Smolen, 2026.
12	484	0.474663507443	Christopher Smolen, 2026.
12	485	0.474719063162	Christopher Smolen, 2026.
12	486	0.474769645887	Vadim Borisov, 2026.
12	487	0.474773298957	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	488	0.474878159574	Christopher Smolen, 2026.
12	489	0.475976748622	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	490	0.476003764804	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	491	0.476041228528	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	492	0.476084859957	Christopher Smolen, 2026.
12	493	0.476382088325	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	494	0.476533545358	Vadim Borisov, 2026.
12	495	0.476533563256	Christopher Smolen, 2026.
12	496	0.476551607480	Christopher Smolen, 2026.
12	497	0.476811878488	Vadim Borisov, 2026.
12	498	0.476815155304	Vadim Borisov, 2026.
12	499	0.476815233784	Christopher Smolen, 2026.
12	500	0.477243882135	Vadim Borisov, 2026.
12	501	0.477276615075	Christopher Smolen, 2026.
12	502	0.477678497999	Vadim Borisov, 2026.
12	503	0.477681147950	Christopher Smolen, 2026.
12	504	0.478165562338	Christopher Smolen, 2026.
12	505	0.478464277378	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	506	0.478480888425	Christopher Smolen, 2026.
12	507	0.478767039495	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	508	0.478834234098	Vadim Borisov, 2026.
12	509	0.478834865947	Christopher Smolen, 2026.
12	510	0.479099183843	Christopher Smolen, 2026.
12	511	0.479137271671	Christopher Smolen, 2026.
12	512	0.479318144881	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	513	0.479348856672	Christopher Smolen, 2026.
12	514	0.479720827085	Vadim Borisov, 2026.
12	515	0.479727387264	Vadim Borisov, 2026.
12	516	0.479727477064	Christopher Smolen, 2026.
12	517	0.480061646352	Christopher Smolen, 2026.
12	518	0.480158176255	Christopher Smolen, 2026.
12	519	0.480424432739	Christopher Smolen, 2026.
12	520	0.480533780722	Christopher Smolen, 2026.
12	521	0.480864041301	Vadim Borisov, 2026.
12	522	0.480864939394	Christopher Smolen, 2026.
12	523	0.481263871865	Vadim Borisov, 2026.
12	524	0.481263938722	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	525	0.481298882801	Christopher Smolen, 2026.
12	526	0.481769652491	Christopher Smolen, 2026.
12	527	0.481792926630	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	528	0.481816668571	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	529	0.482103429982	Vadim Borisov, 2026.
12	530	0.482115741650	Vadim Borisov, 2026.
12	531	0.482116239483	Vadim Borisov, 2026.
12	532	0.482116279141	Christopher Smolen, 2026.
12	533	0.482691439309	Christopher Smolen, 2026.
12	534	0.482746075853	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	535	0.482900968217	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	536	0.483030629034	Christopher Smolen, 2026.
12	537	0.483093223073	Christopher Smolen, 2026.
12	538	0.483217955910	Vadim Borisov, 2026.
12	539	0.483218008239	Christopher Smolen, 2026.
12	540	0.483382710788	Vadim Borisov, 2026.
12	541	0.483382979112	Vadim Borisov, 2026.
12	542	0.483382989625	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	543	0.483747491562	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	544	0.483880861090	Christopher Smolen, 2026.
12	545	0.483951654104	Christopher Smolen, 2026.
12	546	0.484044747902	Christopher Smolen, 2026.
12	547	0.484339363143	Christopher Smolen, 2026.
12	548	0.484513936622	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	549	0.484546095498	Vadim Borisov, 2026.
12	550	0.484546148953	Christopher Smolen, 2026.
12	551	0.485174068050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	552	0.485304877585	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	553	0.485357059036	Christopher Smolen, 2026.
12	558	0.485524086032	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	559	0.485613296657	Christopher Smolen, 2026.
12	560	0.486036302840	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	561	0.486052575549	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	562	0.486314978749	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	563	0.486509579499	Christopher Smolen, 2026.
12	564	0.486579365294	Christopher Smolen, 2026.
12	565	0.486656879329	Christopher Smolen, 2026.
12	566	0.486738968468	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	567	0.486788101978	Christopher Smolen, 2026.
12	568	0.486971705283	Christopher Smolen, 2026.
12	569	0.487059387536	Vadim Borisov, 2026.
12	570	0.487059549831	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	571	0.487144137209	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	572	0.487159570940	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	573	0.487179460045	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	574	0.487452943017	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	575	0.487546146169	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	576	0.487552855718	Vadim Borisov, 2026.
12	577	0.487577049410	Vadim Borisov, 2026.
12	578	0.487591587131	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	579	0.488252421765	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	580	0.488264471391	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	581	0.488281425499	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	582	0.488281453189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	583	0.488281636825	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	584	0.488302732711	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	585	0.488330498376	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	586	0.488345250955	Vadim Borisov, 2026.
12	587	0.488350415563	Christopher Smolen, 2026.
12	588	0.488608494563	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	589	0.488631258541	Christopher Smolen, 2026.
12	590	0.488930545154	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	591	0.488954347678	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	592	0.489002111699	Vadim Borisov, 2026.
12	593	0.489002259516	Vadim Borisov, 2026.
12	594	0.489051587841	Vadim Borisov, 2026.
12	595	0.489055361776	Vadim Borisov, 2026.
12	596	0.489061472787	Vadim Borisov, 2026.
12	597	0.489407700439	Vadim Borisov, 2026.
12	598	0.489498075866	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	599	0.489505624200	Vadim Borisov, 2026.
12	600	0.489604231219	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	601	0.489686284318	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	602	0.489728543555	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	603	0.489781010149	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	604	0.489811922444	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	605	0.490269346433	Christopher Smolen, 2026.
12	606	0.490336108156	Christopher Smolen, 2026.
12	607	0.490357824523	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	608	0.490481779125	Christopher Smolen, 2026.
12	609	0.490532084600	Christopher Smolen, 2026.
12	610	0.490597152566	Christopher Smolen, 2026.
12	611	0.490684588740	Christopher Smolen, 2026.
12	612	0.490701527899	Christopher Smolen, 2026.
12	613	0.490898408700	Christopher Smolen, 2026.
12	614	0.490937242426	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	615	0.490973164506	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	616	0.490973174115	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	617	0.491011289160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	618	0.491403787541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	619	0.491419743993	Christopher Smolen, 2026.
12	620	0.491571418627	Christopher Smolen, 2026.
12	621	0.491650521129	Christopher Smolen, 2026.
12	622	0.491713926387	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	623	0.491745383077	Christopher Smolen, 2026.
12	624	0.491799753077	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	625	0.491851322017	Christopher Smolen, 2026.
12	626	0.491910385379	Christopher Smolen, 2026.
12	627	0.491950820634	Christopher Smolen, 2026.
12	628	0.492032286253	Christopher Smolen, 2026.
12	629	0.492052805809	Christopher Smolen, 2026.
12	630	0.492086942167	Christopher Smolen, 2026.
12	631	0.492121224471	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	632	0.492154060213	Vadim Borisov, 2026.
12	633	0.492157600171	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	634	0.492209663595	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	635	0.492307968685	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	636	0.492350024764	Christopher Smolen, 2026.
12	637	0.492372984246	Vadim Borisov, 2026.
12	638	0.492376718006	Christopher Smolen, 2026.
12	639	0.492427980434	Christopher Smolen, 2026.
12	640	0.492491926555	Christopher Smolen, 2026.
12	641	0.492522234054	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	642	0.492523385776	Christopher Smolen, 2026.
12	643	0.492547239603	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	644	0.492657068626	Christopher Smolen, 2026.
12	645	0.492707525945	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	646	0.492757470881	Christopher Smolen, 2026.
12	647	0.492853241313	Christopher Smolen, 2026.
12	648	0.493225647331	Christopher Smolen, 2026.
12	649	0.493305799103	Christopher Smolen, 2026.
12	650	0.493331854543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	651	0.493391612562	Christopher Smolen, 2026.
12	652	0.493414534091	Christopher Smolen, 2026.
12	653	0.493456144705	Vadim Borisov, 2026.
12	654	0.493464129587	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	655	0.493580867207	Christopher Smolen, 2026.
12	656	0.493608414913	Christopher Smolen, 2026.
12	657	0.493626848224	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	658	0.493746534241	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	659	0.493790091748	Christopher Smolen, 2026.
12	660	0.493819671949	Christopher Smolen, 2026.
12	661	0.493871906786	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	662	0.493926622008	Christopher Smolen, 2026.
12	663	0.493967424067	Vadim Borisov, 2026.
12	664	0.494073677853	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	665	0.494216686484	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	666	0.494266673738	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	667	0.494297477180	Christopher Smolen, 2026.
12	668	0.494333361032	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	669	0.494382019301	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	670	0.494519300641	Christopher Smolen, 2026.
12	671	0.494557906288	Christopher Smolen, 2026.
12	672	0.494615390948	Christopher Smolen, 2026.
12	673	0.494657199846	Vadim Borisov, 2026.
12	674	0.494664167639	Vadim Borisov, 2026.
12	675	0.494671430003	Vadim Borisov, 2026.
12	676	0.494681125765	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	677	0.494702537432	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	678	0.494724523643	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	679	0.494813769437	Christopher Smolen, 2026.
12	680	0.494848876489	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	681	0.494892228743	Christopher Smolen, 2026.
12	682	0.494992400641	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	683	0.495068502347	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	684	0.495092745677	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	685	0.495104067340	Christopher Smolen, 2026.
12	686	0.495125225116	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	687	0.495148827297	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	688	0.495230797785	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	689	0.495306181041	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	690	0.495364462695	Christopher Smolen, 2026.
12	691	0.495423463733	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	692	0.495454643049	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	693	0.495521808009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	694	0.495536088238	Christopher Smolen, 2026.
12	695	0.495564004329	Christopher Smolen, 2026.
12	696	0.495585882197	Christopher Smolen, 2026.
12	697	0.495631512750	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	698	0.495660760438	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	699	0.495711520561	Vadim Borisov, 2026.
12	700	0.495716303506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	701	0.495719312675	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	702	0.495720118270	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	703	0.495722806784	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	704	0.495727692869	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	705	0.495733765396	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	706	0.495735219613	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	707	0.495735876223	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	708	0.495740262437	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	709	0.495741552238	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	710	0.495743411814	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	711	0.495753542020	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	712	0.495761907423	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	713	0.495792674827	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	714	0.495793714964	Vadim Borisov, 2026.
12	715	0.495794037680	Vadim Borisov, 2026.
12	716	0.495794737052	Vadim Borisov, 2026.
12	717	0.495804371708	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	718	0.495807086188	Vadim Borisov, 2026.
12	719	0.495807336005	Vadim Borisov, 2026.
12	720	0.495807346343	Vadim Borisov, 2026.
12	721	0.495808381197	Vadim Borisov, 2026.
12	722	0.495808964629	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	723	0.495820111511	Vadim Borisov, 2026.
12	724	0.495823248393	Vadim Borisov, 2026.
12	725	0.495823416928	Vadim Borisov, 2026.
12	726	0.495824029410	Vadim Borisov, 2026.
12	727	0.495825621548	Vadim Borisov, 2026.
12	728	0.495826324661	Vadim Borisov, 2026.
12	729	0.495826417631	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	730	0.495830694753	Vadim Borisov, 2026.
12	731	0.495834202213	Vadim Borisov, 2026.
12	732	0.495836385979	Vadim Borisov, 2026.
12	733	0.495836474342	Vadim Borisov, 2026.
12	735	0.495839471192	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	736	0.495840787936	Vadim Borisov, 2026.
12	737	0.495853054687	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	738	0.495857468288	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	739	0.495864040150	Vadim Borisov, 2026.
12	740	0.495869436750	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	741	0.495872045108	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	742	0.495876452482	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	743	0.495879726984	Vadim Borisov, 2026.
12	744	0.495882893668	Vadim Borisov, 2026.
12	747	0.495884668549	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	749	0.495885959020	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	750	0.495893530224	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	752	0.495897324324	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	756	0.495899329165	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
12	757	0.495901390631	Vadim Borisov, 2026.
12	758	0.495902944723	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
12	759	0.495904486360	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	760	0.495908093086	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	761	0.495911883629	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	762	0.495912967389	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	763	0.495914549890	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	764	0.495916190443	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	765	0.495917089852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	766	0.495918060991	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	767	0.495919992244	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	768	0.495921007480	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	769	0.495926102377	Vadim Borisov, 2026.
12	770	0.495928459408	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	771	0.495928620573	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	772	0.495929228813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	773	0.495929539377	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	774	0.495930630055	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	775	0.495930884561	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	776	0.495934624622	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	777	0.495939445945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	778	0.495942599211	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	779	0.495943229358	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	780	0.495947077664	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	781	0.495964157916	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	782	0.495973819314	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	783	0.496027291378	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	784	0.496031184562	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	785	0.496033902247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	786	0.496036264975	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	787	0.496042499682	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	788	0.496045837586	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	789	0.496049728678	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	790	0.496050391206	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	791	0.496052860521	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	792	0.496113131743	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	793	0.496171870769	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	794	0.496185669522	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	795	0.496193580026	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	796	0.496196975717	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	797	0.496198047690	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	798	0.496198551966	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	799	0.496638406062	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	800	0.496681970826	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	801	0.497243295431	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	802	0.497272936007	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	803	0.497404059695	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	804	0.497711061180	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	805	0.497752304100	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	806	0.497884517896	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	807	0.498049149659	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	808	0.498061992020	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	809	0.498092386988	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	810	0.498277634091	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	811	0.498335240352	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	812	0.498343222964	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	813	0.498352517608	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	814	0.498360740405	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	815	0.498362057534	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	816	0.498394986010	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	817	0.498401219584	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	818	0.498406984175	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	819	0.498412793942	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	820	0.498441420377	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	821	0.498443401191	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	822	0.498447907548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	823	0.498450154574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	824	0.498455656538	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	825	0.498475210477	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	826	0.498497511689	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	827	0.498505656942	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	828	0.498515855744	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	829	0.498520530078	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	830	0.498649167924	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	831	0.498695679609	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	832	0.498764703918	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	833	0.498771690167	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	834	0.498840424247	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	835	0.498866497189	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	836	0.498873906967	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	837	0.498896861768	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	838	0.498950215865	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	839	0.498954599906	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	840	0.499711582800	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	841	0.499999935708	Christopher Smolen, 2026.
12	842	0.500899990718	Henry Cohn, 2026.
12	843	0.503237075349	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	844	0.504401012175	Henry Cohn, 2026.
12	845	0.505905064596	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	846	0.506628789902	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	847	0.507513825954	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	848	0.508301607948	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	849	0.508582934281	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	850	0.509816206998	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	851	0.510751954758	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	852	0.511401014313	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	853	0.512508193831	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	854	0.512795139707	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	855	0.513201784080	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	856	0.513806622731	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	857	0.514180933343	Vadim Borisov, 2026.
12	858	0.514180979678	Vadim Borisov, 2026.
12	859	0.514181472653	Vadim Borisov, 2026.
12	860	0.514181955500	Vadim Borisov, 2026.
12	861	0.514182281100	Vadim Borisov, 2026.
12	862	0.514185319006	Vadim Borisov, 2026.
12	863	0.514185339280	Vadim Borisov, 2026.
12	864	0.514185346023	Vadim Borisov, 2026.
12	865	0.514185369060	Vadim Borisov, 2026.
12	866	0.514185379500	Vadim Borisov, 2026.
12	867	0.514185415273	Vadim Borisov, 2026.
12	868	0.514185430078	Vadim Borisov, 2026.
12	869	0.514185471899	Christopher Smolen, 2026.
12	870	0.515532682567	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	871	0.515596897096	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	872	0.516110100543	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	875	0.516888840749	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	876	0.517087430337	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	877	0.517158809704	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	878	0.517165493071	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	879	0.517194458464	Vadim Borisov, 2026.
12	880	0.517196576136	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	881	0.517710171615	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	882	0.517763818574	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	883	0.519496762025	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	884	0.521633821758	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	885	0.522329703069	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	886	0.522529017022	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	887	0.522550387289	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	888	0.522921491505	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	889	0.523055729818	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	890	0.523200092836	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	892	0.523823887259	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	893	0.523906735509	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	894	0.523927335313	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	896	0.523994856300	Vadim Borisov, 2026.
12	897	0.523994868988	Christopher Smolen, 2026.
12	898	0.524341681184	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	899	0.524392486984	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	900	0.524560375054	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	901	0.525281036051	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	902	0.525300029186	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	903	0.525306328181	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	904	0.525306465515	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	905	0.525803408049	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	906	0.525925124690	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	907	0.526598159178	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	908	0.526829191895	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	911	0.526832032150	Vadim Borisov, 2026.
12	912	0.526911985232	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	913	0.526913182122	Vadim Borisov, 2026.
12	914	0.526913201425	Vadim Borisov, 2026.
12	915	0.526935444999	Vadim Borisov, 2026.
12	916	0.527061420367	Vadim Borisov, 2026.
12	917	0.527141950300	Vadim Borisov, 2026.
12	918	0.527365656632	Vadim Borisov, 2026.
12	919	0.527426633253	Vadim Borisov, 2026.
12	920	0.527887857670	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	921	0.528123036173	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	922	0.528153831615	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	924	0.528214952502	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	925	0.528236524654	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	926	0.528253081172	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	927	0.528313998937	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	928	0.528327838024	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	929	0.528334905171	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	930	0.528350069434	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	931	0.528361461889	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	932	0.528918265964	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	933	0.529113514491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	934	0.529462118014	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	935	0.529529658153	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	936	0.529575703734	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	937	0.529604557176	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	938	0.529879555674	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	939	0.530577461258	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	940	0.530652074199	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	941	0.531052056506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	942	0.531285310124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	943	0.531654252787	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	944	0.531852921228	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	945	0.532270081051	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	946	0.533323419332	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	948	0.533332280461	Vadim Borisov, 2026.
12	949	0.533402870420	Henry Cohn, 2026.
12	950	0.533714776622	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	951	0.533778422210	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	952	0.533849321052	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	953	0.534140680225	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	954	0.534149430538	Vadim Borisov, 2026.
12	955	0.534404509073	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	956	0.534428549125	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	957	0.534812058457	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	958	0.534982374234	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	959	0.535067708125	Vadim Borisov, 2026.
12	960	0.535067845547	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	961	0.535097792049	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	962	0.536186135615	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	963	0.536278162757	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	964	0.536477243962	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	965	0.536666970709	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	966	0.536936179913	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
12	967	0.537015091067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	968	0.537312300498	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
12	970	0.537348855873	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	971	0.537801439349	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	972	0.538082044871	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	973	0.538214058106	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	974	0.538464855109	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	975	0.538933904906	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	976	0.538942990429	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	977	0.539009716854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	978	0.539142483726	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	979	0.539215883731	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	980	0.539292130021	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	981	0.539377939373	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	982	0.539712860102	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	983	0.539826737191	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	984	0.539924699087	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	985	0.540073065405	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	986	0.540143505669	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	987	0.541000373123	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	988	0.541115087625	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	989	0.541204180001	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
12	990	0.541218158669	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	991	0.541339080243	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	992	0.541496760733	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	993	0.541605687417	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	994	0.541727866817	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	995	0.541783057094	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	996	0.541878333730	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	997	0.541984267572	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	998	0.542102854711	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
12	1000	0.543294868264	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
12	1023	0.546918158873	Henry Cohn, 2026.
12	1024	0.546918158972	Henry Cohn, 2026.
13	27	0.057072523783	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $1573 x^{3} - 169 x^{2} - 13 x + 1$
13	28	0.066666666667	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $15 x - 1$
13	29	0.068098609479	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $2576 x^{4} - 640 x^{3} - 184 x^{2} + 1$
13	30	0.071714034728	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $55 x^{2} + 10 x - 1$
13	31	0.071714034728	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $55 x^{2} + 10 x - 1$
13	32	0.071714034728	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996. $55 x^{2} + 10 x - 1$
13	33	0.089833578043	Henry Cohn, 2026.
13	34	0.090095382331	Henry Cohn, 2023.
13	36	0.092610094433	H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $95 x^{2} + 2 x - 1$
13	37	0.111409136725	Henry Cohn, 2023.
13	38	0.112004618870	Henry Cohn, 2023. $44 x^{2} + 4 x - 1$
13	39	0.116893063508	Henry Cohn, 2024.
13	40	0.121353571480	Henry Cohn, 2026.
13	41	0.124055818526	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	42	0.125	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $8 x - 1$
13	44	0.126079252818	Henry Cohn, 2025. $6095 x^{2} - 126 x - 81$
13	48	0.126131983623	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $47 x^{2} + 2 x - 1$
13	49	0.141095436175	Henry Cohn, 2025.
13	50	0.142459427551	Henry Cohn, 2023. Minimal polynomial of degree 12
13	51	0.145120831484	Henry Cohn, 2023. Minimal polynomial of degree 10
13	52	0.147159522238	Henry Cohn, 2023. $613567 x^{7} + 96585 x^{6} - 98333 x^{5} - 8219 x^{4} + 381 x^{3} + 539 x^{2} + 33 x - 9$
13	53	0.147908231498	Henry Cohn, 2026.
13	54	0.148576022240	Henry Cohn, 2025.
13	55	0.148805252884	Henry Cohn, 2024.
13	56	0.148975682089	Henry Cohn, 2023.
13	57	0.166162190421	Henry Cohn, 2024.
13	60	0.171378280884	Luke Granto, 2026. $1196 x^{4} - 1428 x^{3} + 411 x^{2} + 18 x - 9$
13	61	0.177435551107	Henry Cohn, 2026.
13	62	0.179872103330	Antoine Jay, 2026.
13	66	0.180076545649	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $197541 x^{6} - 1327980 x^{5} + 842815 x^{4} + 93800 x^{3} - 58725 x^{2} + 500 x + 625$
13	67	0.183425281073	Antoine Jay, 2026.
13	68	0.185161141336	Antoine Jay, 2026. $6 x^{3} + 283 x^{2} - 4 x - 9$
13	69	0.192954195111	Antoine Jay, 2026.
13	70	0.201822978078	Antoine Jay, 2026.
13	71	0.204507858381	Henry Cohn, 2026.
13	72	0.205033933572	Antoine Jay, 2026.
13	73	0.206967499369	Antoine Jay, 2026.
13	74	0.208755346974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	75	0.209830747287	Antoine Jay, 2026.
13	76	0.210888412169	Antoine Jay, 2026.
13	77	0.211602349074	Antoine Jay, 2026.
13	84	0.214312873432	Antoine Jay, 2026. $156001 x^{4} - 83068 x^{3} + 2534 x^{2} + 1732 x + 1$
13	85	0.222890239859	Antoine Jay, 2026.
13	86	0.227472980930	Antoine Jay, 2026.
13	87	0.233139140724	Antoine Jay, 2026.
13	88	0.234760407328	Antoine Jay, 2026.
13	89	0.237891400437	Antoine Jay, 2026.
13	90	0.241063931066	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	91	0.241934021280	Antoine Jay, 2026.
13	92	0.242876105918	Antoine Jay, 2026.
13	93	0.243639876215	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	94	0.244020165609	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	95	0.244097836133	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	96	0.244262859504	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	97	0.244358041009	Antoine Jay, 2026.
13	98	0.244460179194	Antoine Jay, 2026.
13	99	0.244875924329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	100	0.246669288331	Antoine Jay, 2026.
13	101	0.249341456786	Henry Cohn, 2026.
13	104	0.25	J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4 x - 1$
13	106	0.251575083557	Henry Cohn, 2026. $1031 x^{2} - 160 x - 25$
13	107	0.257276958698	Antoine Jay, 2026.
13	108	0.258154822753	Antoine Jay, 2026.
13	109	0.258529012806	Antoine Jay, 2026.
13	110	0.258940816433	Antoine Jay, 2026.
13	111	0.259510876672	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	112	0.260459144444	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	113	0.261281196369	Arhan Canli, 2026.
13	114	0.263092922077	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	115	0.264237646845	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	116	0.265769989214	Antoine Jay, 2026.
13	117	0.267439833565	Antoine Jay, 2026.
13	118	0.269171781398	Henry Cohn, 2026.
13	119	0.270144839056	Henry Cohn, 2026.
13	120	0.271249760569	Antoine Jay, 2026.
13	121	0.271315922618	Antoine Jay, 2026.
13	122	0.271455594866	Arhan Canli, 2026.
13	123	0.272084487026	Arhan Canli, 2026.
13	124	0.275380071346	Antoine Jay, 2026.
13	125	0.276023194131	Antoine Jay, 2026.
13	126	0.276107131865	Arhan Canli, 2026.
13	127	0.277969217270	Arhan Canli, 2026.
13	128	0.280087878273	Arhan Canli, 2026.
13	129	0.282295316493	Arhan Canli, 2026.
13	130	0.284578933880	Arhan Canli, 2026.
13	131	0.285522656248	Arhan Canli, 2026.
13	132	0.285875352542	Antoine Jay, 2026.
13	133	0.286588654159	Antoine Jay, 2026.
13	134	0.287345920775	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	135	0.289017972298	Antoine Jay, 2026.
13	136	0.289759756734	Antoine Jay, 2026.
13	137	0.290794448960	Antoine Jay, 2026.
13	138	0.291248136063	Antoine Jay, 2026.
13	139	0.291298832564	Antoine Jay, 2026.
13	140	0.294790367807	Antoine Jay, 2026.
13	141	0.295463243126	Antoine Jay, 2026.
13	142	0.295615159190	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	143	0.295628971601	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	144	0.295790772402	Vadim Borisov, 2026.
13	145	0.295869336953	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	146	0.295945120108	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	147	0.295980470398	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	148	0.296005726259	Antoine Jay, 2026.
13	149	0.296412545845	Antoine Jay, 2026.
13	150	0.296435301088	Antoine Jay, 2026.
13	154	0.296449269170	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $183325 x^{4} - 90460 x^{3} + 8458 x^{2} + 636 x + 9$
13	176	0.299119474480	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $49 x^{2} - 18 x + 1$
13	177	0.301650609168	Antoine Jay, 2026.
13	178	0.303075971297	Antoine Jay, 2026.
13	179	0.307392491149	Antoine Jay, 2026.
13	180	0.309270950113	Antoine Jay, 2026.
13	181	0.310827645083	Antoine Jay, 2026.
13	182	0.311782694311	Antoine Jay, 2026.
13	183	0.312956723731	Antoine Jay, 2026.
13	184	0.313909978515	Arhan Canli, 2026.
13	185	0.315292188827	Antoine Jay, 2026.
13	186	0.316497914744	Antoine Jay, 2026.
13	187	0.317946075836	Antoine Jay, 2026.
13	188	0.318959088333	Antoine Jay, 2026.
13	189	0.320237550814	Antoine Jay, 2026.
13	190	0.320944781477	Antoine Jay, 2026.
13	191	0.321570328548	Antoine Jay, 2026.
13	192	0.322676208247	Antoine Jay, 2026.
13	193	0.324870043749	Antoine Jay, 2026.
13	194	0.327584852394	Antoine Jay, 2026.
13	195	0.327695105949	Arhan Canli, 2026.
13	196	0.327826018761	Antoine Jay, 2026.
13	197	0.328231571972	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	198	0.328497512673	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	199	0.328793304095	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	200	0.328886220832	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	201	0.329056164783	Antoine Jay, 2026.
13	202	0.329150216336	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	203	0.331688526164	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	208	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
13	209	0.339851756282	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	210	0.340536712247	Antoine Jay, 2026.
13	211	0.341197868910	Antoine Jay, 2026.
13	212	0.341490596027	Antoine Jay, 2026.
13	213	0.343248434239	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	214	0.343250007197	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	215	0.343257191106	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	216	0.343266349722	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	217	0.343268572808	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	218	0.343285757885	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	219	0.344395594904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	220	0.346073882890	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	221	0.349465928624	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	222	0.353029742369	Antoine Jay, 2026.
13	223	0.355631140274	Antoine Jay, 2026.
13	224	0.357685297851	Antoine Jay, 2026.
13	225	0.359294983427	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	226	0.361082833150	Antoine Jay, 2026.
13	228	0.361567226955	Antoine Jay, 2026.
13	229	0.364162625998	Antoine Jay, 2026.
13	230	0.365230967695	Antoine Jay, 2026.
13	231	0.366950467054	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	232	0.367413068185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	233	0.368378420609	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
13	240	0.368421052632	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $19 x - 7$
13	249	0.368421052632	Henry Cohn, 2026. $19 x - 7$
13	250	0.369004587146	Antoine Jay, 2026.
13	251	0.369226584609	Antoine Jay, 2026.
13	252	0.372079320418	Antoine Jay, 2026.
13	254	0.372363087871	Antoine Jay, 2026.
13	255	0.373587581815	Antoine Jay, 2026.
13	291	0.376384967370	Antoine Jay, 2026. $23 x^{2} - 6 x - 1$
13	292	0.380112009066	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	293	0.380268413387	Christopher Smolen, 2026.
13	294	0.382291288481	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	295	0.383222724994	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	296	0.383901528558	Christopher Smolen, 2026.
13	306	0.384615384616	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $13 x - 5$
13	313	0.384615384616	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $13 x - 5$
13	314	0.389008084400	Christopher Smolen, 2026.
13	315	0.391707557207	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	316	0.392373552618	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	317	0.393918259100	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	319	0.394295782358	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	320	0.396286326515	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	321	0.396994874949	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	322	0.397156815950	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	336	0.4	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $5 x - 2$
13	337	0.4	Henry Cohn, 2026. $5 x - 2$
13	339	0.4	Antoine Jay, 2026. $5 x - 2$
13	340	0.405512502897	Christopher Smolen, 2026.
13	341	0.405753838001	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	342	0.406025137933	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	343	0.406208389465	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	344	0.406228276563	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	345	0.406334465995	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	346	0.406421528689	Vadim Borisov, 2026.
13	347	0.407401127095	Antoine Jay, 2026.
13	348	0.407703315451	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	349	0.407728617937	Vadim Borisov, 2026.
13	350	0.408311830498	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	351	0.411013162111	Christopher Smolen, 2026.
13	352	0.411568128653	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	353	0.412256768972	Christopher Smolen, 2026.
13	354	0.412853016123	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	355	0.412962197941	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	356	0.413165314906	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	357	0.413337575726	Christopher Smolen, 2026.
13	358	0.415099028334	Antoine Jay, 2026.
13	359	0.415594541546	Antoine Jay, 2026.
13	360	0.416302575534	Christopher Smolen, 2026.
13	383	0.416666666667	Henry Cohn, 2026. $12 x - 5$
13	384	0.418832284307	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	385	0.419421072224	Christopher Smolen, 2026.
13	386	0.421197754986	Christopher Smolen, 2026.
13	387	0.421358832146	Christopher Smolen, 2026.
13	388	0.421967794724	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	389	0.423826636473	Christopher Smolen, 2026.
13	390	0.424212487544	Christopher Smolen, 2026.
13	391	0.424689090593	Christopher Smolen, 2026.
13	392	0.425193405834	Christopher Smolen, 2026.
13	393	0.425962383160	Christopher Smolen, 2026.
13	394	0.426077636809	Christopher Smolen, 2026.
13	395	0.427199116563	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	396	0.427298709580	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	397	0.427541857485	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	416	0.428571428572	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 3$
13	492	0.428571428572	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $7 x - 3$
13	498	0.428571428572	Henry Cohn, 2026. $7 x - 3$
13	499	0.428626358292	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
13	500	0.429496475352	Christopher Smolen, 2026.
13	501	0.429500199023	Christopher Smolen, 2026.
13	502	0.429673368561	Christopher Smolen, 2026.
13	503	0.429681972878	Christopher Smolen, 2026.
13	504	0.429684733638	Christopher Smolen, 2026.
13	505	0.433941909824	Christopher Smolen, 2026.
13	506	0.434215033705	Vadim Borisov, 2026.
13	507	0.434216435007	Vadim Borisov, 2026.
13	508	0.434217032292	Vadim Borisov, 2026.
13	509	0.434217182933	Vadim Borisov, 2026.
13	510	0.434217308288	Vadim Borisov, 2026.
13	511	0.434217774368	Vadim Borisov, 2026.
13	512	0.434218600081	Christopher Smolen, 2026.
13	513	0.434240823964	Vadim Borisov, 2026.
13	514	0.434241060486	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	516	0.434241400270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	517	0.434243952176	Vadim Borisov, 2026.
13	518	0.434243952839	Vadim Borisov, 2026.
13	519	0.434243979581	Vadim Borisov, 2026.
13	527	0.434245160803	Vadim Borisov, 2026.
13	528	0.434248018060	Vadim Borisov, 2026.
13	529	0.434249152841	Vadim Borisov, 2026.
13	530	0.434249476993	Vadim Borisov, 2026.
13	531	0.434249773626	Christopher Smolen, 2026.
13	532	0.434251106359	Vadim Borisov, 2026.
13	533	0.434252035357	Vadim Borisov, 2026.
13	534	0.435317559521	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	540	0.435541081501	Henry Cohn, 2026.
13	546	0.435541081501	Vadim Borisov, 2026.
13	547	0.435541136766	Vadim Borisov, 2026.
13	548	0.435541339531	Vadim Borisov, 2026.
13	549	0.436167816649	Christopher Smolen, 2026.
13	551	0.437043915478	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	552	0.438351941993	Vadim Borisov, 2026.
13	553	0.438740218306	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	556	0.439466688999	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	557	0.440731743321	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	558	0.442716423656	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	560	0.443045755481	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	561	0.443154350852	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	562	0.444205452611	Vadim Borisov, 2026.
13	563	0.444220026952	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	567	0.445545276769	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	574	0.447773802820	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	575	0.447788147884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	576	0.448520421339	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	578	0.450454679460	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	580	0.451661771518	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	582	0.453061134337	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	587	0.455212899795	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	592	0.456137142913	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	593	0.456349000398	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	594	0.456667665984	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	596	0.456669277739	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	599	0.458069206058	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	600	0.458403851970	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	601	0.459736769346	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	602	0.459737630156	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	603	0.459738940338	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	604	0.461183856436	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	605	0.461505986097	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	606	0.462014594856	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	608	0.462760385906	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	612	0.463626537941	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	614	0.464263386194	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	616	0.464542124005	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	617	0.464601828619	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	618	0.465506099463	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	619	0.466195338740	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	622	0.466773871177	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	623	0.467257248828	Vadim Borisov, 2026.
13	624	0.467257252519	Christopher Smolen, 2026.
13	625	0.467321827246	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	626	0.467363042064	Christopher Smolen, 2026.
13	627	0.467441287110	Christopher Smolen, 2026.
13	628	0.467539317589	Christopher Smolen, 2026.
13	629	0.467649767131	Vadim Borisov, 2026.
13	630	0.467690084920	Christopher Smolen, 2026.
13	631	0.469220568659	Christopher Smolen, 2026.
13	632	0.469478433173	Christopher Smolen, 2026.
13	633	0.470306418049	Christopher Smolen, 2026.
13	634	0.470981060149	Christopher Smolen, 2026.
13	635	0.471590785574	Christopher Smolen, 2026.
13	636	0.472064311748	Christopher Smolen, 2026.
13	637	0.472520625252	Christopher Smolen, 2026.
13	638	0.473147587676	Christopher Smolen, 2026.
13	639	0.473598381344	Christopher Smolen, 2026.
13	640	0.474079991067	Christopher Smolen, 2026.
13	641	0.474301800062	Christopher Smolen, 2026.
13	642	0.474851377759	Christopher Smolen, 2026.
13	644	0.475	Henry Cohn, 2026. $40 x - 19$
13	645	0.476047768259	Christopher Smolen, 2026.
13	646	0.476501055437	Christopher Smolen, 2026.
13	647	0.476809822398	Christopher Smolen, 2026.
13	648	0.477170199458	Christopher Smolen, 2026.
13	649	0.477412844177	Christopher Smolen, 2026.
13	650	0.477527666987	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	651	0.477707958409	Vadim Borisov, 2026.
13	652	0.477912116404	Vadim Borisov, 2026.
13	653	0.478129025447	Christopher Smolen, 2026.
13	654	0.478243998249	Christopher Smolen, 2026.
13	655	0.478402436259	Christopher Smolen, 2026.
13	656	0.478406374911	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	657	0.478558036966	Vadim Borisov, 2026.
13	658	0.478726876392	Vadim Borisov, 2026.
13	659	0.478899195284	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	660	0.479072808334	Vadim Borisov, 2026.
13	661	0.479296311648	Christopher Smolen, 2026.
13	662	0.479438478218	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	663	0.479588381200	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	664	0.479697094581	Christopher Smolen, 2026.
13	665	0.479829396581	Christopher Smolen, 2026.
13	666	0.479905152168	Christopher Smolen, 2026.
13	667	0.480038348070	Christopher Smolen, 2026.
13	668	0.480129140445	Vadim Borisov, 2026.
13	669	0.480283255723	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	670	0.480410654397	Vadim Borisov, 2026.
13	671	0.480609126468	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	672	0.480729161454	Christopher Smolen, 2026.
13	673	0.480863547601	Christopher Smolen, 2026.
13	674	0.480967384602	Christopher Smolen, 2026.
13	675	0.481089883656	Christopher Smolen, 2026.
13	676	0.481203672466	Christopher Smolen, 2026.
13	677	0.481317637683	Christopher Smolen, 2026.
13	678	0.481378213843	Christopher Smolen, 2026.
13	679	0.481875529287	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	680	0.481881455600	Vadim Borisov, 2026.
13	681	0.481887841303	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	682	0.482305128087	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	683	0.482361333329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	684	0.482366278701	Vadim Borisov, 2026.
13	685	0.482370922940	Vadim Borisov, 2026.
13	686	0.482372439935	Vadim Borisov, 2026.
13	687	0.482377691322	Vadim Borisov, 2026.
13	688	0.482377742420	Vadim Borisov, 2026.
13	689	0.482377754589	Christopher Smolen, 2026.
13	690	0.482510677543	Christopher Smolen, 2026.
13	691	0.482512066536	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	692	0.482721915061	Vadim Borisov, 2026.
13	693	0.482721930007	Christopher Smolen, 2026.
13	694	0.483000399387	Vadim Borisov, 2026.
13	695	0.483011206910	Vadim Borisov, 2026.
13	696	0.483011368722	Vadim Borisov, 2026.
13	697	0.483011369818	Christopher Smolen, 2026.
13	698	0.483290874051	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	699	0.483291665030	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	700	0.483292161010	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	701	0.484145066498	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	702	0.484177317546	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	703	0.484184522690	Vadim Borisov, 2026.
13	704	0.484191932888	Vadim Borisov, 2026.
13	705	0.484191943764	Vadim Borisov, 2026.
13	706	0.484191945298	Christopher Smolen, 2026.
13	707	0.484322980252	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	708	0.484336880594	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	709	0.484355012980	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	710	0.484370354954	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	711	0.484386099537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	712	0.484388596476	Vadim Borisov, 2026.
13	713	0.484394592874	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	714	0.484400815956	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	715	0.484513203411	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	716	0.484568378930	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	717	0.484580214731	Vadim Borisov, 2026.
13	718	0.484584027570	Christopher Smolen, 2026.
13	719	0.484794831142	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	720	0.484826133371	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	721	0.484845792594	Vadim Borisov, 2026.
13	722	0.484855342152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	723	0.484862339427	Christopher Smolen, 2026.
13	724	0.484943884520	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	725	0.484956500027	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	726	0.485547962060	Christopher Smolen, 2026.
13	727	0.485565757541	Christopher Smolen, 2026.
13	728	0.485635280869	Christopher Smolen, 2026.
13	730	0.485666653229	Vadim Borisov, 2026.
13	731	0.485666668817	Christopher Smolen, 2026.
13	732	0.485776887665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	733	0.485831649455	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	734	0.485834755536	Vadim Borisov, 2026.
13	735	0.485850340310	Vadim Borisov, 2026.
13	736	0.485850863696	Vadim Borisov, 2026.
13	737	0.485851138449	Vadim Borisov, 2026.
13	738	0.485851548609	Vadim Borisov, 2026.
13	739	0.485851612899	Vadim Borisov, 2026.
13	740	0.485851621923	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	741	0.486269155613	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	742	0.486299722996	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	743	0.486316819003	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	744	0.486365667456	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	745	0.486367013199	Christopher Smolen, 2026.
13	746	0.486708564842	Christopher Smolen, 2026.
13	747	0.486724007086	Vadim Borisov, 2026.
13	748	0.486724447203	Vadim Borisov, 2026.
13	749	0.486724447556	Vadim Borisov, 2026.
13	750	0.486724472487	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	751	0.486737312140	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	752	0.486765437086	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	753	0.486809596082	Vadim Borisov, 2026.
13	754	0.486811013098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	755	0.486817988837	Vadim Borisov, 2026.
13	756	0.486822410067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	757	0.487089390257	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	758	0.487090607679	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	759	0.487167934162	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	760	0.487171982439	Vadim Borisov, 2026.
13	761	0.487180409041	Vadim Borisov, 2026.
13	762	0.487183974341	Vadim Borisov, 2026.
13	763	0.487184286682	Vadim Borisov, 2026.
13	764	0.487184675218	Vadim Borisov, 2026.
13	765	0.487184857193	Vadim Borisov, 2026.
13	766	0.487184865884	Christopher Smolen, 2026.
13	767	0.487327253214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	768	0.487816942880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	769	0.487823470086	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	771	0.487893791227	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	772	0.487900870004	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	773	0.487904526390	Vadim Borisov, 2026.
13	774	0.487906880173	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	775	0.487908100227	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	776	0.487951520769	Vadim Borisov, 2026.
13	777	0.487951558346	Vadim Borisov, 2026.
13	778	0.487951560291	Vadim Borisov, 2026.
13	779	0.487951563315	Vadim Borisov, 2026.
13	780	0.487951568243	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	781	0.488341569404	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	782	0.488350379886	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	783	0.488370808202	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	784	0.488402155868	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	785	0.488422100686	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	786	0.488453673226	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	787	0.488454242841	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	788	0.488464928642	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	789	0.488476028179	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	790	0.488484781839	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	791	0.488488896203	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	792	0.488507032245	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	793	0.488515769788	Vadim Borisov, 2026.
13	794	0.488519284969	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	795	0.488537674145	Vadim Borisov, 2026.
13	796	0.488541238848	Vadim Borisov, 2026.
13	797	0.488543124344	Christopher Smolen, 2026.
13	798	0.488676046610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	799	0.488676072256	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	800	0.488678672523	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	801	0.488678837475	Vadim Borisov, 2026.
13	802	0.488679404537	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	803	0.488767559161	Vadim Borisov, 2026.
13	804	0.488767660091	Christopher Smolen, 2026.
13	805	0.488975469206	Vadim Borisov, 2026.
13	806	0.488978911411	Vadim Borisov, 2026.
13	807	0.488979195486	Christopher Smolen, 2026.
13	808	0.489023429819	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	809	0.489166732618	Vadim Borisov, 2026.
13	810	0.489168985324	Vadim Borisov, 2026.
13	811	0.489170004842	Vadim Borisov, 2026.
13	812	0.489170093927	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	813	0.489315263615	Vadim Borisov, 2026.
13	814	0.489317856180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	815	0.489333073024	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	816	0.489344410842	Vadim Borisov, 2026.
13	817	0.489353400984	Vadim Borisov, 2026.
13	818	0.489357866958	Henry Cohn, 2026.
13	819	0.489808022883	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	820	0.489825549851	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	821	0.489847681048	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	822	0.489848820764	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	823	0.489869409257	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	824	0.489873126185	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	826	0.489874500636	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
13	827	0.489900518322	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	828	0.489904347502	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
13	829	0.490360659016	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	830	0.490391116865	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	831	0.490400605562	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	832	0.490411943573	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	833	0.490419642984	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	834	0.490428220117	Vadim Borisov, 2026.
13	835	0.490435022006	Vadim Borisov, 2026.
13	836	0.490437003339	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	837	0.490783903694	Vadim Borisov, 2026.
13	838	0.490783933769	Christopher Smolen, 2026.
13	839	0.490931817610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	840	0.490938418469	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	841	0.491259758160	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
13	842	0.491737098040	Henry Cohn, 2026.
13	843	0.491838706873	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	845	0.491855184869	Vadim Borisov, 2026.
13	846	0.491855354013	Vadim Borisov, 2026.
13	847	0.491861719037	Vadim Borisov, 2026.
13	848	0.491862399739	Vadim Borisov, 2026.
13	849	0.491863069350	Vadim Borisov, 2026.
13	850	0.491863076709	Vadim Borisov, 2026.
13	851	0.491863077737	Vadim Borisov, 2026.
13	852	0.491863155526	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	853	0.492552996901	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	854	0.492585118746	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	855	0.492604108852	Vadim Borisov, 2026.
13	856	0.492611340022	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	857	0.492631094298	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	858	0.492671984558	Vadim Borisov, 2026.
13	859	0.492677041710	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	860	0.493149731792	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	861	0.493186816260	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	862	0.493207234690	Vadim Borisov, 2026.
13	863	0.493214741817	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	864	0.493784665237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	865	0.493849906508	Vadim Borisov, 2026.
13	866	0.493849932128	Christopher Smolen, 2026.
13	867	0.494207140977	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	868	0.494278201085	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	869	0.494564980029	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	870	0.494596968111	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	871	0.494632992745	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	872	0.494644193164	Christopher Smolen, 2026.
13	873	0.494878688036	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	874	0.494895516997	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	875	0.494915483886	Vadim Borisov, 2026.
13	876	0.494918533248	Vadim Borisov, 2026.
13	877	0.494924003576	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	878	0.495184599377	Christopher Smolen, 2026.
13	879	0.495568121095	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	880	0.495589111613	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	881	0.495628376582	Vadim Borisov, 2026.
13	882	0.495634948353	Henry Cohn, 2026.
13	883	0.496810653743	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	884	0.496892064855	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	885	0.496924113202	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	886	0.496944408413	Christopher Smolen, 2026.
13	887	0.497641239884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	888	0.497665852180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	889	0.497685881177	Christopher Smolen, 2026.
13	890	0.498442550770	Henry Cohn, 2026.
13	891	0.498618079040	Christopher Smolen, 2026.
13	892	0.498797485746	Henry Cohn, 2026.
13	893	0.499137028079	Vadim Borisov, 2026.
13	894	0.499137243596	Vadim Borisov, 2026.
13	895	0.499137321641	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	896	0.499178189329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
13	897	0.499526120612	Christopher Smolen, 2026.
13	1024	0.5	Subcode of a kissing configuration from J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3. $2 x - 1$
14	29	0.053426987342	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $2016 x^{3} - 196 x^{2} - 14 x + 1$
14	30	0.0625	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. $16 x - 1$
14	31	0.067582771839	H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14	32	0.071430901841	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14	33	0.071678780313	Henry Cohn, 2025.
14	34	0.071706747799	Henry Cohn, 2025.
14	36	0.080003299193	Henry Cohn, 2023. $2156 x^{2} + 140 x - 25$
14	37	0.087892856445	Henry Cohn, 2023. Minimal polynomial of degree 14
14	38	0.092604004700	Henry Cohn, 2025.
14	39	0.094407135777	Henry Cohn, 2023. Minimal polynomial of degree 12
14	42	0.1	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $10 x - 1$
14	43	0.112004618870	Henry Cohn and Ilmari Vahteristo, 2026. $44 x^{2} + 4 x - 1$
14	45	0.112912613537	Henry Cohn, 2023. $167 x^{2} - 10 x - 1$
14	46	0.114212424977	Henry Cohn, 2024.
14	47	0.114744370065	Henry Cohn, 2026.
14	48	0.114785923011	Henry Cohn, 2023. $1988352 x^{8} + 1963008 x^{7} - 108672 x^{6} - 513152 x^{5} - 92592 x^{4} + 19616 x^{3} + 5240 x^{2} + 72 x - 81$
14	49	0.125031168050	Henry Cohn, 2025.
14	50	0.126129943174	Henry Cohn, 2025.
14	52	0.126131983623	Henry Cohn, 2023. $47 x^{2} + 2 x - 1$
14	53	0.127206262662	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	54	0.135105514018	Antoine Jay, 2026.
14	55	0.136745922263	Henry Cohn, 2023.
14	56	0.139995309534	Antoine Jay, 2026.
14	57	0.142105817153	Antoine Jay, 2026.
14	64	0.142857142858	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $7 x - 1$
14	65	0.165287555076	Henry Cohn, 2024. $25600 x^{4} - 5616 x^{3} - 2736 x^{2} + 81$
14	70	0.166666666667	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $6 x - 1$
14	71	0.177427267176	Henry Cohn, 2024. $196 x^{4} - 56 x^{3} - 28 x^{2} + 1$
14	72	0.180979034910	Henry Cohn, 2026.
14	73	0.184450749802	Antoine Jay, 2026.
14	75	0.185110498562	Henry Cohn, 2026. $16 x^{4} - 44 x^{3} - 54 x^{2} + 6 x + 1$
14	76	0.189882980940	Antoine Olivier, 2026.
14	77	0.190266040190	Henry Cohn, 2026. Minimal polynomial of degree 12
14	78	0.191435237611	Arhan Canli, 2026.
14	79	0.193295679961	Henry Cohn, 2026.
14	80	0.195566522972	Antoine Olivier, 2026.
14	81	0.198091399669	Henry Cohn, 2026.
14	82	0.198234142263	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
14	83	0.198267231140	Henry Cohn, 2026.
14	84	0.198293264299	Henry Cohn, 2026.
14	85	0.198380133558	Henry Cohn, 2026.
14	86	0.198448366076	Antoine Jay, 2026.
14	87	0.198500422890	Antoine Jay, 2026.
14	88	0.198560262904	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
14	89	0.198676700177	Antoine Jay, 2026.
14	90	0.198771473496	Antoine Jay, 2026.
14	91	0.198843416030	Henry Cohn, 2026. Minimal polynomial of degree 10
14	92	0.208456809639	Henry Cohn, 2026.
14	93	0.211614877846	Arhan Canli, 2026.
14	94	0.211902924857	Antoine Jay, 2026.
14	95	0.212156818994	Antoine Jay, 2026.
14	98	0.212267554700	Antoine Jay, 2026.
14	99	0.219093723133	Antoine Jay, 2026.
14	100	0.223656652929	Antoine Jay, 2026.
14	101	0.225611786184	Antoine Jay, 2026.
14	102	0.227324267760	Antoine Jay, 2026.
14	103	0.228434774707	Antoine Jay, 2026.
14	104	0.229433949627	Antoine Jay, 2026.
14	112	0.229910395527	Henry Cohn, 2026. $172881 x^{2} - 2450 x - 8575$
14	113	0.234877677877	Antoine Jay, 2026.
14	114	0.237353905077	Antoine Jay, 2026.
14	115	0.238647655396	Antoine Jay, 2026.
14	116	0.240621710624	Henry Cohn, 2026.
14	117	0.242102335947	Antoine Jay, 2026.
14	118	0.243526373346	Antoine Jay, 2026.
14	119	0.244521891649	Antoine Jay, 2026.
14	120	0.245013623874	Antoine Jay, 2026.
14	121	0.245804193148	Antoine Jay, 2026.
14	122	0.247969565987	Antoine Jay, 2026.
14	123	0.249861636745	Antoine Jay, 2026.
14	124	0.250841630275	Antoine Jay, 2026.
14	125	0.252036955830	Antoine Jay, 2026.
14	126	0.252967865444	Antoine Jay, 2026.
14	127	0.253941619458	Antoine Jay, 2026.
14	128	0.254461455980	Antoine Jay, 2026.
14	129	0.255313221760	Antoine Jay, 2026.
14	130	0.255991032639	Antoine Jay, 2026.
14	131	0.257308533443	Antoine Jay, 2026.
14	132	0.259375896042	Antoine Jay, 2026.
14	133	0.261663671512	Antoine Jay, 2026.
14	134	0.263358888458	Antoine Jay, 2026.
14	135	0.263523285302	Antoine Jay, 2026.
14	136	0.263696522706	Arhan Canli, 2026.
14	137	0.265700466774	Antoine Jay, 2026.
14	138	0.267614408453	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	139	0.268398242800	Antoine Jay, 2026.
14	140	0.269114186344	Arhan Canli, 2026.
14	141	0.269159098387	Arhan Canli, 2026.
14	142	0.269179037445	Arhan Canli, 2026.
14	143	0.269224661861	Arhan Canli, 2026.
14	144	0.269269448784	Antoine Jay, 2026.
14	145	0.269305975303	Antoine Jay, 2026.
14	146	0.269347198112	Arhan Canli, 2026.
14	147	0.269387639919	Arhan Canli, 2026.
14	148	0.269433691988	Arhan Canli, 2026.
14	149	0.269470006218	Antoine Jay, 2026.
14	150	0.269507084831	Antoine Jay, 2026.
14	152	0.269752143390	Antoine Jay, 2026. $17 x^{2} - 12 x + 2$
14	153	0.273185531221	Henry Cohn, 2026.
14	154	0.273722355435	Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
14	155	0.275821287126	Antoine Jay, 2026.
14	156	0.275950380830	Arhan Canli, 2026.
14	157	0.276192708250	Antoine Jay, 2026.
14	158	0.276407065089	Antoine Jay, 2026.
14	159	0.276639427593	Antoine Jay, 2026.
14	160	0.276928172851	Antoine Jay, 2026.
14	161	0.277313316694	Antoine Jay, 2026.
14	162	0.277723572011	Antoine Jay, 2026.
14	163	0.278235519346	Antoine Jay, 2026.
14	164	0.278742069770	Antoine Jay, 2026.
14	165	0.279300566027	Antoine Jay, 2026.
14	166	0.280034629472	Antoine Jay, 2026.
14	167	0.281182078023	Antoine Jay, 2026.
14	168	0.281734140445	Antoine Jay, 2026.
14	169	0.286481765301	Antoine Jay, 2026.
14	170	0.287680856069	Antoine Jay, 2026.
14	171	0.289004235766	Antoine Jay, 2026.
14	172	0.290063551943	Antoine Jay, 2026.
14	173	0.290933323587	Antoine Jay, 2026.
14	174	0.291707450567	Antoine Jay, 2026.
14	175	0.292476108147	Antoine Jay, 2026.
14	176	0.293261763269	Antoine Jay, 2026.
14	177	0.293986945699	Antoine Jay, 2026.
14	178	0.294966846258	Antoine Jay, 2026.
14	179	0.295406643763	Antoine Jay, 2026.
14	180	0.295811389588	Antoine Jay, 2026.
14	181	0.296286226708	Antoine Jay, 2026.
14	182	0.296781002960	Antoine Jay, 2026.
14	183	0.297283997438	Antoine Jay, 2026.
14	184	0.297801008652	Antoine Jay, 2026.
14	185	0.298344248863	Antoine Jay, 2026.
14	186	0.298946683258	Arhan Canli, 2026.
14	187	0.299546636185	Antoine Jay, 2026.
14	188	0.300110731882	Antoine Jay, 2026.
14	189	0.300569928938	Antoine Jay, 2026.
14	190	0.301259934492	Antoine Jay, 2026.
14	191	0.302325733105	Arhan Canli, 2026.
14	192	0.303364423242	Antoine Jay, 2026.
14	193	0.304285127713	Antoine Jay, 2026.
14	194	0.305329882628	Antoine Jay, 2026.
14	195	0.306338157762	Antoine Jay, 2026.
14	196	0.307706828505	Antoine Jay, 2026.
14	197	0.308195338292	Antoine Jay, 2026.
14	198	0.308987593552	Antoine Jay, 2026.
14	199	0.309555693841	Antoine Jay, 2026.
14	200	0.310018830325	Antoine Jay, 2026.
14	201	0.310533842221	Antoine Jay, 2026.
14	202	0.311100596229	Antoine Jay, 2026.
14	203	0.311632103966	Antoine Jay, 2026.
14	204	0.312716371305	Antoine Jay, 2026.
14	205	0.312760223123	Antoine Jay, 2026.
14	206	0.312968007472	Antoine Jay, 2026.
14	207	0.313480358751	Antoine Jay, 2026.
14	208	0.313733010530	Antoine Jay, 2026.
14	209	0.314188989692	Antoine Jay, 2026.
14	210	0.314471401034	Antoine Jay, 2026.
14	211	0.315030963711	Antoine Jay, 2026.
14	212	0.315318005064	Antoine Jay, 2026.
14	213	0.315401926315	Antoine Jay, 2026.
14	214	0.315808571914	Antoine Jay, 2026.
14	215	0.316234760003	Antoine Jay, 2026.
14	216	0.316653816684	Antoine Jay, 2026.
14	217	0.317234021701	Antoine Jay, 2026.
14	218	0.317647987590	Antoine Jay, 2026.
14	219	0.318186418328	Antoine Jay, 2026.
14	220	0.318582073964	Antoine Jay, 2026.
14	221	0.319216055374	Antoine Jay, 2026.
14	222	0.319955587268	Antoine Jay, 2026.
14	224	0.320393060786	Antoine Jay, 2026.
14	225	0.320975850275	Antoine Jay, 2026.
14	226	0.321453491737	Antoine Jay, 2026.
14	227	0.322672250404	Antoine Jay, 2026.
14	228	0.323113091120	Antoine Jay, 2026.
14	229	0.323607245494	Antoine Jay, 2026.
14	230	0.324799997197	Antoine Jay, 2026.
14	231	0.325930534884	Antoine Jay, 2026.
14	232	0.326688433255	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	233	0.327393768235	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	234	0.328555151244	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	235	0.329473684559	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	236	0.330025296754	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	237	0.330939276853	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	238	0.331679997281	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	239	0.332337617579	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	240	0.332976262691	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	241	0.333092549840	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
14	252	0.333333333334	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $3 x - 1$
14	262	0.333811741529	Arhan Canli, 2026.
14	263	0.333865442138	Vadim Borisov, 2026.
14	265	0.333865549933	Vadim Borisov, 2026.
14	266	0.333866090638	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	267	0.336164742540	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	268	0.336850856691	Vadim Borisov, 2026.
14	269	0.337341851621	Christopher Smolen, 2026.
14	279	0.339312508054	Antoine Jay, 2026.
14	281	0.339316362297	Antoine Jay, 2026.
14	282	0.339369250186	Antoine Jay, 2026.
14	283	0.339433427769	Antoine Jay, 2026.
14	284	0.339538164838	Vadim Borisov, 2026.
14	285	0.339602481633	Christopher Smolen, 2026.
14	286	0.341135842942	Antoine Jay, 2026.
14	287	0.342442530234	Christopher Smolen, 2026.
14	288	0.343978652697	Christopher Smolen, 2026.
14	289	0.345063242120	Christopher Smolen, 2026.
14	290	0.345851514206	Christopher Smolen, 2026.
14	296	0.347198310291	Henry Cohn, 2026.
14	297	0.347202707863	Christopher Smolen, 2026.
14	298	0.347249001708	Christopher Smolen, 2026.
14	299	0.347929918984	Christopher Smolen, 2026.
14	300	0.348195102754	Christopher Smolen, 2026.
14	301	0.348672995783	Christopher Smolen, 2026.
14	302	0.348947393845	Christopher Smolen, 2026.
14	303	0.352280816431	Christopher Smolen, 2026.
14	304	0.352911931705	Antoine Jay, 2026.
14	305	0.354084723475	Antoine Jay, 2026.
14	306	0.354967772686	Christopher Smolen, 2026.
14	307	0.354967951381	Christopher Smolen, 2026.
14	308	0.354968159112	Christopher Smolen, 2026.
14	309	0.354970000534	Christopher Smolen, 2026.
14	310	0.354970260130	Christopher Smolen, 2026.
14	311	0.354970499563	Christopher Smolen, 2026.
14	312	0.354970845925	Christopher Smolen, 2026.
14	313	0.354971189166	Christopher Smolen, 2026.
14	317	0.355009068750	Vadim Borisov, 2026.
14	319	0.355009091831	Vadim Borisov, 2026.
14	320	0.355009147852	Christopher Smolen, 2026.
14	321	0.355009738627	Vadim Borisov, 2026.
14	322	0.355009827760	Christopher Smolen, 2026.
14	323	0.355010760676	Christopher Smolen, 2026.
14	324	0.355011426432	Christopher Smolen, 2026.
14	325	0.355011489773	Christopher Smolen, 2026.
14	326	0.355011949659	Christopher Smolen, 2026.
14	327	0.355012583007	Christopher Smolen, 2026.
14	328	0.355012584765	Christopher Smolen, 2026.
14	331	0.355012595025	Christopher Smolen, 2026.
14	332	0.355012691035	Christopher Smolen, 2026.
14	333	0.355013189766	Christopher Smolen, 2026.
14	334	0.355015700740	Christopher Smolen, 2026.
14	335	0.355015717820	Christopher Smolen, 2026.
14	336	0.355045636452	Christopher Smolen, 2026.
14	337	0.355117739085	Vadim Borisov, 2026.
14	338	0.355117793033	Christopher Smolen, 2026.
14	339	0.355577956556	Christopher Smolen, 2026.
14	340	0.356904906022	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	342	0.358051640945	Christopher Smolen, 2026.
14	343	0.358543840235	Christopher Smolen, 2026.
14	344	0.359725453913	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	345	0.360768695747	Christopher Smolen, 2026.
14	346	0.362529546175	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	347	0.362754043705	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	348	0.363152593703	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	349	0.363195293072	Christopher Smolen, 2026.
14	350	0.364017426940	Antoine Jay, 2026.
14	351	0.364407645119	Vadim Borisov, 2026.
14	352	0.367342227563	Christopher Smolen, 2026.
14	353	0.368111668853	Christopher Smolen, 2026.
14	354	0.369258877883	Christopher Smolen, 2026.
14	355	0.370390515325	Christopher Smolen, 2026.
14	356	0.371137006208	Christopher Smolen, 2026.
14	357	0.371998284943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	358	0.373028998747	Christopher Smolen, 2026.
14	359	0.374138336488	Christopher Smolen, 2026.
14	360	0.374986457743	Christopher Smolen, 2026.
14	361	0.375749526220	Antoine Jay, 2026.
14	362	0.376466783705	Christopher Smolen, 2026.
14	363	0.376917138607	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	364	0.377059768465	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	365	0.377259325542	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	366	0.377310905666	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	367	0.377349081982	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	368	0.377361168880	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	369	0.377370428550	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	370	0.377371621478	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	371	0.377378477801	Vadim Borisov, 2026.
14	372	0.377383717894	Vadim Borisov, 2026.
14	373	0.377383724289	Christopher Smolen, 2026.
14	376	0.377410758877	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	377	0.377413074335	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	378	0.377413918720	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	379	0.377415296582	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	380	0.377415842234	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	381	0.377455622905	Christopher Smolen, 2026.
14	382	0.377547265488	Vadim Borisov, 2026.
14	383	0.377547268287	Vadim Borisov, 2026.
14	384	0.377547276458	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	385	0.377912959620	Christopher Smolen, 2026.
14	386	0.378443757939	Christopher Smolen, 2026.
14	387	0.380849597124	Christopher Smolen, 2026.
14	388	0.381421811320	Christopher Smolen, 2026.
14	389	0.381960101844	Christopher Smolen, 2026.
14	390	0.382560816305	Vadim Borisov, 2026.
14	391	0.382560823369	Vadim Borisov, 2026.
14	392	0.382563844828	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	393	0.382587100358	Vadim Borisov, 2026.
14	394	0.382587244838	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	395	0.382587536063	Vadim Borisov, 2026.
14	396	0.382588258250	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	397	0.382589130123	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	398	0.382590034365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	401	0.383102077831	Antoine Jay, 2026.
14	402	0.384705895485	Vadim Borisov, 2026.
14	403	0.385318231102	Vadim Borisov, 2026.
14	405	0.385541177791	Vadim Borisov, 2026.
14	406	0.385541177801	Vadim Borisov, 2026.
14	407	0.385541227595	Vadim Borisov, 2026.
14	408	0.385541227602	Vadim Borisov, 2026.
14	409	0.385541242904	Vadim Borisov, 2026.
14	410	0.385541242909	Vadim Borisov, 2026.
14	412	0.385541255664	Vadim Borisov, 2026.
14	413	0.385541255665	Vadim Borisov, 2026.
14	414	0.385541325314	Christopher Smolen, 2026.
14	415	0.386150442163	Vadim Borisov, 2026.
14	416	0.386730017601	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	417	0.387123954602	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	418	0.387401939942	Christopher Smolen, 2026.
14	419	0.387540423417	Christopher Smolen, 2026.
14	420	0.388281800396	Christopher Smolen, 2026.
14	421	0.390111912744	Christopher Smolen, 2026.
14	422	0.390857551744	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	423	0.391547842028	Christopher Smolen, 2026.
14	435	0.391891891892	Henry Cohn, 2026. $74 x - 29$
14	436	0.394834430044	Christopher Smolen, 2026.
14	437	0.395905395643	Christopher Smolen, 2026.
14	438	0.396518912692	Christopher Smolen, 2026.
14	439	0.396988097466	Christopher Smolen, 2026.
14	440	0.397345834868	Christopher Smolen, 2026.
14	441	0.397630034761	Christopher Smolen, 2026.
14	442	0.398091170777	Christopher Smolen, 2026.
14	443	0.398789624465	Christopher Smolen, 2026.
14	444	0.399265343412	Christopher Smolen, 2026.
14	445	0.399600976436	Christopher Smolen, 2026.
14	466	0.4	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
14	537	0.4	Henry Cohn, 2026. $5 x - 2$
14	538	0.411974578764	Christopher Smolen, 2026.
14	539	0.413388844494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	540	0.414932061699	Christopher Smolen, 2026.
14	541	0.416090523947	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	542	0.417503936067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	543	0.418554697076	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	544	0.418836874734	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	545	0.419536934314	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	546	0.420227864569	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	547	0.420424427904	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	548	0.420556796756	Christopher Smolen, 2026.
14	549	0.421960108571	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	550	0.422264408501	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	580	0.423076923077	Henry Cohn, 2026. $26 x - 11$
14	583	0.423076923077	Christopher Smolen, 2026. $26 x - 11$
14	584	0.423226266838	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	585	0.423702313130	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	586	0.423716576762	Vadim Borisov, 2026.
14	587	0.423886726974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	600	0.428571428572	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330. $7 x - 3$
14	602	0.428571428954	Vadim Borisov, 2026.
14	603	0.429608531267	Vadim Borisov, 2026.
14	604	0.429933541718	Vadim Borisov, 2026.
14	605	0.430094842176	Vadim Borisov, 2026.
14	606	0.430221956341	Vadim Borisov, 2026.
14	607	0.430451836094	Vadim Borisov, 2026.
14	608	0.430503676727	Vadim Borisov, 2026.
14	609	0.430616991342	Vadim Borisov, 2026.
14	610	0.430830666525	Vadim Borisov, 2026.
14	611	0.430947276252	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	612	0.431176363990	Vadim Borisov, 2026.
14	613	0.431373307461	Vadim Borisov, 2026.
14	614	0.431522760348	Vadim Borisov, 2026.
14	615	0.431603237805	Vadim Borisov, 2026.
14	616	0.431699703586	Vadim Borisov, 2026.
14	617	0.431824580743	Vadim Borisov, 2026.
14	618	0.431915165266	Vadim Borisov, 2026.
14	619	0.431978815119	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	620	0.432070583093	Vadim Borisov, 2026.
14	621	0.432116753662	Vadim Borisov, 2026.
14	622	0.432225094244	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	623	0.432275158978	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	624	0.432562478781	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	625	0.432623764461	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	626	0.432722724382	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	627	0.432812260605	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	628	0.432906609197	Vadim Borisov, 2026.
14	629	0.433060098038	Vadim Borisov, 2026.
14	630	0.433156045013	Vadim Borisov, 2026.
14	631	0.433180870421	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	632	0.433233493958	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	633	0.433352304948	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	634	0.433379759905	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	635	0.433464750481	Vadim Borisov, 2026.
14	636	0.433521414685	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	637	0.433637268270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	638	0.433765345355	Vadim Borisov, 2026.
14	639	0.433845199201	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	640	0.433923615906	Vadim Borisov, 2026.
14	641	0.433987299475	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	642	0.434171465919	Vadim Borisov, 2026.
14	643	0.434174426209	Christopher Smolen, 2026.
14	644	0.434210579917	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	645	0.434234913200	Vadim Borisov, 2026.
14	646	0.434902488719	Christopher Smolen, 2026.
14	647	0.435567754465	Christopher Smolen, 2026.
14	648	0.435583646301	Vadim Borisov, 2026.
14	649	0.435583672522	Vadim Borisov, 2026.
14	650	0.436400270611	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	651	0.437161098460	Vadim Borisov, 2026.
14	652	0.437770251035	Vadim Borisov, 2026.
14	653	0.438800348994	Christopher Smolen, 2026.
14	654	0.439031717416	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	655	0.439485963774	Christopher Smolen, 2026.
14	656	0.439505142650	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	657	0.439909148103	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	658	0.440036698727	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	659	0.440078753572	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	660	0.440431874010	Vadim Borisov, 2026.
14	661	0.441271531327	Vadim Borisov, 2026.
14	662	0.441730650638	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	663	0.442077493213	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
14	664	0.442234060803	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	665	0.442462746754	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	666	0.442859667152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	667	0.442981096660	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
14	668	0.443797081769	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	670	0.444048009053	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	671	0.444441255825	Vadim Borisov, 2026.
14	672	0.445325775107	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	673	0.445450517104	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	674	0.445962633534	Vadim Borisov, 2026.
14	675	0.445962650492	Christopher Smolen, 2026.
14	676	0.446619445121	Vadim Borisov, 2026.
14	677	0.446641915910	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	678	0.446791076762	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	679	0.446944896303	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	680	0.447095552625	Vadim Borisov, 2026.
14	681	0.447262971503	Vadim Borisov, 2026.
14	682	0.447558236509	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	683	0.447866364774	Vadim Borisov, 2026.
14	684	0.448085572467	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	685	0.448372486144	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	686	0.448510679316	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	687	0.448511521403	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	688	0.449138696035	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	689	0.449249464238	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	690	0.449428527717	Vadim Borisov, 2026.
14	691	0.449501586200	Vadim Borisov, 2026.
14	692	0.449840972493	Christopher Smolen, 2026.
14	693	0.449905000819	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	694	0.449905449551	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	695	0.450066113221	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	696	0.450097170368	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	697	0.450721498473	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	698	0.450726453859	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	699	0.450848653542	Vadim Borisov, 2026.
14	700	0.453268231489	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	701	0.453288527007	Vadim Borisov, 2026.
14	702	0.453303637006	Vadim Borisov, 2026.
14	703	0.453352788987	Vadim Borisov, 2026.
14	704	0.453383375727	Vadim Borisov, 2026.
14	705	0.453432057419	Vadim Borisov, 2026.
14	706	0.453455073672	Vadim Borisov, 2026.
14	707	0.453484644023	Vadim Borisov, 2026.
14	709	0.453525017038	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	710	0.453561034497	Vadim Borisov, 2026.
14	711	0.453591877155	Vadim Borisov, 2026.
14	712	0.453611235576	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	713	0.453612014122	Vadim Borisov, 2026.
14	714	0.453643845804	Vadim Borisov, 2026.
14	715	0.453784798110	Vadim Borisov, 2026.
14	716	0.453835291003	Vadim Borisov, 2026.
14	717	0.453924510927	Vadim Borisov, 2026.
14	718	0.454015399214	Vadim Borisov, 2026.
14	719	0.454131080547	Christopher Smolen, 2026.
14	896	0.454545454546	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 5$
14	897	0.454719198215	Henry Cohn, 2026.
14	898	0.454765032659	Christopher Smolen, 2026.
14	899	0.454809005961	Vadim Borisov, 2026.
14	900	0.454845696691	Vadim Borisov, 2026.
14	901	0.454858157424	Vadim Borisov, 2026.
14	902	0.454883686336	Vadim Borisov, 2026.
14	903	0.454905636139	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	904	0.454936590966	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	905	0.454949450020	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	906	0.454975806560	Vadim Borisov, 2026.
14	907	0.454997020416	Vadim Borisov, 2026.
14	908	0.455013194240	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	909	0.455028652214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	910	0.455063596859	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	911	0.455071416269	Vadim Borisov, 2026.
14	912	0.455085499937	Vadim Borisov, 2026.
14	913	0.455098812834	Vadim Borisov, 2026.
14	914	0.455108885288	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	915	0.455135817708	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	916	0.455154519023	Vadim Borisov, 2026.
14	917	0.455168296111	Vadim Borisov, 2026.
14	918	0.455181017346	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	919	0.455192368197	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	920	0.455210840629	Christopher Smolen, 2026.
14	921	0.455243596586	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	922	0.455249671016	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	923	0.455261694455	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	924	0.455273295229	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	926	0.455276477662	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	927	0.455309590988	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	929	0.455313279216	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	930	0.455318273617	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	931	0.455318790957	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	932	0.455319042933	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	933	0.455326277706	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	934	0.455338472447	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	935	0.455339650265	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	936	0.455341668773	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	937	0.455341778867	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	938	0.455354742650	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	939	0.455356060414	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	940	0.455367688910	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	941	0.455370492193	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	942	0.455380292848	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	943	0.455380592722	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	944	0.455396075974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	945	0.455402283098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	946	0.455402966895	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	947	0.455413997448	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	948	0.455424225070	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	949	0.455424627981	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	950	0.455438556271	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	951	0.455446716259	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	952	0.455457798156	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	953	0.455465477729	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	954	0.455474898300	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	955	0.455487315398	Vadim Borisov, 2026.
14	956	0.455500020558	Vadim Borisov, 2026.
14	957	0.455505364499	Vadim Borisov, 2026.
14	958	0.455507100013	Vadim Borisov, 2026.
14	959	0.455520374157	Vadim Borisov, 2026.
14	960	0.455528891462	Vadim Borisov, 2026.
14	961	0.455541796033	Vadim Borisov, 2026.
14	962	0.455553503777	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	963	0.455569939576	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	964	0.455583724784	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	965	0.455586347502	Vadim Borisov, 2026.
14	966	0.455588198160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	967	0.455596684965	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	968	0.455598020957	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	969	0.455601274517	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	970	0.455603977820	Vadim Borisov, 2026.
14	971	0.455609488317	Vadim Borisov, 2026.
14	972	0.455619434058	Vadim Borisov, 2026.
14	973	0.455624795620	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	974	0.455630420541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	975	0.455637187555	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	976	0.455648221670	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	977	0.455657449453	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
14	978	0.455663973904	Vadim Borisov, 2026.
14	979	0.455670091633	Vadim Borisov, 2026.
14	980	0.455678023057	Christopher Smolen, 2026.
14	981	0.455690497674	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	982	0.455698893270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	983	0.455709078878	Vadim Borisov, 2026.
14	984	0.455714577329	Vadim Borisov, 2026.
14	985	0.455721171635	Vadim Borisov, 2026.
14	986	0.455726571632	Vadim Borisov, 2026.
14	987	0.455732006954	Vadim Borisov, 2026.
14	988	0.455736729077	Vadim Borisov, 2026.
14	989	0.455739562277	Vadim Borisov, 2026.
14	990	0.455739598921	Vadim Borisov, 2026.
14	991	0.455739617569	Vadim Borisov, 2026.
14	992	0.455744858593	Vadim Borisov, 2026.
14	993	0.455747756178	Vadim Borisov, 2026.
14	994	0.455755155151	Vadim Borisov, 2026.
14	995	0.455758235318	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	996	0.455765694011	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	997	0.455771910516	Vadim Borisov, 2026.
14	998	0.455775589939	Vadim Borisov, 2026.
14	999	0.455780804118	Vadim Borisov, 2026.
14	1000	0.455784225059	Vadim Borisov, 2026.
14	1001	0.455787268599	Vadim Borisov, 2026.
14	1002	0.455789621248	Vadim Borisov, 2026.
14	1003	0.455792767933	Vadim Borisov, 2026.
14	1004	0.455795753070	Vadim Borisov, 2026.
14	1005	0.455797070284	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	1006	0.455798272643	Vadim Borisov, 2026.
14	1009	0.455798272775	Vadim Borisov, 2026.
14	1010	0.455798273070	Vadim Borisov, 2026.
14	1011	0.455798275029	Vadim Borisov, 2026.
14	1012	0.455798290114	Vadim Borisov, 2026.
14	1014	0.455798306539	Vadim Borisov, 2026.
14	1015	0.455798344788	Vadim Borisov, 2026.
14	1016	0.456084205489	Vadim Borisov, 2026.
14	1017	0.456306101793	Vadim Borisov, 2026.
14	1018	0.456326397150	Vadim Borisov, 2026.
14	1019	0.457276895324	Vadim Borisov, 2026.
14	1020	0.457276991896	Vadim Borisov, 2026.
14	1021	0.457277549912	Christopher Smolen, 2026.
14	1023	0.457561484204	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
14	1024	0.457589680104	Henry Cohn, 2026.
15	31	0.050237120373	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $2535 x^{3} - 225 x^{2} - 15 x + 1$
15	32	0.058900808489	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
15	33	0.062706770083	Henry Cohn, 2023. Minimal polynomial of degree 6
15	34	0.066570393658	Henry Cohn, 2025.
15	35	0.070509992992	Henry Cohn, 2023.
15	36	0.070779968044	Henry Cohn, 2023. $5937 x^{4} + 412 x^{3} - 202 x^{2} - 4 x + 1$
15	37	0.078785666352	Henry Cohn, 2025.
15	38	0.079970260232	Henry Cohn, 2026.
15	39	0.082681671944	Henry Cohn, 2023. $347087 x^{8} + 1080416 x^{7} + 305012 x^{6} + 3648 x^{5} - 20054 x^{4} - 160 x^{3} + 276 x^{2} - 1$
15	40	0.086159367074	Henry Cohn, 2023.
15	41	0.093058707265	Antoine Jay, 2026.
15	42	0.096774023869	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	43	0.099863843733	Henry Cohn, 2025.
15	44	0.099976426707	Henry Cohn, 2025.
15	45	0.102626460761	Henry Cohn, 2026.
15	46	0.110795000982	Henry Cohn, 2025.
15	47	0.111165028345	Henry Cohn, 2026.
15	48	0.112184213927	Henry Cohn, 2026.
15	52	0.112912613537	Henry Cohn, 2025. $167 x^{2} - 10 x - 1$
15	57	0.115470053838	Henry Cohn, 2024. $75 x^{2} - 1$
15	58	0.119568545339	Antoine Jay, 2026.
15	61	0.128458591981	Henry Cohn, 2025. $263 x^{2} - 26 x - 1$
15	62	0.129608480812	Antoine Jay, 2026.
15	63	0.129675225483	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	64	0.129675869236	Antoine Jay, 2026.
15	65	0.129676247045	Henry Cohn, 2026.
15	66	0.142833448358	Antoine Jay, 2026.
15	67	0.144244923465	Antoine Jay, 2026. $25 x^{2} - 66 x + 9$
15	68	0.146740170078	Antoine Jay, 2026.
15	69	0.155287992922	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $193 x^{3} - 65 x^{2} - x + 1$
15	70	0.160964563056	Henry Cohn, 2024.
15	73	0.161462093425	Henry Cohn, 2026. $3527 x^{2} - 266 x - 49$
15	74	0.166666666667	Henry Cohn and Ilmari Vahteristo, 2026. $6 x - 1$
15	75	0.168255719819	Henry Cohn, 2026.
15	76	0.168262934174	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	77	0.168268947513	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	78	0.168274198183	Arhan Canli, 2026.
15	92	0.168685175113	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $47 x^{2} - 2 x - 1$
15	93	0.169916676995	Henry Cohn, 2025. $169 x^{4} - 56 x^{3} - 30 x^{2} + 1$
15	94	0.186144699040	Henry Cohn, 2026.
15	95	0.187077042678	Henry Cohn, 2026.
15	96	0.187885637085	Antoine Jay, 2026.
15	97	0.188664973569	Antoine Jay, 2026.
15	99	0.188666328567	Henry Cohn, 2026.
15	100	0.189707861448	Antoine Jay, 2026.
15	101	0.197669703738	Arhan Canli, 2026.
15	102	0.197751520376	Henry Cohn, 2026. $4455 x^{4} + 7056 x^{3} - 8616 x^{2} + 2688 x - 256$
15	108	0.199301661815	Henry Cohn, 2026. $347 x^{2} - 24 x - 9$
15	128	0.2	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $5 x - 1$
15	129	0.209693852047	Henry Cohn, 2026. $2025 x^{4} - 672 x^{3} - 312 x^{2} + 16$
15	130	0.216435024260	Henry Cohn, 2026.
15	131	0.219738142735	Antoine Jay, 2026.
15	132	0.221690909713	Antoine Jay, 2026.
15	133	0.222982964951	Antoine Jay, 2026.
15	134	0.223042839303	Antoine Jay, 2026.
15	135	0.223068626265	Henry Cohn, 2026.
15	136	0.225822528269	Antoine Jay, 2026.
15	137	0.226886048633	Henry Cohn, 2026.
15	142	0.227160244714	Henry Cohn, 2026. $75 x^{4} + 130 x^{3} + 30 x^{2} - 10 x - 1$
15	143	0.231969852439	Antoine Jay, 2026.
15	144	0.235178942009	Arhan Canli, 2026.
15	145	0.237406456442	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	146	0.237726828468	Antoine Jay, 2026.
15	147	0.237805329682	Antoine Jay, 2026.
15	148	0.238417262606	Antoine Jay, 2026.
15	149	0.238748130183	Antoine Jay, 2026.
15	150	0.239511954206	Antoine Jay, 2026.
15	151	0.239558257199	Henry Cohn, 2026.
15	152	0.244361635808	Antoine Jay, 2026.
15	153	0.245232882245	Arhan Canli, 2026.
15	156	0.248124762895	Henry Cohn, 2026.
15	157	0.249069470433	Henry Cohn, 2026.
15	158	0.252500157923	Antoine Jay, 2026.
15	159	0.252897434966	Antoine Jay, 2026.
15	160	0.253443210641	Antoine Jay, 2026.
15	161	0.254174550894	Antoine Jay, 2026.
15	162	0.255968676933	Antoine Jay, 2026.
15	163	0.256209472968	Antoine Jay, 2026.
15	164	0.256236028028	Antoine Jay, 2026.
15	165	0.256264469397	Vadim Borisov, 2026.
15	166	0.256265659710	Henry Cohn, 2026.
15	167	0.256273890788	Arhan Canli, 2026.
15	168	0.256276276525	Antoine Jay, 2026.
15	170	0.256285188381	Antoine Jay, 2026.
15	171	0.257077751827	Antoine Jay, 2026.
15	172	0.257543198869	Antoine Jay, 2026.
15	173	0.257765624910	Vadim Borisov, 2026.
15	180	0.257798380527	Vadim Borisov, 2026.
15	184	0.258146294297	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 11
15	185	0.259982802849	Antoine Jay, 2026.
15	186	0.260377719966	Antoine Jay, 2026.
15	187	0.260799052056	Antoine Jay, 2026.
15	188	0.261259890833	Henry Cohn, 2026.
15	189	0.261661816687	Antoine Jay, 2026.
15	190	0.261671377346	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	191	0.261678234940	Antoine Jay, 2026.
15	192	0.261685783670	Antoine Jay, 2026.
15	193	0.261731557624	Arhan Canli, 2026.
15	194	0.261771973594	Antoine Jay, 2026.
15	195	0.261800246688	Henry Cohn, 2026.
15	196	0.261873230500	Antoine Jay, 2026.
15	197	0.261906377348	Antoine Jay, 2026.
15	198	0.261931281309	Arhan Canli, 2026.
15	199	0.261942195760	Henry Cohn, 2026.
15	200	0.263200518931	Antoine Jay, 2026.
15	201	0.263683674655	Antoine Jay, 2026.
15	202	0.264100168079	Antoine Jay, 2026.
15	203	0.264473203862	Antoine Jay, 2026.
15	204	0.264741821537	Antoine Jay, 2026.
15	205	0.264974967973	Christopher Smolen, 2026.
15	206	0.265112804884	Antoine Jay, 2026.
15	207	0.265362781064	Antoine Jay, 2026.
15	208	0.265513024367	Antoine Jay, 2026.
15	209	0.265651283268	Antoine Jay, 2026.
15	214	0.265700305150	Antoine Jay, 2026.
15	218	0.265700305150	Henry Cohn, 2026.
15	219	0.266188142094	Antoine Jay, 2026.
15	220	0.266583431141	Henry Cohn, 2026. $22009 x^{6} + 8374 x^{5} - 1553 x^{4} - 516 x^{3} - 81 x^{2} - 18 x + 9$
15	221	0.273150769638	Henry Cohn, 2026. $1600 x^{4} - 1512 x^{3} - 792 x^{2} + 81$
15	222	0.281854894892	Christopher Smolen, 2026.
15	223	0.283023873623	Christopher Smolen, 2026.
15	224	0.283850191210	Christopher Smolen, 2026.
15	240	0.284034672467	Henry Cohn, 2026. $527 x^{2} - 118 x - 9$
15	241	0.284811315653	Arhan Canli, 2026.
15	242	0.285672469914	Antoine Jay, 2026.
15	243	0.286368314034	Christopher Smolen, 2026.
15	244	0.286850733216	Antoine Jay, 2026.
15	245	0.287238196824	Antoine Jay, 2026.
15	246	0.287601117830	Antoine Jay, 2026.
15	247	0.287883854977	Antoine Jay, 2026.
15	248	0.288135329500	Antoine Jay, 2026.
15	249	0.291752277916	Arhan Canli, 2026.
15	250	0.294425203635	Christopher Smolen, 2026.
15	251	0.296508220974	Christopher Smolen, 2026.
15	252	0.297451552586	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	253	0.297826348158	Antoine Jay, 2026.
15	254	0.297925369288	Antoine Jay, 2026.
15	256	0.297926304913	Henry Cohn, 2026.
15	257	0.301101206435	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	258	0.304143233195	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	259	0.305490507082	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	260	0.305826317905	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	261	0.308188730595	Christopher Smolen, 2026.
15	262	0.308895271718	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	263	0.309285922252	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	264	0.309577229343	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
15	284	0.311493911798	Antoine Jay, 2026.
15	286	0.311493911798	Henry Cohn, 2026. $135 x^{2} - 26 x - 5$
15	287	0.327598486006	Henry Cohn, 2026.
15	288	0.332309458583	Henry Cohn, 2026.
15	320	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
15	321	0.339291238734	Christopher Smolen, 2026.
15	322	0.340371816789	Christopher Smolen, 2026.
15	323	0.341167433471	Christopher Smolen, 2026.
15	324	0.341829402025	Christopher Smolen, 2026.
15	325	0.342381303403	Christopher Smolen, 2026.
15	326	0.342760908284	Christopher Smolen, 2026.
15	327	0.343116639249	Christopher Smolen, 2026.
15	328	0.343550688615	Christopher Smolen, 2026.
15	329	0.343818872610	Christopher Smolen, 2026.
15	330	0.344476273140	Christopher Smolen, 2026.
15	331	0.345230129109	Christopher Smolen, 2026.
15	332	0.345738226336	Christopher Smolen, 2026.
15	333	0.346487047675	Christopher Smolen, 2026.
15	334	0.346802418691	Christopher Smolen, 2026.
15	335	0.347032081696	Christopher Smolen, 2026.
15	336	0.347429683090	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	337	0.347598090728	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	338	0.347996876453	Christopher Smolen, 2026.
15	339	0.348165957010	Christopher Smolen, 2026.
15	340	0.348370623656	Christopher Smolen, 2026.
15	341	0.348550035060	Christopher Smolen, 2026.
15	342	0.348830084049	Christopher Smolen, 2026.
15	343	0.349068332919	Christopher Smolen, 2026.
15	344	0.349234881169	Christopher Smolen, 2026.
15	345	0.349398559886	Christopher Smolen, 2026.
15	346	0.349616334753	Christopher Smolen, 2026.
15	347	0.350144291598	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	348	0.350468196487	Christopher Smolen, 2026.
15	349	0.350824212665	Christopher Smolen, 2026.
15	350	0.351096045873	Christopher Smolen, 2026.
15	351	0.351295754524	Christopher Smolen, 2026.
15	352	0.351429894499	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	353	0.351652651712	Christopher Smolen, 2026.
15	354	0.352269011228	Christopher Smolen, 2026.
15	355	0.352542008917	Christopher Smolen, 2026.
15	356	0.352743598383	Christopher Smolen, 2026.
15	357	0.352948140172	Christopher Smolen, 2026.
15	358	0.353274953876	Christopher Smolen, 2026.
15	359	0.353524417522	Christopher Smolen, 2026.
15	360	0.353747547368	Christopher Smolen, 2026.
15	361	0.354097889274	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	362	0.354423658305	Vadim Borisov, 2026.
15	363	0.354739568957	Vadim Borisov, 2026.
15	364	0.354991216752	Christopher Smolen, 2026.
15	365	0.355235018191	Christopher Smolen, 2026.
15	370	0.355388595948	Vadim Borisov, 2026.
15	371	0.355388598220	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	372	0.355679815456	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	373	0.355784735679	Christopher Smolen, 2026.
15	374	0.356232929788	Vadim Borisov, 2026.
15	375	0.356361294052	Vadim Borisov, 2026.
15	376	0.356788997937	Vadim Borisov, 2026.
15	377	0.357117707001	Vadim Borisov, 2026.
15	378	0.357369380244	Christopher Smolen, 2026.
15	379	0.358181727441	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	380	0.358286655424	Christopher Smolen, 2026.
15	381	0.359705044364	Christopher Smolen, 2026.
15	382	0.360734885032	Christopher Smolen, 2026.
15	383	0.361398711798	Christopher Smolen, 2026.
15	384	0.362087794731	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	385	0.362806799400	Christopher Smolen, 2026.
15	386	0.363440881450	Christopher Smolen, 2026.
15	387	0.363717745557	Christopher Smolen, 2026.
15	388	0.364711277628	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	389	0.365789777261	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	390	0.365812474227	Christopher Smolen, 2026.
15	391	0.366751495432	Christopher Smolen, 2026.
15	392	0.367719552919	Christopher Smolen, 2026.
15	393	0.368226946500	Christopher Smolen, 2026.
15	394	0.368745319208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	395	0.369223743896	Christopher Smolen, 2026.
15	396	0.369639605606	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	397	0.370266339028	Christopher Smolen, 2026.
15	424	0.370431040067	Henry Cohn, 2026. $287 x^{2} - 190 x + 31$
15	425	0.370431040067	A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization. $287 x^{2} - 190 x + 31$
15	426	0.371505827166	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	427	0.373139529831	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	428	0.373371863994	Christopher Smolen, 2026.
15	429	0.373452982949	Christopher Smolen, 2026.
15	430	0.373493520838	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	431	0.373593282734	Christopher Smolen, 2026.
15	432	0.373897457790	Vadim Borisov, 2026.
15	434	0.374135896470	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	435	0.374143804935	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	436	0.374149700430	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	437	0.374337428866	Christopher Smolen, 2026.
15	438	0.374350159809	Vadim Borisov, 2026.
15	439	0.374350400839	Vadim Borisov, 2026.
15	440	0.374385248252	Vadim Borisov, 2026.
15	441	0.374934575289	Christopher Smolen, 2026.
15	442	0.374967940540	Christopher Smolen, 2026.
15	444	0.374991081433	Christopher Smolen, 2026.
15	445	0.375084028767	Christopher Smolen, 2026.
15	464	0.376462890261	Henry Cohn, 2026. $3864 x^{3} - 157 x^{2} - 1134 x + 243$
15	465	0.376564746972	Vadim Borisov, 2026.
15	466	0.376621608297	Henry Cohn, 2026.
15	467	0.381191987437	Christopher Smolen, 2026.
15	468	0.382726485742	Christopher Smolen, 2026.
15	469	0.383963226749	Christopher Smolen, 2026.
15	470	0.385340639824	Christopher Smolen, 2026.
15	471	0.386196765579	Christopher Smolen, 2026.
15	472	0.386904753196	Christopher Smolen, 2026.
15	480	0.387503295973	Henry Cohn, 2026.
15	481	0.390059911803	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	482	0.392055262532	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	483	0.392057393455	Vadim Borisov, 2026.
15	484	0.392058233031	Vadim Borisov, 2026.
15	485	0.392059684020	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	486	0.392076053885	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	487	0.392112367922	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	489	0.392149981297	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	490	0.392161465942	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	491	0.392175053612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	492	0.392196652025	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	493	0.392219404765	Vadim Borisov, 2026.
15	494	0.392220436737	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	495	0.392220469692	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	496	0.392221023409	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	497	0.392264824771	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	498	0.392269143200	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	499	0.392284723631	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	500	0.392302526581	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	501	0.392313722494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	502	0.392331943762	Vadim Borisov, 2026.
15	503	0.392334259188	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	504	0.392335085346	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	505	0.393005119321	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	506	0.393025247898	Vadim Borisov, 2026.
15	507	0.393130382328	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	508	0.393141702705	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	509	0.393303157479	Christopher Smolen, 2026.
15	510	0.393335695485	Vadim Borisov, 2026.
15	511	0.393732045800	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	512	0.393887679897	Vadim Borisov, 2026.
15	513	0.393896619731	Christopher Smolen, 2026.
15	514	0.394022247008	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	515	0.394053624754	Christopher Smolen, 2026.
15	516	0.394078191172	Christopher Smolen, 2026.
15	517	0.394318785921	Christopher Smolen, 2026.
15	518	0.394663415428	Christopher Smolen, 2026.
15	519	0.394780702939	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	520	0.394993906700	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	521	0.395257724487	Christopher Smolen, 2026.
15	522	0.395564751816	Christopher Smolen, 2026.
15	524	0.395672267600	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	525	0.395686620938	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	526	0.395728158905	Vadim Borisov, 2026.
15	527	0.395753945129	Vadim Borisov, 2026.
15	528	0.395755811288	Vadim Borisov, 2026.
15	529	0.395761517028	Vadim Borisov, 2026.
15	530	0.395764611480	Vadim Borisov, 2026.
15	531	0.395920195281	Vadim Borisov, 2026.
15	532	0.396374971077	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	533	0.396410794653	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	534	0.396730217296	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	535	0.396753946214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	536	0.396828547422	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	537	0.396852928733	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	538	0.396869627931	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	539	0.396869659892	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	540	0.398517738293	Christopher Smolen, 2026.
15	541	0.398592976817	Christopher Smolen, 2026.
15	542	0.398705691964	Christopher Smolen, 2026.
15	543	0.398775063586	Christopher Smolen, 2026.
15	544	0.399041009793	Vadim Borisov, 2026.
15	545	0.399113948552	Christopher Smolen, 2026.
15	546	0.399334732854	Christopher Smolen, 2026.
15	547	0.399632328920	Christopher Smolen, 2026.
15	672	0.4	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
15	688	0.4	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
15	689	0.404117037740	Henry Cohn, 2026. $768 x^{9} - 3328 x^{8} - 1152 x^{7} + 896 x^{6} + 528 x^{5} + 16 x^{4} - 72 x^{3} - 8 x^{2} + 3 x - 1$
15	690	0.407438982467	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	691	0.410953440907	Henry Cohn, 2026.
15	692	0.412755315335	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	693	0.412884102106	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	694	0.413097451293	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	695	0.413241695538	Vadim Borisov, 2026.
15	696	0.413550169544	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	697	0.414944700351	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	698	0.415001649308	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	699	0.415077905213	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	701	0.415129668410	Vadim Borisov, 2026.
15	702	0.415137841939	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	703	0.418183192196	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	704	0.418342976943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	705	0.418466504256	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	706	0.418508312721	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	709	0.419761712053	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	710	0.420386723758	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	711	0.420986734699	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	712	0.421046777385	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	713	0.421078178494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	714	0.421152484636	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	715	0.421232829141	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	716	0.421439843350	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	717	0.421593567212	Vadim Borisov, 2026.
15	718	0.421593611375	Christopher Smolen, 2026.
15	719	0.422630883420	Christopher Smolen, 2026.
15	720	0.422812977268	Christopher Smolen, 2026.
15	721	0.423000727180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	722	0.423247445283	Henry Cohn, 2026.
15	723	0.423564811178	Christopher Smolen, 2026.
15	724	0.423840228811	Christopher Smolen, 2026.
15	725	0.423950902610	Christopher Smolen, 2026.
15	726	0.424346136725	Christopher Smolen, 2026.
15	727	0.424521047353	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	728	0.424714691791	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	729	0.425034586123	Christopher Smolen, 2026.
15	730	0.425114736245	Vadim Borisov, 2026.
15	731	0.425312378870	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	732	0.425480527515	Christopher Smolen, 2026.
15	733	0.425629422910	Christopher Smolen, 2026.
15	734	0.425816151675	Christopher Smolen, 2026.
15	735	0.426015162525	Christopher Smolen, 2026.
15	736	0.426104536790	Henry Cohn, 2026.
15	737	0.426443760821	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	738	0.426650013537	Christopher Smolen, 2026.
15	739	0.426758052230	Henry Cohn, 2026.
15	740	0.426963535012	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
15	741	0.427196083262	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	742	0.427334327991	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	743	0.427568781408	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	744	0.427606505819	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	745	0.427683964255	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	746	0.427953683117	Christopher Smolen, 2026.
15	747	0.428041104426	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	748	0.428318676033	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	749	0.428444995107	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	990	0.428571428572	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $7 x - 3$
15	991	0.439533615304	Vadim Borisov, 2026.
15	992	0.441929160497	Vadim Borisov, 2026.
15	993	0.442956971146	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	994	0.443645321949	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
15	995	0.444576348059	Vadim Borisov, 2026.
15	996	0.445205588186	Vadim Borisov, 2026.
15	997	0.445851635941	Vadim Borisov, 2026.
15	998	0.446276836013	Vadim Borisov, 2026.
15	999	0.446749031461	Vadim Borisov, 2026.
15	1000	0.447442543864	Vadim Borisov, 2026.
15	1001	0.447820475558	Vadim Borisov, 2026.
15	1024	0.454545454546	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $11 x - 5$
16	33	0.047421028894	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3136 x^{3} - 256 x^{2} - 16 x + 1$
16	34	0.055555555556	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $18 x - 1$
16	36	0.056002309435	Henry Cohn, 2023. $176 x^{2} + 8 x - 1$
16	38	0.065186804094	Henry Cohn, 2023. $7312 x^{4} + 864 x^{3} - 200 x^{2} - 8 x + 1$
16	39	0.074285234713	Henry Cohn, 2025.
16	40	0.077433436468	Henry Cohn, 2024.
16	41	0.078328485376	Henry Cohn, 2023.
16	42	0.084589607356	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	44	0.085376587737	Henry Cohn, 2023. $512 x^{2} - 32 x - 1$
16	45	0.090651346396	Henry Cohn, 2023. Minimal polynomial of degree 10
16	46	0.093714773474	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $793984 x^{8} + 2769888 x^{7} - 316860 x^{6} - 393992 x^{5} - 62620 x^{4} - 1308 x^{3} + 460 x^{2} + 40 x + 1$
16	47	0.097443031003	Henry Cohn, 2025.
16	48	0.098771717854	Henry Cohn, 2023. $143 x^{2} - 4 x - 1$
16	49	0.104996942285	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	50	0.108589157773	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	51	0.110326320630	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	52	0.111429542518	Antoine Jay, 2026.
16	53	0.112355100713	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	54	0.112897448890	Henry Cohn, 2026.
16	55	0.113130733100	Henry Cohn, 2026. Minimal polynomial of degree 16
16	58	0.113835450316	Henry Cohn, 2026. $288 x^{2} - 24 x - 1$
16	59	0.115465967185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	60	0.115470027179	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	61	0.119282864595	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
16	62	0.125768177302	Henry Cohn, 2025.
16	63	0.127279043994	Arhan Canli, 2026.
16	74	0.127284656799	Henry Cohn, 2023. $156 x^{2} - 12 x - 1$
16	75	0.142327657262	Antoine Jay, 2026.
16	76	0.155902506876	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	77	0.156169461704	Antoine Jay, 2026.
16	78	0.156302278803	Arhan Canli, 2026.
16	79	0.156681637965	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	80	0.156933571315	Henry Cohn, 2026.
16	81	0.157220506242	Antoine Jay, 2026.
16	82	0.158219981270	Antoine Jay, 2026.
16	83	0.158831583908	Henry Cohn, 2026. Minimal polynomial of degree 8
16	84	0.159473252851	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $17856 x^{3} + 2064 x^{2} - 476 x - 49$
16	85	0.161129083237	Antoine Jay, 2026.
16	86	0.168620878713	Arhan Canli, 2026.
16	87	0.168626112124	Arhan Canli, 2026.
16	88	0.168628803038	Henry Cohn, 2026.
16	89	0.168633914730	Henry Cohn, 2026.
16	90	0.168641610264	Arhan Canli, 2026.
16	91	0.168679902316	Arhan Canli, 2026.
16	92	0.168684604646	Henry Cohn, 2025.
16	93	0.168684767443	Arhan Canli, 2026.
16	94	0.168684943106	Henry Cohn, 2026.
16	95	0.168685174869	Arhan Canli, 2026.
16	96	0.168685177103	Henry Cohn, 2026.
16	97	0.169879571132	Antoine Jay, 2026.
16	102	0.170753175474	Henry Cohn, 2026. $128 x^{2} - 16 x - 1$
16	103	0.174178397911	Henry Cohn, 2026. $2025 x^{4} - 180 x^{3} - 116 x^{2} - 8 x + 4$
16	104	0.179202077062	Henry Cohn, 2026.
16	105	0.183397573886	Antoine Jay, 2026.
16	106	0.185700040468	Antoine Jay, 2026.
16	107	0.188003446628	Antoine Jay, 2026.
16	108	0.190646755749	Antoine Jay, 2026.
16	109	0.191484537198	Antoine Jay, 2026.
16	110	0.191935850162	Antoine Jay, 2026.
16	111	0.192290990057	Antoine Jay, 2026.
16	112	0.192351726673	Arhan Canli, 2026.
16	113	0.192449549925	Henry Cohn, 2026.
16	114	0.192449657311	Henry Cohn, 2026.
16	115	0.192449738060	Henry Cohn, 2026.
16	116	0.192449821530	Henry Cohn, 2026.
16	117	0.192449865947	Henry Cohn, 2026.
16	118	0.192450089716	Henry Cohn, 2026.
16	122	0.198089808558	Kevin Li, 2026. $167044 x^{4} + 7656 x^{3} - 8896 x^{2} - 84 x + 49$
16	123	0.199970397832	Arhan Canli, 2026.
16	124	0.199983522439	Antoine Jay, 2026.
16	125	0.199990589938	Arhan Canli, 2026.
16	126	0.199991767996	Arhan Canli, 2026.
16	127	0.199995845425	Henry Cohn, 2025.
16	128	0.199997080222	Arhan Canli, 2026.
16	129	0.199999695524	Henry Cohn, 2026.
16	130	0.199999918321	Henry Cohn, 2025.
16	132	0.199999999923	Henry Cohn, 2026.
16	133	0.201680197728	Antoine Jay, 2026.
16	159	0.202913709779	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $44 x^{2} - 4 x - 1$
16	160	0.204972875483	Henry Cohn, 2026.
16	161	0.221562135223	Antoine Jay, 2026.
16	162	0.229540738948	Antoine Jay, 2026.
16	165	0.230995927542	Antoine Jay, 2026. $744016 x^{8} - 1439648 x^{7} + 1078648 x^{6} - 387608 x^{5} + 60577 x^{4} + 460 x^{3} - 1250 x^{2} + 100 x + 1$
16	166	0.234433486339	Vadim Borisov, 2026.
16	169	0.236031010307	Antoine Jay, 2026.
16	170	0.237448797461	Antoine Jay, 2026.
16	171	0.238394471457	Antoine Jay, 2026.
16	173	0.239265173403	Antoine Jay, 2026.
16	174	0.241218958758	Antoine Jay, 2026.
16	175	0.242225294068	Vadim Borisov, 2026.
16	176	0.244612743641	Christopher Smolen, 2026.
16	177	0.245298854217	Christopher Smolen, 2026.
16	178	0.245466691906	Antoine Jay, 2026.
16	179	0.245487521196	Arhan Canli, 2026.
16	180	0.245673189211	Arhan Canli, 2026.
16	181	0.245803620272	Antoine Jay, 2026.
16	182	0.246087737591	Arhan Canli, 2026.
16	183	0.246219291877	Arhan Canli, 2026.
16	184	0.246421765960	Arhan Canli, 2026.
16	185	0.246593605629	Antoine Jay, 2026.
16	186	0.246791151429	Antoine Jay, 2026.
16	187	0.246972605612	Christopher Smolen, 2026.
16	188	0.247105049636	Antoine Jay, 2026.
16	189	0.247253458246	Antoine Jay, 2026.
16	190	0.247329243444	Antoine Jay, 2026.
16	191	0.248282850170	Antoine Jay, 2026.
16	192	0.248473734545	Antoine Jay, 2026.
16	193	0.248654201905	Antoine Jay, 2026.
16	194	0.248892893493	Arhan Canli, 2026.
16	195	0.249045598570	Antoine Jay, 2026.
16	196	0.249161221394	Antoine Jay, 2026.
16	197	0.249252382842	Antoine Jay, 2026.
16	198	0.249443218019	Christopher Smolen, 2026.
16	199	0.249583186098	Antoine Jay, 2026.
16	200	0.249685006061	Christopher Smolen, 2026.
16	201	0.249778828655	Christopher Smolen, 2026.
16	202	0.249819380913	Christopher Smolen, 2026.
16	203	0.249874060581	Christopher Smolen, 2026.
16	204	0.249906361679	Christopher Smolen, 2026.
16	205	0.249928974355	Christopher Smolen, 2026.
16	206	0.249969831573	Christopher Smolen, 2026.
16	207	0.249976669134	Christopher Smolen, 2026.
16	208	0.249982725226	Christopher Smolen, 2026.
16	209	0.249987537775	Christopher Smolen, 2026.
16	210	0.249990688990	Vadim Borisov, 2026.
16	211	0.249991396920	Christopher Smolen, 2026.
16	288*	0.25	V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $4 x - 1$
16	289	0.285672436063	Henry Cohn, 2026.
16	290	0.288751039799	Henry Cohn, 2026.
16	291	0.294585013181	Christopher Smolen, 2026.
16	292	0.294705040579	Christopher Smolen, 2026.
16	294	0.294888199065	Antoine Jay, 2026.
16	295	0.296913508732	Henry Cohn, 2026.
16	296	0.298636022459	Antoine Jay, 2026.
16	297	0.302352327281	Christopher Smolen, 2026.
16	301	0.302456657937	Henry Cohn, 2026.
16	302	0.302628554368	Antoine Jay, 2026.
16	303	0.308227741514	Christopher Smolen, 2026.
16	312	0.308244047741	Antoine Jay, 2026.
16	313	0.308876104731	Henry Cohn, 2026.
16	314	0.310247708300	Henry Cohn, 2026.
16	315	0.311893285982	Antoine Jay, 2026.
16	316	0.313216726264	Antoine Jay, 2026.
16	317	0.317286618372	Christopher Smolen, 2026.
16	318	0.319992139495	Christopher Smolen, 2026.
16	319	0.321890728604	Christopher Smolen, 2026.
16	320	0.323044258399	Christopher Smolen, 2026.
16	321	0.325625143311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	322	0.326025972191	Christopher Smolen, 2026.
16	323	0.326576032308	Vadim Borisov, 2026.
16	324	0.326711283873	Vadim Borisov, 2026.
16	325	0.326811677780	Vadim Borisov, 2026.
16	326	0.326923540026	Vadim Borisov, 2026.
16	327	0.327034004934	Vadim Borisov, 2026.
16	328	0.327157993055	Vadim Borisov, 2026.
16	329	0.327246434246	Vadim Borisov, 2026.
16	330	0.327348855422	Vadim Borisov, 2026.
16	331	0.327507780160	Vadim Borisov, 2026.
16	332	0.327606596494	Christopher Smolen, 2026.
16	333	0.327608368278	Henry Cohn and Ilmari Vahteristo, 2026. $2816 x^{4} + 3648 x^{3} + 576 x^{2} - 432 x - 81$
16	340	0.328947368422	Henry Cohn, 2026. $76 x - 25$
16	341	0.329650454393	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	342	0.329800093565	Vadim Borisov, 2026.
16	343	0.329802145860	Vadim Borisov, 2026.
16	344	0.329923198665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	345	0.330010929843	Christopher Smolen, 2026.
16	346	0.330279727604	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	347	0.330516978675	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	348	0.330592500322	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	349	0.330624036667	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	350	0.330795177229	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	351	0.330902038877	Christopher Smolen, 2026.
16	352	0.331030497282	Christopher Smolen, 2026.
16	353	0.331244210356	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	354	0.331531960669	Christopher Smolen, 2026.
16	355	0.331622953160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	356	0.331665842432	Christopher Smolen, 2026.
16	357	0.331818489444	Christopher Smolen, 2026.
16	358	0.332027286009	Christopher Smolen, 2026.
16	359	0.332083035007	Christopher Smolen, 2026.
16	360	0.332246869953	Christopher Smolen, 2026.
16	361	0.332491582234	Christopher Smolen, 2026.
16	362	0.332564229620	Christopher Smolen, 2026.
16	363	0.332718808712	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	364	0.332750304389	Christopher Smolen, 2026.
16	365	0.332907956764	Christopher Smolen, 2026.
16	366	0.332913339734	Vadim Borisov, 2026.
16	367	0.332958558661	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	368	0.333067637736	Christopher Smolen, 2026.
16	369	0.333176679024	Christopher Smolen, 2026.
16	370	0.333194214746	Christopher Smolen, 2026.
16	512	0.333333333334	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $3 x - 1$
16	513	0.350751124091	Christopher Smolen, 2026.
16	514	0.351224805918	Christopher Smolen, 2026.
16	515	0.352910061727	Christopher Smolen, 2026.
16	516	0.354162743222	Vadim Borisov, 2026.
16	517	0.355877079801	Vadim Borisov, 2026.
16	518	0.358081511964	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	519	0.358882789791	Christopher Smolen, 2026.
16	520	0.359930377260	Christopher Smolen, 2026.
16	521	0.360636765322	Christopher Smolen, 2026.
16	522	0.360828964137	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	523	0.361223104845	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	524	0.362554893465	Christopher Smolen, 2026.
16	525	0.362990620480	Christopher Smolen, 2026.
16	526	0.363464351981	Christopher Smolen, 2026.
16	527	0.363996174393	Christopher Smolen, 2026.
16	528	0.364541522831	Christopher Smolen, 2026.
16	529	0.365190961940	Christopher Smolen, 2026.
16	530	0.365497806819	Christopher Smolen, 2026.
16	531	0.365821769208	Christopher Smolen, 2026.
16	532	0.366424197725	Christopher Smolen, 2026.
16	533	0.366969369588	Christopher Smolen, 2026.
16	534	0.367325473194	Christopher Smolen, 2026.
16	535	0.367805854408	Christopher Smolen, 2026.
16	536	0.368164942960	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	537	0.368381301518	Christopher Smolen, 2026.
16	538	0.369121684756	Christopher Smolen, 2026.
16	567	0.369248411466	Henry Cohn, 2026. $29 x^{2} - 8 x - 1$
16	575	0.375	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $8 x - 3$
16	625	0.375	Henry Cohn, 2026. $8 x - 3$
16	626	0.378830677638	Christopher Smolen, 2026.
16	627	0.379603055136	Christopher Smolen, 2026.
16	628	0.380186391761	Christopher Smolen, 2026.
16	629	0.381040311125	Christopher Smolen, 2026.
16	630	0.381288062682	Vadim Borisov, 2026.
16	631	0.381518385467	Vadim Borisov, 2026.
16	632	0.382229449524	Vadim Borisov, 2026.
16	633	0.382461158395	Vadim Borisov, 2026.
16	634	0.382923964614	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	635	0.383375360361	Christopher Smolen, 2026.
16	636	0.383996345483	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	642	0.384615384616	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $13 x - 5$
16	643	0.386118033663	Christopher Smolen, 2026.
16	644	0.386242492071	Christopher Smolen, 2026.
16	645	0.386380503444	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	646	0.386495323751	Vadim Borisov, 2026.
16	647	0.386686676336	Vadim Borisov, 2026.
16	648	0.386801445353	Vadim Borisov, 2026.
16	649	0.386943031351	Vadim Borisov, 2026.
16	650	0.387010725952	Vadim Borisov, 2026.
16	651	0.387071193214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	652	0.387347222189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	653	0.387391774306	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	654	0.387458708734	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	655	0.387543411184	Vadim Borisov, 2026.
16	656	0.387645916422	Vadim Borisov, 2026.
16	657	0.387704262840	Vadim Borisov, 2026.
16	658	0.387814984809	Vadim Borisov, 2026.
16	659	0.387835187110	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	660	0.387860582359	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	661	0.387886661087	Vadim Borisov, 2026.
16	662	0.388076907881	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	663	0.388146276813	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	664	0.388262652170	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	665	0.388312013784	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	666	0.388324346041	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	667	0.388344518802	Vadim Borisov, 2026.
16	668	0.388357351182	Vadim Borisov, 2026.
16	669	0.388366036491	Vadim Borisov, 2026.
16	670	0.388366076776	Vadim Borisov, 2026.
16	671	0.388366241978	Vadim Borisov, 2026.
16	672	0.388426243412	Vadim Borisov, 2026.
16	673	0.388426253560	Vadim Borisov, 2026.
16	674	0.388426317203	Vadim Borisov, 2026.
16	675	0.388426389479	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	676	0.388501647924	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	677	0.388601015082	Vadim Borisov, 2026.
16	678	0.388601251323	Vadim Borisov, 2026.
16	679	0.388609726225	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	680	0.388640048917	Vadim Borisov, 2026.
16	681	0.388640445793	Vadim Borisov, 2026.
16	682	0.388785564846	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	684	0.388850576909	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	689	0.389345247397	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	691	0.389350616812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	692	0.389806425022	Vadim Borisov, 2026.
16	693	0.389806697084	Vadim Borisov, 2026.
16	694	0.390234177339	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	695	0.390911355011	Vadim Borisov, 2026.
16	696	0.390912845531	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	697	0.390994558643	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	698	0.391407023875	Christopher Smolen, 2026.
16	704	0.391407227220	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	705	0.391416869535	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	706	0.391784010410	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	707	0.391879044098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	708	0.391882615009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	709	0.392030861929	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	710	0.392052700540	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	711	0.392696025762	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	712	0.392904839710	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	713	0.393158688123	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	714	0.393355075361	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	715	0.393361525763	Vadim Borisov, 2026.
16	723	0.393432192133	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	724	0.396769305879	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	725	0.396826539379	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	726	0.396875375920	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	727	0.397207509162	Vadim Borisov, 2026.
16	728	0.397758681382	Vadim Borisov, 2026.
16	729	0.398116485229	Vadim Borisov, 2026.
16	768	0.4	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
16	769	0.4	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 2$
16	771	0.4	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $5 x - 2$
16	772	0.400742606578	Henry Cohn, 2026.
16	773	0.400872738192	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	774	0.400987023054	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	775	0.401066106464	Vadim Borisov, 2026.
16	776	0.401133301550	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	777	0.401205918595	Vadim Borisov, 2026.
16	778	0.401259159937	Vadim Borisov, 2026.
16	779	0.401316962197	Vadim Borisov, 2026.
16	780	0.401348483139	Vadim Borisov, 2026.
16	781	0.401393753735	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	782	0.401537677783	Vadim Borisov, 2026.
16	783	0.401594856716	Vadim Borisov, 2026.
16	784	0.401647161129	Vadim Borisov, 2026.
16	785	0.401686480733	Vadim Borisov, 2026.
16	786	0.401758189491	Vadim Borisov, 2026.
16	787	0.401892053578	Vadim Borisov, 2026.
16	788	0.402078902373	Robert Dallara, 2026.
16	789	0.402225742014	Vadim Borisov, 2026.
16	790	0.402291661216	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	796	0.406592143967	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	797	0.407607407428	Vadim Borisov, 2026.
16	798	0.407756668947	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	799	0.407789822522	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	800	0.407794096553	Vadim Borisov, 2026.
16	801	0.407802109031	Vadim Borisov, 2026.
16	804	0.407806039438	Vadim Borisov, 2026.
16	805	0.408443560485	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	806	0.408527523055	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	807	0.408821436114	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	808	0.408914813689	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	809	0.408933069386	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	810	0.408962750560	Vadim Borisov, 2026.
16	811	0.408969286516	Vadim Borisov, 2026.
16	813	0.408969289358	Vadim Borisov, 2026.
16	814	0.408969291404	Vadim Borisov, 2026.
16	815	0.409226537683	Vadim Borisov, 2026.
16	816	0.409278635311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	817	0.409287691298	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	818	0.409323277042	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	819	0.409368222033	Vadim Borisov, 2026.
16	820	0.409369669265	Vadim Borisov, 2026.
16	821	0.409873328607	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	822	0.410003859377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	823	0.410035339408	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	824	0.410094618396	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	825	0.410142023021	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	826	0.410208050193	Vadim Borisov, 2026.
16	827	0.410841895902	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	828	0.410896955189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	829	0.411015321929	Vadim Borisov, 2026.
16	830	0.411324914572	Vadim Borisov, 2026.
16	831	0.411438305673	Vadim Borisov, 2026.
16	832	0.412653617132	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	833	0.412750500185	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	834	0.412934886474	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	835	0.412980817590	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	836	0.413004071518	Vadim Borisov, 2026.
16	837	0.413018774865	Vadim Borisov, 2026.
16	838	0.413018776082	Vadim Borisov, 2026.
16	839	0.413635121714	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	840	0.413807007644	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	841	0.413878760447	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	842	0.414059946077	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	843	0.414123306343	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	844	0.414319393234	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	845	0.414360133575	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	846	0.414516915481	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	847	0.414641524062	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	848	0.414686311162	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	849	0.414711824481	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	850	0.414781154747	Vadim Borisov, 2026.
16	851	0.414805099069	Vadim Borisov, 2026.
16	852	0.414805208168	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	853	0.415304423440	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	854	0.415336539245	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	855	0.415471892376	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	856	0.415534451489	Vadim Borisov, 2026.
16	857	0.415647516022	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	858	0.415715223380	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	859	0.415767902384	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	861	0.415830279984	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	862	0.415830403753	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	863	0.416102337025	Christopher Smolen, 2026.
16	864	0.416149244668	Henry Cohn, 2026.
16	865	0.417730134397	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	866	0.417909924841	Vadim Borisov, 2026.
16	915	0.423076923077	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $26 x - 11$
16	916	0.425366929278	Vadim Borisov, 2026.
16	917	0.425925368069	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	918	0.426349107316	Vadim Borisov, 2026.
16	919	0.426706379787	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	920	0.426952139395	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
16	921	0.427335185150	Vadim Borisov, 2026.
16	922	0.427588736894	Vadim Borisov, 2026.
16	1024	0.428571428572	Subcode of a code of size 1056 from T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $7 x - 3$
17	35	0.044915529038	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3825 x^{3} - 289 x^{2} - 17 x + 1$
17	36	0.052701899358	Henry Cohn, 2025.
17	37	0.055949316790	Henry Cohn, 2026.
17	38	0.055983875620	Henry Cohn, 2025.
17	39	0.062879614874	Henry Cohn, 2024.
17	40	0.064963088389	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	41	0.070153821556	Henry Cohn, 2025.
17	42	0.073269797523	Henry Cohn, 2025.
17	45	0.073591871415	Henry Cohn, 2023. $239 x^{2} - 4 x - 1$
17	46	0.080184930575	Henry Cohn, 2026.
17	52	0.084342587557	Henry Cohn, 2023. $188 x^{2} - 4 x - 1$
17	53	0.098937215086	Henry Cohn, 2024. $2304 x^{4} - 96 x^{3} - 95 x^{2} - 2 x + 1$
17	55	0.099686435548	Henry Cohn, 2026. $153 x^{4} + 480 x^{3} - 150 x^{2} + 1$
17	56	0.102993455487	Henry Cohn, 2026.
17	57	0.104796880087	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	58	0.108405584144	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	64	0.111111111112	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 1$
17	65	0.120819518077	Henry Cohn, 2026.
17	66	0.124443665548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	67	0.125750191268	Antoine Jay, 2026.
17	68	0.125849453172	Antoine Jay, 2026.
17	69	0.127153183547	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	70	0.127263309273	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	71	0.127270310008	Henry Cohn, 2025.
17	72	0.127276381331	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	73	0.127278697335	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	74	0.127282531626	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	75	0.127283313870	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	76	0.127284594470	Henry Cohn, 2026.
17	77	0.127301897398	Henry Cohn, 2026.
17	78	0.135229770561	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	79	0.142554962940	Antoine Jay, 2026.
17	80	0.146641417383	Antoine Jay, 2026.
17	81	0.149798231118	Antoine Jay, 2026.
17	82	0.149909121569	Arhan Canli, 2026.
17	83	0.149970574466	Christopher Smolen, 2026.
17	84	0.149991393024	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	85	0.149994256949	Arhan Canli, 2026.
17	86	0.149997901942	Arhan Canli, 2026.
17	87	0.151340636556	Antoine Jay, 2026. $3294225 x^{8} + 72600 x^{7} - 14520 x^{6} - 87120 x^{5} - 10990 x^{4} + 20 x^{3} + 120 x^{2} + 9$
17	88	0.156158056242	Antoine Jay, 2026.
17	89	0.158627365814	Antoine Jay, 2026.
17	90	0.163935338020	Antoine Jay, 2026.
17	91	0.165647079245	Antoine Jay, 2026.
17	93	0.165769115717	Henry Cohn, 2026.
17	94	0.166861153292	Henry Cohn, 2026.
17	95	0.167496184909	Arhan Canli, 2026.
17	96	0.167670995928	Antoine Jay, 2026.
17	97	0.168471952633	Antoine Jay, 2026.
17	98	0.168527003653	Arhan Canli, 2026.
17	99	0.168572903770	Arhan Canli, 2026.
17	100	0.168653925739	Arhan Canli, 2026.
17	101	0.168685133548	Christopher Smolen, 2026.
17	102	0.169521436283	Antoine Jay, 2026.
17	103	0.170712532762	Arhan Canli, 2026.
17	104	0.170741063879	Arhan Canli, 2026.
17	105	0.170744894972	Arhan Canli, 2026.
17	106	0.170749222429	Arhan Canli, 2026.
17	107	0.170757524719	Antoine Jay, 2026.
17	108	0.174934103786	Antoine Jay, 2026.
17	109	0.177558450562	Antoine Jay, 2026.
17	110	0.179792416049	Antoine Jay, 2026.
17	111	0.182361554034	Arhan Canli, 2026.
17	112	0.184247183944	Antoine Jay, 2026.
17	115	0.184252183279	Henry Cohn, 2026. $1991 x^{2} - 318 x - 9$
17	116	0.184847525793	Henry Cohn, 2026.
17	117	0.186580978028	Henry Cohn, 2026.
17	118	0.187721373339	Antoine Jay, 2026.
17	119	0.189940924423	Antoine Jay, 2026.
17	120	0.190639194713	Antoine Jay, 2026.
17	121	0.192191226811	Antoine Jay, 2026.
17	122	0.192324127688	Antoine Jay, 2026.
17	123	0.192356592165	Antoine Jay, 2026.
17	124	0.192908016514	Henry Cohn, 2026.
17	125	0.192908036827	Henry Cohn, 2026.
17	126	0.192978307532	Arhan Canli, 2026.
17	127	0.193824582853	Arhan Canli, 2026.
17	128	0.195734935764	Antoine Jay, 2026.
17	129	0.196692150052	Christopher Smolen, 2026.
17	130	0.197510829950	Antoine Jay, 2026.
17	131	0.198825234025	Antoine Jay, 2026.
17	132	0.198977116394	Antoine Jay, 2026.
17	133	0.199548362754	Arhan Canli, 2026.
17	134	0.199766808081	Christopher Smolen, 2026.
17	135	0.199800789928	Christopher Smolen, 2026.
17	136	0.199963607611	Christopher Smolen, 2026.
17	137	0.199982429944	Christopher Smolen, 2026.
17	138	0.199998850847	Vadim Borisov, 2026.
17	139	0.199999128000	Christopher Smolen, 2026.
17	140	0.2	Henry Cohn and Ilmari Vahteristo, 2026. $5 x - 1$
17	141	0.201562902712	Antoine Jay, 2026.
17	142	0.202807941098	Antoine Jay, 2026.
17	143	0.202854769575	Christopher Smolen, 2026.
17	144	0.202857234778	Christopher Smolen, 2026.
17	145	0.202861828906	Vadim Borisov, 2026.
17	146	0.202863997803	Christopher Smolen, 2026.
17	147	0.202867825336	Christopher Smolen, 2026.
17	148	0.202874143736	Henry Cohn, 2026.
17	149	0.202876845173	Christopher Smolen, 2026.
17	150	0.202893222954	Christopher Smolen, 2026.
17	151	0.202896250137	Christopher Smolen, 2026.
17	152	0.202897695720	Christopher Smolen, 2026.
17	153	0.202906303573	Christopher Smolen, 2026.
17	154	0.202908133431	Christopher Smolen, 2026.
17	155	0.202909285760	Christopher Smolen, 2026.
17	156	0.202910226208	Christopher Smolen, 2026.
17	157	0.202910856895	Christopher Smolen, 2026.
17	158	0.202911797304	Christopher Smolen, 2026.
17	159	0.202913168373	Christopher Smolen, 2026.
17	164	0.202913709779	Henry Cohn, 2026.
17	165	0.203268790204	Christopher Smolen, 2026.
17	166	0.209186347459	Antoine Jay, 2026.
17	167	0.209346066218	Christopher Smolen, 2026.
17	168	0.209696026937	Antoine Jay, 2026.
17	177	0.214580576913	Henry Cohn, 2026. $59 x^{2} - 8 x - 1$
17	178	0.215890665682	Henry Cohn, 2026.
17	179	0.223188580348	Christopher Smolen, 2026.
17	180	0.224729846788	Christopher Smolen, 2026.
17	181	0.226958235410	Christopher Smolen, 2026.
17	182	0.227086247808	Antoine Jay, 2026.
17	183	0.228325646935	Antoine Jay, 2026.
17	190	0.228481712325	Henry Cohn, 2026. $38025 x^{6} + 44850 x^{5} - 29537 x^{4} - 28836 x^{3} - 441 x^{2} + 1458 x + 81$
17	192	0.228481712325	Antoine Jay, 2026. $38025 x^{6} + 44850 x^{5} - 29537 x^{4} - 28836 x^{3} - 441 x^{2} + 1458 x + 81$
17	193	0.233271833544	Henry Cohn, 2026.
17	194	0.234551859500	Antoine Jay, 2026.
17	195	0.235022456914	Antoine Jay, 2026.
17	196	0.236950430306	Antoine Jay, 2026.
17	197	0.237728704550	Antoine Jay, 2026.
17	198	0.238349150124	Antoine Jay, 2026.
17	200	0.238867691493	Antoine Jay, 2026.
17	201	0.239060915559	Henry Cohn, 2026.
17	202	0.241446344171	Antoine Jay, 2026.
17	203	0.242031228619	Christopher Smolen, 2026.
17	204	0.242720130362	Christopher Smolen, 2026.
17	205	0.243054178067	Antoine Jay, 2026.
17	206	0.243493592591	Antoine Jay, 2026.
17	207	0.243899457859	Antoine Jay, 2026.
17	208	0.244371965995	Antoine Jay, 2026.
17	209	0.244526177636	Antoine Jay, 2026.
17	210	0.244745836815	Antoine Jay, 2026.
17	211	0.245004426037	Antoine Jay, 2026.
17	212	0.245319206440	Antoine Jay, 2026.
17	213	0.245444484388	Antoine Jay, 2026.
17	214	0.245981457056	Antoine Jay, 2026.
17	215	0.246105182368	Antoine Jay, 2026.
17	216	0.246357697955	Christopher Smolen, 2026.
17	217	0.246623000470	Antoine Jay, 2026.
17	218	0.246860278924	Antoine Jay, 2026.
17	219	0.246984277708	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	220	0.247141295924	Christopher Smolen, 2026.
17	221	0.247351591371	Vadim Borisov, 2026.
17	222	0.247422609526	Antoine Jay, 2026.
17	223	0.247634259278	Antoine Jay, 2026.
17	224	0.247948194587	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	225	0.248085407135	Christopher Smolen, 2026.
17	226	0.248538988120	Christopher Smolen, 2026.
17	227	0.248653327358	Christopher Smolen, 2026.
17	228	0.248761583814	Christopher Smolen, 2026.
17	229	0.248831101505	Antoine Jay, 2026.
17	230	0.249105350064	Christopher Smolen, 2026.
17	231	0.249159304252	Christopher Smolen, 2026.
17	232	0.249200693128	Christopher Smolen, 2026.
17	233	0.249231542844	Christopher Smolen, 2026.
17	234	0.249257757799	Christopher Smolen, 2026.
17	235	0.249289352520	Christopher Smolen, 2026.
17	236	0.249349243153	Christopher Smolen, 2026.
17	237	0.249389253472	Christopher Smolen, 2026.
17	238	0.249399403228	Christopher Smolen, 2026.
17	239	0.249515869720	Christopher Smolen, 2026.
17	240	0.249584573658	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	241	0.249639700726	Christopher Smolen, 2026.
17	242	0.249721282976	Christopher Smolen, 2026.
17	243	0.249728036762	Christopher Smolen, 2026.
17	244	0.249737133671	Christopher Smolen, 2026.
17	245	0.249752742790	Christopher Smolen, 2026.
17	246	0.249761536280	Christopher Smolen, 2026.
17	247	0.249799948684	Christopher Smolen, 2026.
17	248	0.249807345955	Christopher Smolen, 2026.
17	249	0.249850246295	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	250	0.249878573093	Christopher Smolen, 2026.
17	251	0.249905349377	Christopher Smolen, 2026.
17	252	0.249913275440	Christopher Smolen, 2026.
17	253	0.249981333556	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	254	0.249984689419	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	255	0.249985230198	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	256	0.249986404139	Vadim Borisov, 2026.
17	257	0.249986776912	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	258	0.249988846536	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	259	0.249990425765	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	260	0.249993027082	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	261	0.249994387189	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	262	0.249994860491	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	263	0.249995296973	Henry Cohn, 2026.
17	264	0.249995296974	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	265	0.249995452411	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	266	0.249995812003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	267	0.249996389512	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	268	0.249996812505	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	269	0.249997161122	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	270	0.249997699114	Christopher Smolen, 2026.
17	271	0.249997925276	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	272	0.249998174815	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	273	0.249998410879	Christopher Smolen, 2026.
17	274	0.249998481085	Christopher Smolen, 2026.
17	275	0.249998587055	Vadim Borisov, 2026.
17	276	0.249998723605	Christopher Smolen, 2026.
17	277	0.249998856679	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	278	0.249998878966	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	279	0.249998879181	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	280	0.249999070611	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	281	0.249999134423	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	282	0.249999152745	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	283	0.249999263692	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	284	0.249999330349	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	285	0.249999379638	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	286	0.249999443279	Henry Cohn, 2026.
17	287	0.249999443797	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	288	0.249999737350	Christopher Smolen, 2026.
17	289	0.249999830091	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	290	0.249999930579	Henry Cohn, 2026.
17	294	0.249999999999	Henry Cohn, 2026.
17	295	0.250317937224	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	296	0.252523490576	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	297	0.255469746604	Christopher Smolen, 2026.
17	298	0.256370333246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	299	0.258683360982	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	300	0.259097119863	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	301	0.259139404371	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	302	0.259271051323	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	303	0.259427247740	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	304	0.259544638827	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	305	0.259985071512	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	306	0.260625289096	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	307	0.260856287700	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	308	0.260895707597	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	309	0.260965383541	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	310	0.261001171578	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	311	0.261035169109	Christopher Smolen, 2026.
17	312	0.261039233456	Christopher Smolen, 2026.
17	313	0.261048000334	Christopher Smolen, 2026.
17	314	0.261052974170	Christopher Smolen, 2026.
17	315	0.261073590382	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	316	0.261075165023	Christopher Smolen, 2026.
17	317	0.261078957787	Vadim Borisov, 2026.
17	318	0.261079833865	Christopher Smolen, 2026.
17	319	0.261094123550	Christopher Smolen, 2026.
17	320	0.261094130017	Christopher Smolen, 2026.
17	321	0.281458624142	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	322	0.286285472916	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
17	323	0.289489438364	Christopher Smolen, 2026.
17	324	0.291595883409	Christopher Smolen, 2026.
17	325	0.293575794879	Christopher Smolen, 2026.
17	352	0.294117647059	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $17 x - 5$
17	353	0.296535165409	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $8 x^{2} + x - 1$
17	354	0.303054205683	Christopher Smolen, 2026.
17	355	0.304366840303	Christopher Smolen, 2026.
17	356	0.305238431472	Christopher Smolen, 2026.
17	357	0.306093007644	Christopher Smolen, 2026.
17	358	0.306688791017	Christopher Smolen, 2026.
17	359	0.307431986056	Christopher Smolen, 2026.
17	360	0.308031913960	Christopher Smolen, 2026.
17	361	0.308321574525	Christopher Smolen, 2026.
17	362	0.308713742276	Christopher Smolen, 2026.
17	363	0.309147278622	Christopher Smolen, 2026.
17	364	0.309522581154	Christopher Smolen, 2026.
17	365	0.309893241719	Christopher Smolen, 2026.
17	366	0.310326696714	Christopher Smolen, 2026.
17	367	0.310570720086	Christopher Smolen, 2026.
17	368	0.310892788658	Christopher Smolen, 2026.
17	369	0.311196810879	Christopher Smolen, 2026.
17	370	0.311456276096	Christopher Smolen, 2026.
17	371	0.311796387240	Christopher Smolen, 2026.
17	372	0.312062590299	Christopher Smolen, 2026.
17	373	0.312278858406	Christopher Smolen, 2026.
17	374	0.312606387031	Christopher Smolen, 2026.
17	375	0.312911977139	Christopher Smolen, 2026.
17	376	0.313083589025	Christopher Smolen, 2026.
17	377	0.313357443261	Christopher Smolen, 2026.
17	378	0.313536734334	Christopher Smolen, 2026.
17	379	0.313732444800	Christopher Smolen, 2026.
17	380	0.313949555972	Christopher Smolen, 2026.
17	381	0.314107326647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	382	0.314316668038	Christopher Smolen, 2026.
17	383	0.314496102304	Christopher Smolen, 2026.
17	384	0.314683589184	Christopher Smolen, 2026.
17	385	0.314750301291	Christopher Smolen, 2026.
17	386	0.315149702958	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	387	0.315155048648	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	388	0.315420455394	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	389	0.315790909941	Christopher Smolen, 2026.
17	390	0.316045332994	Christopher Smolen, 2026.
17	391	0.316325397040	Christopher Smolen, 2026.
17	392	0.316439837245	Vadim Borisov, 2026.
17	393	0.316596545552	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	394	0.316733835519	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	395	0.316883226595	Vadim Borisov, 2026.
17	396	0.316988926075	Vadim Borisov, 2026.
17	397	0.317140125506	Vadim Borisov, 2026.
17	398	0.317216225771	Vadim Borisov, 2026.
17	399	0.317361167563	Christopher Smolen, 2026.
17	400	0.317528959662	Vadim Borisov, 2026.
17	401	0.317627826498	Vadim Borisov, 2026.
17	402	0.317771223952	Vadim Borisov, 2026.
17	403	0.317934894413	Vadim Borisov, 2026.
17	404	0.318142020249	Vadim Borisov, 2026.
17	405	0.318259842975	Vadim Borisov, 2026.
17	406	0.318399077968	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	407	0.318494303177	Vadim Borisov, 2026.
17	408	0.318623663723	Vadim Borisov, 2026.
17	409	0.318766260639	Christopher Smolen, 2026.
17	410	0.318870083295	Christopher Smolen, 2026.
17	411	0.318942518430	Christopher Smolen, 2026.
17	412	0.318993704823	Christopher Smolen, 2026.
17	434	0.319025504452	Henry Cohn, 2026.
17	435	0.320843410356	Christopher Smolen, 2026.
17	436	0.322285599545	Christopher Smolen, 2026.
17	437	0.322623837931	Christopher Smolen, 2026.
17	438	0.323530357660	Christopher Smolen, 2026.
17	439	0.323875329063	Christopher Smolen, 2026.
17	440	0.324304796250	Christopher Smolen, 2026.
17	441	0.324671091239	Christopher Smolen, 2026.
17	442	0.325040747207	Christopher Smolen, 2026.
17	443	0.325685285490	Christopher Smolen, 2026.
17	444	0.326271218927	Christopher Smolen, 2026.
17	445	0.326588284663	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	446	0.327284547078	Christopher Smolen, 2026.
17	447	0.327506468369	Christopher Smolen, 2026.
17	448	0.327648886290	Christopher Smolen, 2026.
17	449	0.327798877780	Christopher Smolen, 2026.
17	450	0.329748481359	Christopher Smolen, 2026.
17	451	0.330606258155	Christopher Smolen, 2026.
17	452	0.331287702906	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	453	0.332563081825	Christopher Smolen, 2026.
17	546	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
17	578	0.333333333334	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $3 x - 1$
17	738	0.341506350947	Henry Cohn, 2026. $32 x^{2} - 8 x - 1$
17	739	0.343910155565	Christopher Smolen, 2026.
17	740	0.352563667104	Vadim Borisov, 2026.
17	741	0.354418996384	Vadim Borisov, 2026.
17	742	0.354695704984	Vadim Borisov, 2026.
17	743	0.355955532625	Vadim Borisov, 2026.
17	744	0.356345230894	Vadim Borisov, 2026.
17	745	0.356798158019	Vadim Borisov, 2026.
17	746	0.357014634102	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	747	0.357190741712	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	748	0.357356506687	Vadim Borisov, 2026.
17	749	0.357497125619	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	750	0.357579268166	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	751	0.357654707906	Vadim Borisov, 2026.
17	769	0.36	Henry Cohn, 2026. $25 x - 9$
17	770	0.365878117251	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	771	0.366475132566	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	772	0.368318501356	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	773	0.368916000007	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	774	0.369932626670	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	775	0.370929838214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	776	0.371896865540	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
17	777	0.372380282732	Henry Cohn, 2026.
17	778	0.373183626105	Vadim Borisov, 2026.
17	779	0.373513232193	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	780	0.374210411048	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	781	0.374782390779	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	782	0.375182548214	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	783	0.375503708319	Vadim Borisov, 2026.
17	784	0.376196470884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	785	0.376710875512	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	786	0.377129942050	Vadim Borisov, 2026.
17	787	0.377629686109	Vadim Borisov, 2026.
17	788	0.378282694525	Vadim Borisov, 2026.
17	789	0.379121858313	Vadim Borisov, 2026.
17	790	0.379573831677	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	791	0.379925875099	Vadim Borisov, 2026.
17	792	0.380223343812	Vadim Borisov, 2026.
17	793	0.380667458044	Vadim Borisov, 2026.
17	794	0.380994636338	Vadim Borisov, 2026.
17	795	0.381112189462	Vadim Borisov, 2026.
17	796	0.381624292945	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	797	0.381723031586	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	798	0.381839827151	Vadim Borisov, 2026.
17	799	0.382237380534	Vadim Borisov, 2026.
17	800	0.382791472009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	801	0.382902954043	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	802	0.383313851330	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
17	803	0.383374379360	Vadim Borisov, 2026.
17	1024	0.384615384616	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $13 x - 5$
18	37	0.042671058118	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4608 x^{3} - 324 x^{2} - 18 x + 1$
18	38	0.050085070755	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	39	0.055224148787	Henry Cohn, 2025.
18	40	0.055678193348	Henry Cohn, 2025. $1856 x^{4} + 736 x^{3} + 204 x^{2} + 4 x - 1$
18	41	0.060967744952	Henry Cohn, 2023.
18	42	0.063457905214	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	43	0.066629754705	Henry Cohn, 2025.
18	44	0.066804066179	Henry Cohn, 2023.
18	45	0.071480323505	Henry Cohn, 2026.
18	46	0.073552043366	Henry Cohn, 2025.
18	47	0.073575768177	Henry Cohn, 2025. Minimal polynomial of degree 8
18	48	0.074706792917	Henry Cohn, 2024. $49250304 x^{8} - 30019584 x^{7} - 3769088 x^{6} - 1665536 x^{5} + 436432 x^{4} + 8256 x^{3} - 3792 x^{2} + 9$
18	50	0.078219048073	Henry Cohn, 2025. $368 x^{2} - 16 x - 1$
18	51	0.084258729168	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	52	0.084267508224	Antoine Jay, 2026.
18	53	0.084306482303	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	54	0.084331756953	Henry Cohn, 2026. Minimal polynomial of degree 8
18	55	0.087707155784	Henry Cohn, 2025. $1893264 x^{8} - 1540752 x^{7} - 326156 x^{6} + 37720 x^{5} + 15340 x^{4} - 308 x^{3} - 220 x^{2} + 1$
18	57	0.092724727985	Henry Cohn, 2025. $332 x^{2} - 20 x - 1$
18	58	0.096106487484	Antoine Jay, 2026. $27 x^{2} - 13 x + 1$
18	59	0.096317631192	Henry Cohn, 2025. Minimal polynomial of degree 9
18	60	0.096621974569	Henry Cohn, 2025. $1392 x^{5} + 5600 x^{4} - 2304 x^{3} + 152 x^{2} + 12 x - 1$
18	69	0.101456854890	Henry Cohn, 2024. $176 x^{2} - 8 x - 1$
18	71	0.107360417201	Henry Cohn, 2026. $252 x^{4} - 672 x^{3} + 156 x^{2} - 1$
18	72	0.109540130282	Henry Cohn, 2026. $360 x^{3} - 68 x^{2} - 6 x + 1$
18	73	0.117125796978	Antoine Jay, 2026.
18	74	0.119652337905	Antoine Jay, 2026. Minimal polynomial of degree 10
18	75	0.120367585569	Antoine Jay, 2026. Minimal polynomial of degree 15
18	80	0.121417162017	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $31 x^{2} - 12 x + 1$
18	81	0.126904281671	Henry Cohn, 2026.
18	82	0.127626473233	Antoine Jay, 2026.
18	83	0.129097400889	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	84	0.130577223388	Antoine Jay, 2026.
18	85	0.132288436915	Antoine Jay, 2026.
18	86	0.132700003712	Henry Cohn, 2026.
18	87	0.133632203004	Henry Cohn, 2026.
18	88	0.134255586334	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	96	0.142857142858	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 1$
18	97	0.152402949200	Henry Cohn, 2026. $16 x^{2} - 9 x + 1$
18	98	0.155249851767	Henry Cohn, 2026. $64 x^{4} + 32 x^{3} - 48 x^{2} + 1$
18	100	0.155555555556	Henry Cohn and Ilmari Vahteristo, 2026. $45 x - 7$
18	101	0.161087011866	Henry Cohn, 2026. $52 x^{2} - 27 x + 3$
18	104	0.162407002682	Henry Cohn, 2026. $671 x^{4} - 1296 x^{3} + 534 x^{2} - 9$
18	105	0.164921962691	Henry Cohn, 2026.
18	106	0.166070240074	Henry Cohn, 2026.
18	108	0.166586736179	Henry Cohn, 2026. Minimal polynomial of degree 12
18	109	0.167620271520	Arhan Canli, 2026.
18	110	0.168420213361	Arhan Canli, 2026.
18	111	0.169247849122	Arhan Canli, 2026.
18	112	0.169837632923	Antoine Jay, 2026.
18	113	0.170561788297	Antoine Jay, 2026.
18	114	0.172117056752	Arhan Canli, 2026.
18	115	0.172912754537	Antoine Jay, 2026.
18	116	0.174475260620	Antoine Jay, 2026. Minimal polynomial of degree 16
18	117	0.177748575135	Vadim Borisov, 2026.
18	118	0.180941270358	Antoine Jay, 2026.
18	119	0.182508766992	Antoine Jay, 2026.
18	120	0.184835329639	Antoine Jay, 2026.
18	121	0.185547953776	Antoine Jay, 2026.
18	122	0.186952176805	Antoine Jay, 2026.
18	123	0.188109726075	Antoine Jay, 2026.
18	128	0.188405797102	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $69 x - 13$
18	129	0.188801907500	Christopher Smolen, 2026.
18	130	0.188960803287	Antoine Jay, 2026.
18	131	0.190522135309	Antoine Jay, 2026.
18	132	0.191489361703	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $47 x - 9$
18	133	0.193070622502	Antoine Jay, 2026.
18	134	0.193719737379	Antoine Jay, 2026.
18	135	0.194297958267	Antoine Jay, 2026.
18	136	0.194621734867	Antoine Jay, 2026.
18	137	0.194954057753	Antoine Jay, 2026.
18	138	0.195225824558	Antoine Jay, 2026.
18	140	0.195281232516	Antoine Jay, 2026.
18	141	0.195969850290	Antoine Jay, 2026.
18	142	0.196269084953	Antoine Jay, 2026.
18	143	0.196565866210	Antoine Jay, 2026.
18	144	0.196844587634	Antoine Jay, 2026.
18	145	0.197165734113	Antoine Jay, 2026.
18	146	0.197523851139	Antoine Jay, 2026.
18	147	0.197844422013	Antoine Jay, 2026.
18	148	0.198104275704	Antoine Jay, 2026.
18	149	0.198640883276	Antoine Jay, 2026.
18	150	0.199135411215	Antoine Jay, 2026.
18	151	0.199469044790	Arhan Canli, 2026.
18	152	0.199830569980	Antoine Jay, 2026.
18	153	0.199993687091	Christopher Smolen, 2026.
18	154	0.200156452952	Christopher Smolen, 2026.
18	155	0.200591311767	Antoine Jay, 2026.
18	159	0.201106459525	Antoine Jay, 2026.
18	160	0.201636431893	Antoine Jay, 2026.
18	161	0.201957890574	Antoine Jay, 2026.
18	162	0.202100131206	Antoine Jay, 2026.
18	163	0.202198830250	Christopher Smolen, 2026.
18	164	0.202198947783	Henry Cohn, 2026.
18	165	0.202499852580	Christopher Smolen, 2026.
18	166	0.202703590240	Antoine Jay, 2026.
18	167	0.202866663946	Christopher Smolen, 2026.
18	168	0.202913235946	Vadim Borisov, 2026.
18	169	0.202913237123	Christopher Smolen, 2026.
18	170	0.202913421357	Christopher Smolen, 2026.
18	171	0.203057390050	Christopher Smolen, 2026.
18	172	0.203990215529	Antoine Jay, 2026.
18	173	0.205759392391	Christopher Smolen, 2026.
18	174	0.208492975025	Antoine Jay, 2026.
18	175	0.208896958003	Antoine Jay, 2026.
18	176	0.212707576300	Antoine Jay, 2026.
18	177	0.213961001219	Antoine Jay, 2026.
18	178	0.214574339616	Christopher Smolen, 2026.
18	179	0.214575912566	Christopher Smolen, 2026.
18	180	0.214579207315	Christopher Smolen, 2026.
18	181	0.214580484229	Christopher Smolen, 2026.
18	182	0.214580593347	Christopher Smolen, 2026.
18	184	0.214580613828	Christopher Smolen, 2026.
18	185	0.214580641284	Christopher Smolen, 2026.
18	186	0.214580662276	Christopher Smolen, 2026.
18	187	0.214580777335	Christopher Smolen, 2026.
18	188	0.214670912351	Christopher Smolen, 2026.
18	189	0.216532528667	Christopher Smolen, 2026.
18	197	0.218766018322	Henry Cohn, 2026.
18	198	0.218766693205	Henry Cohn, 2026.
18	199	0.222171019211	Christopher Smolen, 2026.
18	210	0.224009237740	Antoine Jay, 2026. $11 x^{2} + 2 x - 1$
18	211	0.225864132550	Christopher Smolen, 2026.
18	212	0.228628685372	Antoine Jay, 2026.
18	213	0.228672182096	Christopher Smolen, 2026.
18	225	0.231925424534	Antoine Jay, 2026.
18	226	0.232403546258	Arhan Canli, 2026.
18	227	0.236132326052	Christopher Smolen, 2026.
18	228	0.237222829980	Christopher Smolen, 2026.
18	229	0.237840924841	Christopher Smolen, 2026.
18	230	0.238318245893	Christopher Smolen, 2026.
18	231	0.238819897329	Christopher Smolen, 2026.
18	232	0.239382045202	Antoine Jay, 2026.
18	233	0.239778321665	Antoine Jay, 2026.
18	234	0.240315775694	Antoine Jay, 2026.
18	235	0.240721024491	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	236	0.241202546815	Christopher Smolen, 2026.
18	237	0.241611279679	Christopher Smolen, 2026.
18	238	0.242012162471	Antoine Jay, 2026.
18	239	0.242532435187	Antoine Jay, 2026.
18	240	0.242762586579	Christopher Smolen, 2026.
18	241	0.243031624145	Christopher Smolen, 2026.
18	242	0.243157072626	Christopher Smolen, 2026.
18	243	0.243694538886	Christopher Smolen, 2026.
18	244	0.243948700784	Antoine Jay, 2026.
18	245	0.244284942803	Christopher Smolen, 2026.
18	246	0.244421880428	Christopher Smolen, 2026.
18	247	0.244595110462	Christopher Smolen, 2026.
18	248	0.244849346454	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	249	0.244877734513	Antoine Jay, 2026.
18	250	0.245252011692	Christopher Smolen, 2026.
18	251	0.245418402980	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	252	0.245576456095	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	253	0.245745973372	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	254	0.245767094331	Christopher Smolen, 2026.
18	255	0.245866084470	Christopher Smolen, 2026.
18	256	0.245968475988	Christopher Smolen, 2026.
18	257	0.245977411389	Christopher Smolen, 2026.
18	258	0.246109982214	Christopher Smolen, 2026.
18	259	0.246238727612	Christopher Smolen, 2026.
18	260	0.246248830733	Vadim Borisov, 2026.
18	261	0.246250290900	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	262	0.246364266948	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	263	0.246433410730	Christopher Smolen, 2026.
18	264	0.246478416428	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	265	0.246621330620	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	266	0.246945279304	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	267	0.246969114742	Christopher Smolen, 2026.
18	268	0.246995794411	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	269	0.247091674270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	270	0.247453312832	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	271	0.247486993811	Arhan Canli, 2026.
18	272	0.247529113196	Vadim Borisov, 2026.
18	273	0.247531812544	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	274	0.247561731751	Christopher Smolen, 2026.
18	275	0.247573769690	Christopher Smolen, 2026.
18	276	0.247593579210	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	277	0.247611213164	Christopher Smolen, 2026.
18	278	0.247633938724	Christopher Smolen, 2026.
18	279	0.247727363756	Christopher Smolen, 2026.
18	280	0.247741663517	Christopher Smolen, 2026.
18	281	0.247779642403	Christopher Smolen, 2026.
18	282	0.247788468479	Christopher Smolen, 2026.
18	284	0.247855313826	Christopher Smolen, 2026.
18	286	0.247855377383	Christopher Smolen, 2026.
18	287	0.248144122151	Henry Cohn, 2026.
18	288	0.248762015491	Christopher Smolen, 2026.
18	289	0.248919152750	Christopher Smolen, 2026.
18	290	0.249103697760	Christopher Smolen, 2026.
18	291	0.249245308498	Vadim Borisov, 2026.
18	292	0.249245732422	Christopher Smolen, 2026.
18	293	0.249606623068	Christopher Smolen, 2026.
18	294	0.249867453097	Vadim Borisov, 2026.
18	295	0.249873276855	Christopher Smolen, 2026.
18	296	0.249912481585	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	297	0.249930962802	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	298	0.249947588200	Christopher Smolen, 2026.
18	299	0.249967831333	Christopher Smolen, 2026.
18	300	0.249988805797	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	301	0.249995637706	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	302	0.249995796407	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	303	0.249996724237	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	306	0.249999999998	Henry Cohn, 2026.
18	307	0.250462400472	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	308	0.251553413783	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	309	0.252611265371	Christopher Smolen, 2026.
18	310	0.253756448349	Christopher Smolen, 2026.
18	311	0.254716945356	Christopher Smolen, 2026.
18	312	0.256211569149	Christopher Smolen, 2026.
18	313	0.256822422569	Christopher Smolen, 2026.
18	314	0.258090156810	Christopher Smolen, 2026.
18	315	0.258482948242	Christopher Smolen, 2026.
18	316	0.258557635131	Christopher Smolen, 2026.
18	317	0.258676711927	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	318	0.258726771752	Christopher Smolen, 2026.
18	319	0.258932419209	Christopher Smolen, 2026.
18	320	0.259042195045	Christopher Smolen, 2026.
18	321	0.259161352622	Christopher Smolen, 2026.
18	322	0.259164844820	Christopher Smolen, 2026.
18	323	0.259180082979	Christopher Smolen, 2026.
18	324	0.259334392448	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	325	0.259827844076	Christopher Smolen, 2026.
18	326	0.259897789519	Christopher Smolen, 2026.
18	327	0.259929815722	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	328	0.260155960213	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	329	0.260178954039	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
18	330	0.260233710507	Christopher Smolen, 2026.
18	331	0.260267019283	Christopher Smolen, 2026.
18	332	0.260284329837	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	333	0.260325948011	Vadim Borisov, 2026.
18	334	0.260325955086	Christopher Smolen, 2026.
18	335	0.260486976939	Christopher Smolen, 2026.
18	336	0.260596256445	Christopher Smolen, 2026.
18	337	0.260669506329	Christopher Smolen, 2026.
18	338	0.260725921945	Christopher Smolen, 2026.
18	339	0.260732565303	Christopher Smolen, 2026.
18	340	0.260770424758	Christopher Smolen, 2026.
18	341	0.260835478683	Christopher Smolen, 2026.
18	342	0.260852737278	Christopher Smolen, 2026.
18	343	0.260865543359	Christopher Smolen, 2026.
18	344	0.260867595906	Christopher Smolen, 2026.
18	345	0.260888912603	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	346	0.260905424159	Christopher Smolen, 2026.
18	347	0.260939493222	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	348	0.260955420103	Christopher Smolen, 2026.
18	349	0.260958672932	Christopher Smolen, 2026.
18	350	0.260970320677	Christopher Smolen, 2026.
18	351	0.260986761471	Christopher Smolen, 2026.
18	352	0.260993513914	Christopher Smolen, 2026.
18	353	0.262893065933	Christopher Smolen, 2026.
18	354	0.277833130337	Christopher Smolen, 2026.
18	355	0.280347670082	Christopher Smolen, 2026.
18	356	0.284675069053	Christopher Smolen, 2026.
18	357	0.287363460173	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	358	0.290321570213	Christopher Smolen, 2026.
18	359	0.290751908437	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	360	0.292373270420	Christopher Smolen, 2026.
18	362	0.294117661466	Vadim Borisov, 2026.
18	363	0.294117663252	Christopher Smolen, 2026.
18	364	0.294117663319	Christopher Smolen, 2026.
18	365	0.294117663428	Christopher Smolen, 2026.
18	366	0.294117663792	Christopher Smolen, 2026.
18	367	0.294117671103	Christopher Smolen, 2026.
18	368	0.294117671802	Christopher Smolen, 2026.
18	369	0.294117672038	Christopher Smolen, 2026.
18	371	0.294117673031	Christopher Smolen, 2026.
18	372	0.294117677326	Christopher Smolen, 2026.
18	373	0.294117677756	Christopher Smolen, 2026.
18	374	0.294117678483	Christopher Smolen, 2026.
18	375	0.294117678492	Christopher Smolen, 2026.
18	376	0.294117678817	Christopher Smolen, 2026.
18	377	0.294117679642	Christopher Smolen, 2026.
18	378	0.294117679682	Christopher Smolen, 2026.
18	379	0.294117685502	Christopher Smolen, 2026.
18	380	0.294117685569	Christopher Smolen, 2026.
18	381	0.294117686157	Christopher Smolen, 2026.
18	382	0.294117701867	Vadim Borisov, 2026.
18	383	0.294117703251	Christopher Smolen, 2026.
18	384	0.294117705384	Vadim Borisov, 2026.
18	385	0.294117705747	Vadim Borisov, 2026.
18	386	0.294117707208	Christopher Smolen, 2026.
18	387	0.294117708027	Christopher Smolen, 2026.
18	389	0.294117714670	Vadim Borisov, 2026.
18	390	0.294117716119	Christopher Smolen, 2026.
18	391	0.294117720032	Vadim Borisov, 2026.
18	392	0.294117720058	Vadim Borisov, 2026.
18	393	0.294117723886	Vadim Borisov, 2026.
18	396	0.294117725646	Vadim Borisov, 2026.
18	397	0.294117726552	Vadim Borisov, 2026.
18	398	0.294117726792	Vadim Borisov, 2026.
18	399	0.294117728761	Christopher Smolen, 2026.
18	400	0.294117728837	Christopher Smolen, 2026.
18	401	0.294117729654	Christopher Smolen, 2026.
18	402	0.294117772647	Vadim Borisov, 2026.
18	403	0.294117778343	Christopher Smolen, 2026.
18	404	0.294117804046	Vadim Borisov, 2026.
18	405	0.294117809463	Vadim Borisov, 2026.
18	406	0.294117817584	Vadim Borisov, 2026.
18	407	0.294117845318	Vadim Borisov, 2026.
18	408	0.294117849120	Vadim Borisov, 2026.
18	409	0.294117859690	Vadim Borisov, 2026.
18	410	0.294117872648	Vadim Borisov, 2026.
18	411	0.294117873881	Vadim Borisov, 2026.
18	413	0.294117967131	Vadim Borisov, 2026.
18	414	0.294117982472	Christopher Smolen, 2026.
18	415	0.294118190626	Christopher Smolen, 2026.
18	416	0.294118261533	Vadim Borisov, 2026.
18	417	0.294118330329	Christopher Smolen, 2026.
18	418	0.294120585932	Vadim Borisov, 2026.
18	419	0.294120675794	Vadim Borisov, 2026.
18	420	0.294120794454	Christopher Smolen, 2026.
18	421	0.294120917654	Christopher Smolen, 2026.
18	422	0.294141080172	Vadim Borisov, 2026.
18	423	0.294141631644	Vadim Borisov, 2026.
18	424	0.294142345940	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	426	0.294190644102	Vadim Borisov, 2026.
18	427	0.294191870055	Vadim Borisov, 2026.
18	428	0.294192468698	Vadim Borisov, 2026.
18	429	0.294425581289	Vadim Borisov, 2026.
18	480	0.296296296297	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $27 x - 8$
18	481	0.298380787556	Christopher Smolen, 2026.
18	482	0.300180849388	Christopher Smolen, 2026.
18	483	0.301454669444	Christopher Smolen, 2026.
18	484	0.302682467838	Christopher Smolen, 2026.
18	485	0.303478191798	Christopher Smolen, 2026.
18	486	0.305662830467	Christopher Smolen, 2026.
18	487	0.307359235723	Christopher Smolen, 2026.
18	488	0.308247509750	Christopher Smolen, 2026.
18	489	0.308630250612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	490	0.308979693736	Vadim Borisov, 2026.
18	491	0.309366477951	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	492	0.309725839884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	493	0.310048423693	Vadim Borisov, 2026.
18	494	0.310444968149	Vadim Borisov, 2026.
18	495	0.310873337332	Christopher Smolen, 2026.
18	496	0.311413742131	Vadim Borisov, 2026.
18	497	0.311721896332	Vadim Borisov, 2026.
18	498	0.311788816454	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	499	0.312438160410	Vadim Borisov, 2026.
18	500	0.313187333967	Christopher Smolen, 2026.
18	501	0.314013270489	Christopher Smolen, 2026.
18	502	0.314665984092	Vadim Borisov, 2026.
18	503	0.315133111042	Vadim Borisov, 2026.
18	504	0.316734978910	Christopher Smolen, 2026.
18	505	0.317102468828	Christopher Smolen, 2026.
18	506	0.317419506530	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	507	0.317883187514	Christopher Smolen, 2026.
18	508	0.318208544948	Vadim Borisov, 2026.
18	509	0.318303942612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	510	0.318409064446	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	511	0.318606188278	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	512	0.318714174071	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	513	0.319073248293	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	514	0.319330514960	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	515	0.319680212947	Christopher Smolen, 2026.
18	516	0.319850552542	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	517	0.320199029954	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	518	0.320386870202	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	519	0.321010528293	Vadim Borisov, 2026.
18	520	0.321321215644	Vadim Borisov, 2026.
18	521	0.321617967532	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	522	0.322365680566	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	524	0.322855244364	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	525	0.323111694019	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	526	0.323243926295	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	527	0.323504070832	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	528	0.323883686230	Christopher Smolen, 2026.
18	529	0.324440405544	Christopher Smolen, 2026.
18	530	0.324930584830	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	531	0.325262166694	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	532	0.325685723005	Christopher Smolen, 2026.
18	533	0.326007398912	Christopher Smolen, 2026.
18	534	0.326333209838	Christopher Smolen, 2026.
18	535	0.326367285154	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	536	0.326875239218	Christopher Smolen, 2026.
18	537	0.327102966062	Christopher Smolen, 2026.
18	538	0.327723849075	Christopher Smolen, 2026.
18	539	0.327903785300	Christopher Smolen, 2026.
18	540	0.328307482020	Christopher Smolen, 2026.
18	541	0.328383087744	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	542	0.328494483691	Christopher Smolen, 2026.
18	543	0.329066167049	Christopher Smolen, 2026.
18	544	0.329516116207	Christopher Smolen, 2026.
18	545	0.329665010291	Christopher Smolen, 2026.
18	546	0.330029456987	Christopher Smolen, 2026.
18	547	0.330236313930	Christopher Smolen, 2026.
18	548	0.330494621423	Christopher Smolen, 2026.
18	549	0.330590926914	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	550	0.330758346558	Christopher Smolen, 2026.
18	551	0.331636377239	Christopher Smolen, 2026.
18	552	0.331922723329	Christopher Smolen, 2026.
18	553	0.332346141622	Christopher Smolen, 2026.
18	554	0.332422002938	Christopher Smolen, 2026.
18	555	0.332557872217	Christopher Smolen, 2026.
18	556	0.332757624156	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	557	0.332822811395	Christopher Smolen, 2026.
18	558	0.333148980745	Christopher Smolen, 2026.
18	576	0.333168577784	Henry Cohn, 2026.
18	577	0.333331323973	Vadim Borisov, 2026.
18	578	0.333331352191	Vadim Borisov, 2026.
18	579	0.333331391016	Vadim Borisov, 2026.
18	580	0.333332341881	Christopher Smolen, 2026.
18	672	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
18	704	0.333333333334	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $3 x - 1$
18	762	0.341506350947	Henry Cohn, 2026. $32 x^{2} - 8 x - 1$
18	763	0.341532947590	Vadim Borisov, 2026.
18	764	0.341540090079	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	767	0.341542017920	Vadim Borisov, 2026.
18	768	0.341542277204	Vadim Borisov, 2026.
18	769	0.341548793660	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	777	0.341549003972	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	779	0.341601511289	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	780	0.342420325256	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	781	0.342421978408	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	783	0.343976021711	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	784	0.344526425546	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
18	867	0.357142857143	Henry Cohn, 2025, by modifying a construction from C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $14 x - 5$
18	868	0.357142857143	Kevin Li, 2026. $14 x - 5$
18	869	0.373254031890	Vadim Borisov, 2026.
18	1024	0.375	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $8 x - 3$
19	39	0.040648168399	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5491 x^{3} - 361 x^{2} - 19 x + 1$
19	40	0.047619047620	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $21 x - 1$
19	41	0.053165944699	Henry Cohn, 2023.
19	42	0.053978364917	Henry Cohn, 2025.
19	43	0.058551084358	Henry Cohn, 2025.
19	44	0.059131790994	Henry Cohn, 2023.
19	45	0.059418524383	Henry Cohn, 2023. Minimal polynomial of degree 8
19	48	0.063706690497	Henry Cohn, 2023. $215 x^{2} + 2 x - 1$
19	50	0.069767441861	Henry Cohn, 2023. $43 x - 3$
19	51	0.075262310219	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	52	0.076923076924	Antoine Jay, 2026. $13 x - 1$
19	54	0.076923076924	Henry Cohn and Ilmari Vahteristo, 2026. $13 x - 1$
19	55	0.082178889828	Henry Cohn, 2025.
19	56	0.083233613334	Henry Cohn, 2026.
19	57	0.084523219261	Henry Cohn, 2026.
19	58	0.087689053617	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	60	0.090909090910	Kissing configuration of 81 points in 20 dimensions from A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K. $11 x - 1$
19	62	0.093346164763	Henry Cohn, 2026. $479 x^{2} - 34 x - 1$
19	66	0.097744360903	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $133 x - 13$
19	69	0.101319957445	Antoine Jay, 2026. $65739 x^{5} - 40846 x^{4} + 8166 x^{3} - 464 x^{2} - 21 x + 2$
19	70	0.101392647883	Antoine Jay, 2026.
19	71	0.101456840932	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	72	0.101838513946	Antoine Jay, 2026. Minimal polynomial of degree 10
19	73	0.102201317334	Henry Cohn, 2026. $311 x^{2} - 22 x - 1$
19	74	0.104236915649	Antoine Jay, 2026.
19	75	0.107816370259	Antoine Jay, 2026.
19	76	0.111553215377	Antoine Jay, 2026.
19	77	0.112762187144	Arhan Canli, 2026.
19	89	0.112912613537	Henry Cohn, 2023. $167 x^{2} - 10 x - 1$
19	90	0.121308037796	Henry Cohn, 2024. $2809 x^{4} - 192 x^{3} - 86 x^{2} + 1$
19	91	0.128902034016	Antoine Jay, 2026.
19	92	0.132376265090	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	93	0.141277885852	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	94	0.142465088813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
19	100	0.142857142858	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 1$
19	102	0.142857142858	Henry Cohn, 2023, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 1$
19	103	0.149928121676	Henry Cohn, 2026. $387809 x^{8} - 966576 x^{7} + 416044 x^{6} - 3392 x^{5} - 20538 x^{4} + 2192 x^{3} + 172 x^{2} - 32 x + 1$
19	104	0.150748959688	Henry Cohn, 2026. $311 x^{4} - 352 x^{3} + 90 x^{2} - 1$
19	106	0.152679567196	Antoine Jay, 2026. $34192 x^{4} - 15480 x^{3} + 2113 x^{2} - 90 x + 1$
19	108	0.153846153847	Antoine Jay, 2026. $13 x - 2$
19	132	0.157894736843	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $19 x - 3$
19	133	0.168802199651	Henry Cohn, 2026. $5929 x^{4} - 1152 x^{3} - 536 x^{2} + 16$
19	134	0.174059290326	Antoine Jay, 2026.
19	135	0.174801787121	Antoine Jay, 2026.
19	136	0.175550053808	Christopher Smolen, 2026.
19	137	0.176518129994	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	138	0.177090903188	Antoine Jay, 2026.
19	139	0.177604508470	Christopher Smolen, 2026.
19	140	0.178019811191	Antoine Jay, 2026.
19	141	0.178297225859	Arhan Canli, 2026.
19	142	0.178652812730	Antoine Jay, 2026.
19	143	0.178909005009	Henry Cohn, 2026.
19	144	0.179651654187	Antoine Jay, 2026.
19	145	0.180306088125	Antoine Jay, 2026.
19	146	0.180685030890	Antoine Jay, 2026.
19	147	0.182309206945	Antoine Jay, 2026.
19	148	0.183200271585	Antoine Jay, 2026.
19	149	0.183225490259	Antoine Jay, 2026.
19	150	0.184646543855	Antoine Jay, 2026. $1007 x^{4} + 740 x^{3} + 10 x^{2} - 28 x - 1$
19	151	0.186838119459	Antoine Jay, 2026.
19	166	0.189189189190	Henry Cohn, 2026. $37 x - 7$
19	176	0.191919191920	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $99 x - 19$
19	177	0.193637369253	Henry Cohn, 2026. $100489 x^{4} - 30400 x^{3} - 14550 x^{2} + 625$
19	178	0.194661393927	Henry Cohn, 2026.
19	179	0.195464657299	Arhan Canli, 2026.
19	180	0.195821119718	Antoine Jay, 2026.
19	181	0.196870703033	Antoine Jay, 2026.
19	182	0.197578666900	Antoine Jay, 2026.
19	183	0.198393261324	Antoine Jay, 2026.
19	184	0.199205109236	Henry Cohn, 2026.
19	185	0.199756703642	Antoine Jay, 2026.
19	192	0.2	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 1$
19	193	0.203357314598	Henry Cohn, 2026. $112896 x^{4} - 30400 x^{3} - 13600 x^{2} + 625$
19	194	0.205762308446	Christopher Smolen, 2026.
19	195	0.206601200687	Antoine Jay, 2026.
19	196	0.206640693014	Antoine Jay, 2026.
19	197	0.208044009202	Christopher Smolen, 2026.
19	198	0.208915963894	Antoine Jay, 2026.
19	199	0.209678879257	Antoine Jay, 2026.
19	200	0.210436202917	Antoine Jay, 2026.
19	202	0.210526315790	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $19 x - 4$
19	203	0.210989195856	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	204	0.211045036371	Antoine Jay, 2026.
19	207	0.211132179390	Vadim Borisov, 2026.
19	208	0.213163239575	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	209	0.213210347171	Antoine Jay, 2026.
19	210	0.214506282074	Christopher Smolen, 2026.
19	211	0.215123288741	Antoine Jay, 2026.
19	212	0.215575863167	Antoine Jay, 2026.
19	213	0.216090804393	Christopher Smolen, 2026.
19	214	0.216350290612	Antoine Jay, 2026.
19	215	0.216823517513	Christopher Smolen, 2026.
19	216	0.217362568252	Antoine Jay, 2026.
19	217	0.217537729813	Antoine Jay, 2026.
19	218	0.217683390452	Christopher Smolen, 2026.
19	219	0.218633425600	Christopher Smolen, 2026.
19	220	0.219412259110	Antoine Jay, 2026.
19	221	0.220080296839	Christopher Smolen, 2026.
19	222	0.220570640196	Christopher Smolen, 2026.
19	223	0.220678534960	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	224	0.221041087109	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	225	0.221169754543	Antoine Jay, 2026.
19	226	0.221347049042	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	227	0.221379518514	Vadim Borisov, 2026.
19	228	0.221454258731	Christopher Smolen, 2026.
19	229	0.221460443949	Vadim Borisov, 2026.
19	230	0.221592558330	Christopher Smolen, 2026.
19	231	0.221698532445	Christopher Smolen, 2026.
19	232	0.221748818218	Arhan Canli, 2026.
19	237	0.221860313442	Antoine Jay, 2026. Minimal polynomial of degree 8
19	238	0.221860313442	Henry Cohn, 2026. Minimal polynomial of degree 8
19	239	0.222925714741	Arhan Canli, 2026.
19	240	0.225918288156	Christopher Smolen, 2026.
19	241	0.226241850521	Christopher Smolen, 2026.
19	242	0.226789063136	Antoine Jay, 2026.
19	243	0.227019597288	Christopher Smolen, 2026.
19	244	0.227555059386	Vadim Borisov, 2026.
19	245	0.227570626542	Antoine Jay, 2026.
19	246	0.227577244946	Antoine Jay, 2026.
19	247	0.227580021539	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	248	0.227584305957	Antoine Jay, 2026.
19	249	0.227586671471	Christopher Smolen, 2026.
19	250	0.227587112466	Vadim Borisov, 2026.
19	251	0.227589953401	Vadim Borisov, 2026.
19	252	0.227594046290	Vadim Borisov, 2026.
19	253	0.227597126798	Antoine Jay, 2026.
19	255	0.227597794389	Henry Cohn, 2026.
19	256	0.228942415948	Antoine Jay, 2026.
19	277	0.230769230770	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $13 x - 3$
19	278	0.235886069168	Christopher Smolen, 2026.
19	279	0.237008158690	Christopher Smolen, 2026.
19	280	0.237984011162	Christopher Smolen, 2026.
19	291	0.238519273263	Henry Cohn, 2026. $199 x^{3} + 33 x^{2} - 15 x - 1$
19	292	0.240704635253	Henry Cohn, 2026.
19	293	0.241974456122	Christopher Smolen, 2026.
19	294	0.243800509556	Christopher Smolen, 2026.
19	295	0.244482753637	Christopher Smolen, 2026.
19	296	0.244727830630	Christopher Smolen, 2026.
19	297	0.245791714248	Christopher Smolen, 2026.
19	298	0.245992427988	Christopher Smolen, 2026.
19	299	0.246428038499	Christopher Smolen, 2026.
19	300	0.246526068936	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	301	0.247749153773	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	302	0.248002375089	Christopher Smolen, 2026.
19	303	0.248787664436	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	304	0.248930802734	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	305	0.249253089919	Christopher Smolen, 2026.
19	306	0.249514673161	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	307	0.249850007603	Vadim Borisov, 2026.
19	308	0.249855218902	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	309	0.249883468995	Christopher Smolen, 2026.
19	310	0.249890465746	Christopher Smolen, 2026.
19	311	0.249894642175	Christopher Smolen, 2026.
19	312	0.249897396154	Vadim Borisov, 2026.
19	313	0.249897400946	Vadim Borisov, 2026.
19	314	0.249899772262	Vadim Borisov, 2026.
19	315	0.249904120887	Vadim Borisov, 2026.
19	316	0.249906025953	Christopher Smolen, 2026.
19	317	0.249934908004	Vadim Borisov, 2026.
19	318	0.249937967384	Christopher Smolen, 2026.
19	319	0.249950715794	Vadim Borisov, 2026.
19	320	0.249950872970	Vadim Borisov, 2026.
19	321	0.249952481979	Christopher Smolen, 2026.
19	322	0.249999734790	Christopher Smolen, 2026.
19	323	0.249999865326	Vadim Borisov, 2026.
19	324	0.250000149954	Christopher Smolen, 2026.
19	325	0.250043184867	Christopher Smolen, 2026.
19	326	0.250142353613	Christopher Smolen, 2026.
19	327	0.250515530833	Christopher Smolen, 2026.
19	328	0.251509327771	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	329	0.252744587924	Christopher Smolen, 2026.
19	330	0.252970511437	Christopher Smolen, 2026.
19	331	0.253767140383	Christopher Smolen, 2026.
19	332	0.255659361923	Christopher Smolen, 2026.
19	333	0.256135735953	Christopher Smolen, 2026.
19	334	0.257972488625	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	335	0.258029050041	Christopher Smolen, 2026.
19	336	0.258100710507	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	337	0.258187896503	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	338	0.258246947796	Christopher Smolen, 2026.
19	339	0.258353658533	Christopher Smolen, 2026.
19	340	0.258478726452	Christopher Smolen, 2026.
19	341	0.258539328726	Christopher Smolen, 2026.
19	342	0.258639569956	Christopher Smolen, 2026.
19	343	0.258804052958	Christopher Smolen, 2026.
19	344	0.258815752873	Christopher Smolen, 2026.
19	345	0.258816546321	Christopher Smolen, 2026.
19	346	0.258826067039	Christopher Smolen, 2026.
19	347	0.258827285808	Christopher Smolen, 2026.
19	348	0.258871260626	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	349	0.258924467714	Christopher Smolen, 2026.
19	350	0.259050647297	Christopher Smolen, 2026.
19	351	0.259173480193	Christopher Smolen, 2026.
19	352	0.259220579277	Christopher Smolen, 2026.
19	353	0.259287439910	Christopher Smolen, 2026.
19	354	0.259359372593	Christopher Smolen, 2026.
19	355	0.259407189034	Christopher Smolen, 2026.
19	356	0.259433890680	Christopher Smolen, 2026.
19	357	0.259526510428	Christopher Smolen, 2026.
19	358	0.259769833040	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	359	0.259951686024	Christopher Smolen, 2026.
19	360	0.260413018329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	361	0.260420436688	Christopher Smolen, 2026.
19	362	0.261507721231	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	363	0.262234913851	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	364	0.263446341250	Vadim Borisov, 2026.
19	365	0.265042428139	Vadim Borisov, 2026.
19	366	0.266204802663	Vadim Borisov, 2026.
19	367	0.267364099034	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	368	0.268620010676	Vadim Borisov, 2026.
19	369	0.268967036804	Vadim Borisov, 2026.
19	404	0.272727272728	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $11 x - 3$
19	405	0.278180703475	Christopher Smolen, 2026.
19	406	0.279344564620	Christopher Smolen, 2026.
19	407	0.280367636794	Christopher Smolen, 2026.
19	408	0.281286857586	Vadim Borisov, 2026.
19	409	0.282093841951	Christopher Smolen, 2026.
19	410	0.282455900086	Christopher Smolen, 2026.
19	411	0.282665884904	Christopher Smolen, 2026.
19	412	0.282899985353	Christopher Smolen, 2026.
19	413	0.283124626669	Christopher Smolen, 2026.
19	414	0.283380334574	Christopher Smolen, 2026.
19	415	0.283810018502	Christopher Smolen, 2026.
19	416	0.285042949140	Vadim Borisov, 2026.
19	417	0.285843165456	Vadim Borisov, 2026.
19	418	0.286273969514	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	419	0.286556583948	Vadim Borisov, 2026.
19	420	0.287132806194	Vadim Borisov, 2026.
19	477	0.287671232877	Henry Cohn, 2026. $73 x - 21$
19	478	0.287771012571	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	479	0.287868400931	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	480	0.287925858706	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	481	0.293564060353	Vadim Borisov, 2026.
19	482	0.293564072303	Vadim Borisov, 2026.
19	569	0.294117647059	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $17 x - 5$
19	578	0.294117647059	Henry Cohn, 2026. $17 x - 5$
19	579	0.295154601374	Christopher Smolen, 2026.
19	581	0.295319639665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	582	0.295990108214	Vadim Borisov, 2026.
19	583	0.296254601791	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	584	0.296463021277	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	585	0.296934341230	Christopher Smolen, 2026.
19	586	0.297170038237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	587	0.297366006160	Christopher Smolen, 2026.
19	588	0.297835404606	Christopher Smolen, 2026.
19	589	0.297976301007	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	590	0.298065482716	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	591	0.298282913394	Vadim Borisov, 2026.
19	592	0.298428464370	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	593	0.298518486579	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	594	0.298822099499	Vadim Borisov, 2026.
19	595	0.298834681853	Vadim Borisov, 2026.
19	596	0.298916704604	Vadim Borisov, 2026.
19	597	0.299190994964	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	598	0.299388121186	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	599	0.299836835245	Vadim Borisov, 2026.
19	600	0.299940785881	Vadim Borisov, 2026.
19	601	0.300146841077	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	602	0.300521628401	Vadim Borisov, 2026.
19	603	0.300634282650	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	604	0.300696756270	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	605	0.300954175861	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	606	0.301071578990	Vadim Borisov, 2026.
19	607	0.301444856026	Vadim Borisov, 2026.
19	608	0.301766404450	Vadim Borisov, 2026.
19	609	0.302014710128	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	610	0.302390798904	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	611	0.302565606544	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	612	0.302755123561	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	613	0.302912187258	Vadim Borisov, 2026.
19	614	0.303097832009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	616	0.303194880308	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	617	0.303200770899	Vadim Borisov, 2026.
19	618	0.303387332362	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	619	0.303766403206	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	620	0.303957978386	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	621	0.304042612582	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	622	0.304186563516	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	623	0.304692800352	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	624	0.304805027061	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	625	0.304875439199	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	626	0.305053171922	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	627	0.305097878326	Vadim Borisov, 2026.
19	628	0.305109037130	Vadim Borisov, 2026.
19	629	0.305115947808	Vadim Borisov, 2026.
19	630	0.305124962106	Vadim Borisov, 2026.
19	633	0.305125016556	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	634	0.305129337530	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	635	0.305134527268	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	636	0.305138847894	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	637	0.305148949523	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	638	0.305152531798	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	639	0.305165421070	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	641	0.305173770452	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	642	0.305185857413	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	643	0.305193063509	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	644	0.308281614068	Christopher Smolen, 2026.
19	645	0.309116804398	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	646	0.309462732634	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	647	0.310564820294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	648	0.310959394699	Christopher Smolen, 2026.
19	649	0.311339318341	Christopher Smolen, 2026.
19	650	0.311459517183	Henry Cohn, 2026.
19	651	0.311956748427	Henry Cohn, 2026.
19	652	0.312208654879	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	653	0.312267857276	Henry Cohn, 2026.
19	654	0.312731781336	Christopher Smolen, 2026.
19	655	0.312977276184	Henry Cohn, 2026.
19	656	0.313150662390	Henry Cohn, 2026.
19	657	0.313386494498	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	658	0.313755638107	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	659	0.313950422840	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	660	0.314098084603	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	661	0.314384872205	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	662	0.314544277613	Henry Cohn, 2026.
19	663	0.314761094819	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	664	0.314926138164	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	665	0.315117254715	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	666	0.315351816148	Christopher Smolen, 2026.
19	667	0.315390508412	Henry Cohn, 2026.
19	668	0.315672865234	Christopher Smolen, 2026.
19	669	0.315848499254	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	670	0.316054038634	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	671	0.316449593273	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	672	0.316543787084	Henry Cohn, 2026.
19	673	0.316700029764	Christopher Smolen, 2026.
19	674	0.316802213210	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	675	0.317078342262	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	676	0.317243091256	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	677	0.317315443882	Henry Cohn, 2026.
19	678	0.317572741340	Christopher Smolen, 2026.
19	679	0.317887211108	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	680	0.318054536737	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	681	0.318366692530	Christopher Smolen, 2026.
19	682	0.318478926403	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	683	0.318745918311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	684	0.319133003329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	685	0.319433829449	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	686	0.319629517486	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	687	0.319730768007	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	688	0.320100137159	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	689	0.320222379964	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	690	0.320489392477	Henry Cohn, 2026.
19	691	0.320723883596	Christopher Smolen, 2026.
19	693	0.320924210633	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	694	0.321173359186	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	695	0.321320479443	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	696	0.321663570146	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	697	0.321987971272	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	698	0.322224458094	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	699	0.322398454152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	700	0.322608870507	Henry Cohn, 2026.
19	701	0.322685573713	Henry Cohn, 2026.
19	702	0.322920339413	Henry Cohn, 2026.
19	703	0.323133949420	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	704	0.323523028350	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	705	0.323707248476	Henry Cohn, 2026.
19	706	0.323801337479	Henry Cohn, 2026.
19	707	0.323987738831	Henry Cohn, 2026.
19	708	0.324098738459	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	709	0.324202173973	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	710	0.324379906859	Henry Cohn, 2026.
19	711	0.324395758586	Christopher Smolen, 2026.
19	712	0.324548861338	Henry Cohn, 2026.
19	713	0.324677316304	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	714	0.324918594919	Henry Cohn, 2026.
19	715	0.325139979907	Christopher Smolen, 2026.
19	716	0.325304553812	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
19	717	0.325612434609	Henry Cohn, 2026.
19	718	0.325804006852	Henry Cohn, 2026.
19	719	0.325990010625	Vadim Borisov, 2026.
19	720	0.326042330303	Vadim Borisov, 2026.
19	721	0.326185132302	Vadim Borisov, 2026.
19	722	0.326393363664	Vadim Borisov, 2026.
19	723	0.326633829683	Vadim Borisov, 2026.
19	724	0.326711127454	Henry Cohn, 2026.
19	725	0.326817379176	Henry Cohn, 2026.
19	726	0.326984995732	Henry Cohn, 2026.
19	727	0.327093603724	Henry Cohn, 2026.
19	728	0.327249635022	Henry Cohn, 2026.
19	729	0.327400827943	Henry Cohn, 2026.
19	730	0.327591360344	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	731	0.327798553231	Henry Cohn, 2026.
19	732	0.327922977525	Christopher Smolen, 2026.
19	733	0.328107487283	Christopher Smolen, 2026.
19	734	0.328247528722	Henry Cohn, 2026.
19	735	0.328425126581	Henry Cohn, 2026.
19	736	0.328566423648	Henry Cohn, 2026.
19	737	0.328755706981	Henry Cohn, 2026.
19	738	0.328944344929	Henry Cohn, 2026.
19	739	0.329136714337	Henry Cohn, 2026.
19	740	0.329436596719	Henry Cohn, 2026.
19	741	0.329591905302	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	742	0.329870931013	Vadim Borisov, 2026.
19	743	0.330128046560	Henry Cohn, 2026.
19	744	0.330386838510	Christopher Smolen, 2026.
19	745	0.330484236946	Henry Cohn, 2026.
19	746	0.330686532103	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	747	0.330830514165	Henry Cohn, 2026.
19	748	0.331084328133	Henry Cohn, 2026.
19	749	0.331220815943	Henry Cohn, 2026.
19	750	0.331398724290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	751	0.331645333101	Henry Cohn, 2026.
19	752	0.331821762419	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	753	0.332132311598	Christopher Smolen, 2026.
19	754	0.332340460086	Henry Cohn, 2026.
19	755	0.332672510612	Henry Cohn, 2026.
19	756	0.332848022595	Henry Cohn, 2026.
19	757	0.333055194269	Henry Cohn, 2026.
19	896	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
19	897	0.339468221701	Vadim Borisov, 2026.
19	898	0.341072683546	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	899	0.342272244858	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	900	0.343184895665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	901	0.344449037532	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	902	0.345158913990	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	903	0.346054586189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	904	0.346740197544	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	905	0.347140875314	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	906	0.348069315884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	907	0.348402049328	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	908	0.348528558265	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	909	0.348736856705	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	910	0.349102747936	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	911	0.349709328452	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	912	0.350041698160	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	913	0.350357428477	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	916	0.351186881732	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	917	0.351389431996	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	918	0.351557106262	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	919	0.351793158307	Henry Cohn, 2026.
19	920	0.351910920606	Henry Cohn, 2026.
19	921	0.352058910180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
19	922	0.352185280406	Henry Cohn, 2026.
19	923	0.352263455320	Henry Cohn, 2026.
19	924	0.352459780257	Henry Cohn, 2026.
19	925	0.352529652799	Henry Cohn, 2026.
19	926	0.352729997533	Henry Cohn, 2026.
19	927	0.352981149585	Henry Cohn, 2026.
19	928	0.353075857925	Henry Cohn, 2026.
19	929	0.353213856650	Henry Cohn, 2026.
19	930	0.353417600507	Henry Cohn, 2026.
19	931	0.353667822805	Henry Cohn, 2026.
19	932	0.353766517940	Henry Cohn, 2026.
19	933	0.353855407925	Henry Cohn, 2026.
19	934	0.354022188138	Henry Cohn, 2026.
19	935	0.354183261505	Henry Cohn, 2026.
19	936	0.354326432779	Henry Cohn, 2026.
19	937	0.354508371511	Henry Cohn, 2026.
19	938	0.354673829334	Henry Cohn, 2026.
19	1024	0.354838709678	Henry Cohn, 2026, subcode of a code of size 1040. $31 x - 11$
20	41	0.038815055717	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $6480 x^{3} - 400 x^{2} - 20 x + 1$
20	42	0.045454545455	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $22 x - 1$
20	43	0.050117159654	Henry Cohn, 2024. $6493504 x^{6} + 4442432 x^{5} - 359919 x^{4} - 90844 x^{3} + 13006 x^{2} - 588 x + 9$
20	44	0.051781487230	Henry Cohn, 2023.
20	45	0.053400898990	Henry Cohn, 2023. Minimal polynomial of degree 12
20	46	0.053968966531	Henry Cohn, 2025.
20	47	0.053993355922	Henry Cohn, 2023. $120 x^{2} - 25 x + 1$
20	48	0.055838151510	Henry Cohn, 2023. $464 x^{2} - 8 x - 1$
20	49	0.060513303142	Henry Cohn, 2023. Minimal polynomial of degree 11
20	50	0.063702950432	Henry Cohn, 2025.
20	56*	0.066666666667	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $15 x - 1$
20	60	0.076923076924	Kissing configuration of 77 points in 21 dimensions. $13 x - 1$
20	63	0.081967213115	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $61 x - 5$
20	64	0.087282748333	Henry Cohn, 2026.
20	65	0.087640553688	Henry Cohn, 2026. $185075 x^{5} - 15027 x^{4} - 1354 x^{3} + 82 x^{2} - 9 x + 1$
20	66	0.089335555280	Antoine Jay, 2026. $1098289 x^{4} - 254252 x^{3} + 10910 x^{2} + 708 x - 39$
20	67	0.090150903490	Henry Cohn, 2026. $2103 x^{4} - 1376 x^{3} + 230 x^{2} - 1$
20	68	0.092978419163	Henry Cohn, 2026.
20	69	0.094913515239	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
20	70	0.095127924312	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. Minimal polynomial of degree 8
20	71	0.098281336418	Antoine Jay, 2026.
20	81	0.1	A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K. $10 x - 1$
20	82	0.111111111112	Henry Cohn, 2026. $9 x - 1$
20	83	0.112462092273	Christopher Smolen, 2026.
20	84	0.112889958832	Antoine Jay, 2026.
20	85	0.112902505491	Henry Cohn, 2026.
20	86	0.112907237611	Arhan Canli, 2026.
20	87	0.112907889483	Arhan Canli, 2026.
20	89	0.112909329960	Arhan Canli, 2026.
20	90	0.112912075384	Henry Cohn, 2026.
20	91	0.112912613358	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
20	92	0.112912613537	Henry Cohn, 2025.
20	93	0.118699001808	Henry Cohn, 2026.
20	94	0.124468630127	Antoine Jay, 2026.
20	105	0.125	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $8 x - 1$
20	106	0.136915269061	Henry Cohn, 2026. $7225 x^{4} - 990 x^{3} - 480 x^{2} + 9$
20	120	0.142857142858	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $7 x - 1$
20	124	0.145853791080	Henry Cohn, 2026. Minimal polynomial of degree 12
20	125	0.147670835571	Henry Cohn, 2026.
20	126	0.148571041390	Antoine Jay, 2026. $7553200 x^{4} - 11360760 x^{3} - 6230840 x^{2} + 589560 x + 83521$
20	127	0.149442790439	Antoine Jay, 2026.
20	128	0.149899837872	Antoine Jay, 2026.
20	129	0.150189228511	Antoine Jay, 2026.
20	130	0.150241126556	Arhan Canli, 2026.
20	131	0.150478646418	Arhan Canli, 2026.
20	132	0.150479515514	Antoine Jay, 2026.
20	133	0.151424111892	Antoine Jay, 2026.
20	136	0.151500526296	Henry Cohn, 2026. $960 x^{3} + 339 x^{2} - 146 x + 11$
20	137	0.153035916461	Antoine Jay, 2026.
20	138	0.154344356262	Antoine Jay, 2026.
20	139	0.154944920631	Henry Cohn, 2026.
20	140	0.155950356108	Antoine Jay, 2026.
20	141	0.157229456154	Henry Cohn, 2026.
20	142	0.161808718897	Antoine Jay, 2026.
20	143	0.166497672243	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	170	0.166666666667	E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7. $6 x - 1$
20	171	0.181511878216	Antoine Jay, 2026.
20	172	0.187872471230	Christopher Smolen, 2026.
20	190	0.189189189190	Kevin Li, 2026. $37 x - 7$
20	191	0.189238254657	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	203	0.191919191920	Henry Cohn, 2026. $99 x - 19$
20	204	0.192054325921	Henry Cohn, 2026.
20	231	0.192307692308	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $26 x - 5$
20	256	0.2	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $5 x - 1$
20	257	0.203357314598	Henry Cohn, 2026. $112896 x^{4} - 30400 x^{3} - 13600 x^{2} + 625$
20	258	0.205762308446	Henry Cohn, 2026.
20	259	0.206601200687	Henry Cohn, 2026.
20	261	0.208061269728	Antoine Jay, 2026.
20	263	0.208064142127	Antoine Jay, 2026.
20	264	0.208816158548	Antoine Jay, 2026.
20	265	0.211446621937	Arhan Canli, 2026.
20	266	0.211882683928	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	267	0.212207433728	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	268	0.212543420571	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	269	0.212813424656	Christopher Smolen, 2026.
20	270	0.213125072189	Arhan Canli, 2026.
20	271	0.213443503508	Arhan Canli, 2026.
20	272	0.213882969851	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	273	0.214278782790	Arhan Canli, 2026.
20	274	0.214675731073	Christopher Smolen, 2026.
20	275	0.214939185709	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	276	0.215241007191	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	277	0.215509151600	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	278	0.215893592301	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	279	0.216231009257	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	280	0.216526595602	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	281	0.216758683305	Christopher Smolen, 2026.
20	282	0.217022557792	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	283	0.217336005303	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	284	0.217546038065	Christopher Smolen, 2026.
20	285	0.217581393896	Christopher Smolen, 2026.
20	286	0.217820225756	Christopher Smolen, 2026.
20	287	0.217994714328	Christopher Smolen, 2026.
20	288	0.217996119869	Christopher Smolen, 2026.
20	289	0.219882814094	Christopher Smolen, 2026.
20	290	0.220197021075	Christopher Smolen, 2026.
20	291	0.220578959202	Christopher Smolen, 2026.
20	292	0.220686359551	Christopher Smolen, 2026.
20	293	0.220688754271	Christopher Smolen, 2026.
20	294	0.220689205360	Christopher Smolen, 2026.
20	301	0.222222222223	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 2$
20	322	0.222222222223	Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 2$
20	323	0.232387029873	Antoine Jay, 2026.
20	324	0.236094945577	Christopher Smolen, 2026.
20	378	0.236363636364	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $55 x - 13$
20	379	0.239589889398	Vadim Borisov, 2026.
20	380	0.239745635963	Vadim Borisov, 2026.
20	381	0.239823078331	Vadim Borisov, 2026.
20	382	0.239897986181	Vadim Borisov, 2026.
20	383	0.239997909623	Vadim Borisov, 2026.
20	384	0.240044155452	Vadim Borisov, 2026.
20	385	0.240137029697	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	386	0.240190650146	Vadim Borisov, 2026.
20	387	0.240243272072	Vadim Borisov, 2026.
20	388	0.240283204221	Vadim Borisov, 2026.
20	389	0.240334155084	Vadim Borisov, 2026.
20	390	0.240367912420	Vadim Borisov, 2026.
20	391	0.240408865453	Vadim Borisov, 2026.
20	392	0.240454227774	Vadim Borisov, 2026.
20	393	0.240509132719	Vadim Borisov, 2026.
20	394	0.240546487553	Vadim Borisov, 2026.
20	395	0.240588095551	Vadim Borisov, 2026.
20	396	0.240629783469	Vadim Borisov, 2026.
20	397	0.240659818030	Vadim Borisov, 2026.
20	398	0.240702723526	Vadim Borisov, 2026.
20	399	0.240733122898	Vadim Borisov, 2026.
20	400	0.240764422490	Vadim Borisov, 2026.
20	401	0.240801184921	Vadim Borisov, 2026.
20	402	0.240826673931	Vadim Borisov, 2026.
20	403	0.240842549232	Vadim Borisov, 2026.
20	404	0.240877893067	Vadim Borisov, 2026.
20	405	0.240898242116	Vadim Borisov, 2026.
20	406	0.240923982740	Vadim Borisov, 2026.
20	407	0.240948549264	Vadim Borisov, 2026.
20	408	0.240965013402	Vadim Borisov, 2026.
20	409	0.240976150858	Vadim Borisov, 2026.
20	412	0.241038042800	Vadim Borisov, 2026.
20	413	0.241146683009	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 10
20	414	0.248314516843	Henry Cohn, 2026.
20	437	0.256652310119	Henry Cohn and Ilmari Vahteristo, 2026. $3431375 x^{4} + 2993320 x^{3} + 182226 x^{2} - 244904 x - 14641$
20	438	0.257440171132	Henry Cohn and Ilmari Vahteristo, 2026. $820 x^{4} - 288 x^{3} - 116 x^{2} + 9$
20	473	0.266666666667	Henry Cohn, 2025. $15 x - 4$
20	474	0.269855637233	Christopher Smolen, 2026.
20	475	0.270933955657	Christopher Smolen, 2026.
20	476	0.271647286531	Christopher Smolen, 2026.
20	477	0.272474965836	Vadim Borisov, 2026.
20	524	0.272727272728	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $11 x - 3$
20	567	0.273861278753	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $40 x^{2} - 3$
20	568	0.280556233523	Christopher Smolen, 2026.
20	569	0.282760187186	Vadim Borisov, 2026.
20	640	0.285714285715	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $7 x - 2$
20	641	0.291043025090	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	642	0.291821898397	Vadim Borisov, 2026.
20	643	0.292743282111	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	644	0.293224886454	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	645	0.293777213754	Vadim Borisov, 2026.
20	646	0.295483534421	Vadim Borisov, 2026.
20	647	0.297073091460	Vadim Borisov, 2026.
20	840	0.3	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $10 x - 3$
20	841	0.303064565750	Henry Cohn, 2026.
20	842	0.304746917541	Vadim Borisov, 2026.
20	843	0.305581210494	Vadim Borisov, 2026.
20	1002	0.307692307693	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $13 x - 4$
20	1006	0.314814742253	Vadim Borisov, 2026.
20	1007	0.314815157770	Christopher Smolen, 2026.
20	1008	0.316766828069	Vadim Borisov, 2026.
20	1009	0.316828234826	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1010	0.317490484316	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1011	0.317985370339	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1012	0.318367361595	Vadim Borisov, 2026.
20	1013	0.318798528376	Vadim Borisov, 2026.
20	1014	0.319209288794	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1015	0.319509103767	Vadim Borisov, 2026.
20	1016	0.319750687231	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1017	0.320047178011	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1018	0.320300358051	Vadim Borisov, 2026.
20	1019	0.320506961275	Vadim Borisov, 2026.
20	1020	0.320605669525	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
20	1021	0.321506705182	Vadim Borisov, 2026.
20	1022	0.322360551569	Vadim Borisov, 2026.
20	1023	0.322790479642	Vadim Borisov, 2026.
20	1024	0.323976597631	Christopher Smolen, 2026.
21	43	0.037145782135	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7581 x^{3} - 441 x^{2} - 21 x + 1$
21	44	0.043532808199	Henry Cohn, 2023.
21	50*	0.047619047620	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $21 x - 1$
21	51	0.058781524104	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	52	0.062634852632	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	53	0.066653866627	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	54	0.066663400245	Arhan Canli, 2026.
21	55	0.066665901555	Arhan Canli, 2026.
21	56	0.066666614051	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	57	0.066666660446	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	58	0.066666666335	Henry Cohn, 2026.
21	59	0.072019011748	Henry Cohn, 2025. Minimal polynomial of degree 8
21	60	0.074662292991	Henry Cohn, 2026. Minimal polynomial of degree 14
21	61	0.076923073145	Henry Cohn, 2025.
21	62	0.076923075369	Henry Cohn, 2025.
21	63	0.078689325834	Henry Cohn, 2026. $9 x^{2} + 12 x - 1$
21	64	0.080216778694	Henry Cohn, 2026. $14481 x^{4} - 18000 x^{3} + 4848 x^{2} - 480 x + 16$
21	65	0.081966195796	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	77*	0.083333333334	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $12 x - 1$
21	78	0.089655172414	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $145 x - 13$
21	82	0.093297851017	Henry Cohn, 2026. $144 x^{4} - 840 x^{3} + 192 x^{2} - 1$
21	83	0.095419617997	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	84	0.096073235105	Henry Cohn, 2026. $196416 x^{5} - 20976 x^{4} - 1408 x^{3} + 88 x^{2} - 4 x + 1$
21	85	0.097701632396	Henry Cohn, 2026.
21	87	0.103204295473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $168 x^{3} - 156 x^{2} + 24 x - 1$
21	88	0.106199014100	Henry Cohn, 2026. $2135 x^{3} + 1782 x^{2} - 25 x - 20$
21	89	0.107226089904	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	90	0.108104321417	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
21	92	0.109918568058	Henry Cohn, 2026. Minimal polynomial of degree 8
21	93	0.110695455304	Henry Cohn, 2026.
21	112*	0.111111111112	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $9 x - 1$
21	113	0.127363959709	Henry Cohn, 2026. $6125 x^{4} - 672 x^{3} - 322 x^{2} + 5$
21	119	0.131782945737	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $129 x - 17$
21	120	0.139344261657	Henry Cohn, 2026.
21	121	0.139344261810	Henry Cohn, 2026.
21	122	0.139344262227	Henry Cohn, 2026.
21	123	0.139383168789	Christopher Smolen, 2026.
21	124	0.140534115806	Arhan Canli, 2026.
21	162*	0.142857142858	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $7 x - 1$
21	163	0.153926281042	Henry Cohn, 2026. $576 x^{4} - 90 x^{3} - 42 x^{2} + 1$
21	164	0.160000000017	Henry Cohn, 2026.
21	165	0.160002030147	Christopher Smolen, 2026.
21	166	0.160159396364	Christopher Smolen, 2026.
21	167	0.161786919899	Antoine Jay, 2026.
21	198	0.161904761905	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $105 x - 17$
21	199	0.172187000249	Henry Cohn, 2026. $24649 x^{4} - 4608 x^{3} - 2096 x^{2} + 64$
21	210	0.173428756326	Henry Cohn, 2026. $7695 x^{4} + 15012 x^{3} + 4122 x^{2} - 924 x - 49$
21	217	0.174875298960	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $119 x^{4} + 580 x^{3} + 42 x^{2} - 20 x - 1$
21	218	0.177242654655	Antoine Jay, 2026.
21	219	0.177401482790	Antoine Jay, 2026.
21	220	0.177459495833	Christopher Smolen, 2026.
21	221	0.177479906478	Christopher Smolen, 2026.
21	224	0.177492046263	Henry Cohn, 2026.
21	225	0.178085751307	Henry Cohn, 2026.
21	226	0.185423144319	Antoine Jay, 2026.
21	227	0.190596972220	Christopher Smolen, 2026.
21	233	0.192307692308	Code with 231 points in 20 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $26 x - 5$
21	235	0.192307692308	Henry Cohn, 2026. $26 x - 5$
21	236	0.194536353193	Christopher Smolen, 2026.
21	237	0.195306284010	Antoine Jay, 2026.
21	336	0.2	E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7. $5 x - 1$
21	352	0.214285714286	Henry Cohn, 2026. $14 x - 3$
21	353	0.222395820677	Henry Cohn, 2026. $144 x^{4} - 42 x^{3} - 18 x^{2} + 1$
21	373	0.227586206897	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $145 x - 33$
21	388	0.227586206897	Antoine Jay, 2026. $145 x - 33$
21	397	0.230769230770	Henry Cohn, 2026. $13 x - 3$
21	398	0.232494597432	Vadim Borisov, 2026.
21	554	0.238095238096	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $21 x - 5$
21	567	0.25	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $4 x - 1$
21	568	0.253536493698	Christopher Smolen, 2026.
21	569	0.254499244630	Christopher Smolen, 2026.
21	570	0.255064875877	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	571	0.255477267996	Christopher Smolen, 2026.
21	572	0.255805538966	Christopher Smolen, 2026.
21	573	0.256122245518	Christopher Smolen, 2026.
21	574	0.256383914921	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	575	0.256601162666	Christopher Smolen, 2026.
21	576	0.256818499646	Christopher Smolen, 2026.
21	577	0.257065124872	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	578	0.257277671066	Christopher Smolen, 2026.
21	579	0.257423048231	Christopher Smolen, 2026.
21	580	0.257574567090	Christopher Smolen, 2026.
21	581	0.257695087400	Christopher Smolen, 2026.
21	582	0.257814773286	Christopher Smolen, 2026.
21	583	0.257901489962	Christopher Smolen, 2026.
21	584	0.258015664154	Christopher Smolen, 2026.
21	585	0.258106830253	Christopher Smolen, 2026.
21	586	0.258234369511	Christopher Smolen, 2026.
21	587	0.258300374703	Christopher Smolen, 2026.
21	588	0.258372941586	Christopher Smolen, 2026.
21	589	0.258443898692	Christopher Smolen, 2026.
21	590	0.258598876559	Christopher Smolen, 2026.
21	591	0.258699041520	Henry Cohn, 2026.
21	592	0.258733579358	Henry Cohn, 2026.
21	593	0.258970475781	Henry Cohn, 2026.
21	594	0.259074389822	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	595	0.259213139547	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	596	0.259290937743	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	597	0.259458419673	Henry Cohn, 2026.
21	598	0.259547758802	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	600	0.259658118098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	601	0.259788362521	Henry Cohn, 2026.
21	602	0.259827595092	Christopher Smolen, 2026.
21	603	0.259903542222	Christopher Smolen, 2026.
21	604	0.259937010769	Christopher Smolen, 2026.
21	605	0.260041515570	Christopher Smolen, 2026.
21	606	0.260130721900	Christopher Smolen, 2026.
21	607	0.260226375063	Christopher Smolen, 2026.
21	608	0.260272870753	Christopher Smolen, 2026.
21	609	0.260313783874	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	610	0.260493672873	Christopher Smolen, 2026.
21	611	0.260597893595	Christopher Smolen, 2026.
21	612	0.260661856210	Christopher Smolen, 2026.
21	613	0.260783565021	Christopher Smolen, 2026.
21	614	0.260874726329	Christopher Smolen, 2026.
21	615	0.260931924325	Henry Cohn, 2026.
21	616	0.261024529155	Christopher Smolen, 2026.
21	617	0.261082030955	Christopher Smolen, 2026.
21	618	0.261158091120	Christopher Smolen, 2026.
21	619	0.261226645411	Christopher Smolen, 2026.
21	620	0.261266474727	Christopher Smolen, 2026.
21	621	0.261304889845	Christopher Smolen, 2026.
21	622	0.261344828583	Christopher Smolen, 2026.
21	623	0.261388958923	Christopher Smolen, 2026.
21	624	0.261423926963	Christopher Smolen, 2026.
21	625	0.261459555970	Christopher Smolen, 2026.
21	626	0.261499922877	Christopher Smolen, 2026.
21	627	0.261571978993	Christopher Smolen, 2026.
21	628	0.261627090927	Christopher Smolen, 2026.
21	629	0.261682605692	Christopher Smolen, 2026.
21	630	0.261958107459	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	631	0.262154566463	Vadim Borisov, 2026.
21	632	0.262367373679	Vadim Borisov, 2026.
21	633	0.262613941786	Christopher Smolen, 2026.
21	634	0.262684544306	Christopher Smolen, 2026.
21	635	0.262734882092	Christopher Smolen, 2026.
21	636	0.262885692674	Christopher Smolen, 2026.
21	637	0.263006174366	Christopher Smolen, 2026.
21	638	0.263137948719	Christopher Smolen, 2026.
21	639	0.263227153629	Christopher Smolen, 2026.
21	640	0.263327544852	Henry Cohn, 2026.
21	641	0.263415262102	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	642	0.263576836221	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	643	0.263702458722	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	644	0.263824985632	Christopher Smolen, 2026.
21	645	0.263933494809	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	646	0.263971426703	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	647	0.264048009784	Christopher Smolen, 2026.
21	648	0.264123734385	Henry Cohn, 2026.
21	649	0.264185344988	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	650	0.264291721257	Henry Cohn, 2026.
21	651	0.264364702947	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	652	0.264436381302	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	653	0.264503958922	Henry Cohn, 2026.
21	654	0.264557731519	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	655	0.264633936308	Henry Cohn, 2026.
21	656	0.264732807067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	657	0.264801543255	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	658	0.264893785471	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	659	0.264987722415	Christopher Smolen, 2026.
21	660	0.265122401050	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	661	0.265178179819	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	662	0.265230317401	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	663	0.265294808301	Henry Cohn, 2026.
21	664	0.265373969374	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	665	0.265446032004	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	666	0.265519616027	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	667	0.265557370516	Christopher Smolen, 2026.
21	668	0.265602712145	Henry Cohn, 2026.
21	669	0.265630783153	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	670	0.265666521208	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	671	0.265729895748	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	672	0.265768260309	Christopher Smolen, 2026.
21	673	0.265851473883	Christopher Smolen, 2026.
21	674	0.265900185636	Christopher Smolen, 2026.
21	676	0.265955826534	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	677	0.266078401887	Henry Cohn, 2026.
21	678	0.266134800029	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	679	0.266165727230	Henry Cohn, 2026.
21	680	0.266222532921	Christopher Smolen, 2026.
21	681	0.266278292165	Christopher Smolen, 2026.
21	682	0.266341764878	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	683	0.266503145348	Henry Cohn, 2026.
21	684	0.266585283786	Christopher Smolen, 2026.
21	715	0.266666666667	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $15 x - 4$
21	728	0.267171850610	Henry Cohn, 2026.
21	729	0.267261241913	Henry Cohn, 2026. $14 x^{2} - 1$
21	730	0.277219643394	Christopher Smolen, 2026.
21	731	0.281998176128	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	732	0.284670115135	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
21	815	0.285278978151	Henry Cohn and Ilmari Vahteristo, 2026. $9684311 x^{4} + 9406656 x^{3} + 688338 x^{2} - 979776 x - 59049$
21	850	0.285714285715	Henry Cohn, 2026. $7 x - 2$
21	851	0.290297025840	Henry Cohn, 2026.
21	852	0.291094893025	Henry Cohn, 2026.
21	853	0.291722388514	Henry Cohn, 2026.
21	854	0.292104559801	Henry Cohn, 2026.
21	855	0.292429821196	Henry Cohn, 2026.
21	856	0.292762588812	Henry Cohn, 2026.
21	857	0.293056607458	Henry Cohn, 2026.
21	858	0.293321667431	Henry Cohn, 2026.
21	859	0.293634136878	Henry Cohn, 2026.
21	974	0.294117647059	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $17 x - 5$
21	975	0.299221123909	Henry Cohn, 2026.
21	1024	0.3	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $10 x - 3$
22	45	0.035618974680	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $8800 x^{3} - 484 x^{2} - 22 x + 1$
22	46	0.041709010468	Henry Cohn, 2026.
22	47	0.046962270332	Henry Cohn, 2026, continuous family of codes without rattlers. $736 x^{3} + 236 x^{2} - 34 x + 1$
22	48	0.047524915294	Henry Cohn, 2025, continuous family of codes without rattlers. $64 x^{2} + 18 x - 1$
22	49	0.047603596723	Henry Cohn, 2026, continuous family of codes without rattlers. $3021824 x^{6} + 71680 x^{5} - 194624 x^{4} + 31816 x^{3} - 2252 x^{2} + 76 x - 1$
22	50	0.047616424396	Arhan Canli, 2026. $14176 x^{4} + 2160 x^{3} - 702 x^{2} + 48 x - 1$
22	51	0.047618598602	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 9
22	52	0.047619038000	Henry Cohn, 2026.
22	53	0.057403269990	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	54	0.060108520250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	55	0.062592707017	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	56	0.062633806388	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	57	0.066559109857	Henry Cohn, 2026.
22	58	0.066623756300	Arhan Canli, 2026.
22	59	0.066648627499	Arhan Canli, 2026.
22	60	0.066658733220	Arhan Canli, 2026.
22	61	0.069638781739	Henry Cohn, 2026.
22	62	0.071702992424	Henry Cohn, 2026. $140 x^{3} + 45 x^{2} + 10 x - 1$
22	63	0.076899986863	Arhan Canli, 2026.
22	64	0.076908450545	Arhan Canli, 2026.
22	65	0.076923310773	Henry Cohn, 2026.
22	66	0.078232998313	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988, continuous family of codes without rattlers. $10 x^{2} + 12 x - 1$
22	67	0.079295575063	Henry Cohn, 2026.
22	68	0.080927905651	Henry Cohn, 2026.
22	69	0.082211649807	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	70	0.082987101128	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	71	0.083331298889	Henry Cohn, 2026.
22	72	0.083332905177	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	73	0.083333206111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	74	0.083333297185	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	75	0.083333333299	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 24
22	76	0.083333333328	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 16
22	77	0.083333333333	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 36
22	79	0.083333333334	Code with 77 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $12 x - 1$
22	80	0.086876541301	Henry Cohn, 2026. $550 x^{3} - 410 x^{2} + 66 x - 3$
22	100*	0.090909090910	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $11 x - 1$
22	101	0.109433688331	Henry Cohn, 2026. $6912 x^{4} - 560 x^{3} - 272 x^{2} + 3$
22	102	0.111104168854	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	104	0.111108614436	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 34
22	105	0.111109826504	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
22	107	0.111110682967	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 41
22	110	0.111111037661	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 52
22	113	0.111111098510	Henry Cohn, 2026.
22	114	0.111111111112	Code with 112 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 1$
22	115	0.112789665003	Henry Cohn, 2026. $68 x^{2} - 52 x + 5$
22	116	0.117359909647	Henry Cohn, 2026. $30 x^{2} + 5 x - 1$
22	117	0.122747047396	Christopher Smolen, 2026.
22	118	0.126131983623	Kevin Li, 2026. $47 x^{2} + 2 x - 1$
22	119	0.126738682709	Arhan Canli, 2026.
22	120	0.131231549706	Henry Cohn, 2026. Minimal polynomial of degree 8
22	127	0.131782945737	Henry Cohn, 2026. $129 x - 17$
22	136	0.135135135136	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $37 x - 5$
22	141	0.135135135136	Henry Cohn, 2026. $37 x - 5$
22	142	0.135516832876	Christopher Smolen, 2026.
22	143	0.137877527773	Vadim Borisov, 2026.
22	144	0.139612236038	Azmi C. Özgen, 2026.
22	166	0.142857142858	Henry Cohn, 2026. $7 x - 1$
22	167	0.144948974279	Henry Cohn, 2026. $20 x^{2} + 4 x - 1$
22	169	0.149071198500	Henry Cohn, 2026. $45 x^{2} - 1$
22	170	0.153808582906	Henry Cohn, 2026. $3193200 x^{4} - 2981880 x^{3} + 586608 x^{2} + 63888 x - 14641$
22	171	0.156572050095	Henry Cohn, 2026.
22	172	0.158260507796	Azmi C. Özgen, 2026.
22	173	0.159107132818	Henry Cohn, 2026.
22	174	0.161494540981	Christopher Smolen, 2026.
22	202	0.161904761905	Henry Cohn, 2026. $105 x - 17$
22	203	0.165014613150	Christopher Smolen, 2026.
22	275*	0.166666666667	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $6 x - 1$
22	276	0.178506323194	Henry Cohn, 2026.
22	277	0.185913605688	Christopher Smolen, 2026.
22	278	0.189278821912	Azmi C. Özgen, 2026.
22	279	0.191548734977	Azmi C. Özgen, 2026.
22	280	0.193231566176	Azmi C. Özgen, 2026.
22	281	0.194502382039	Azmi C. Özgen, 2026.
22	282	0.195683008514	Azmi C. Özgen, 2026.
22	283	0.196310422011	Christopher Smolen, 2026.
22	285	0.196327532186	Henry Cohn, 2026.
22	286	0.196362023435	Henry Cohn, 2026.
22	287	0.199227355721	Azmi C. Özgen, 2026.
22	352	0.2	C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391. $5 x - 1$
22	353	0.201777989817	Henry Cohn, 2026. $1308736 x^{4} - 332640 x^{3} - 147312 x^{2} + 6561$
22	354	0.202832443486	Vadim Borisov, 2026.
22	355	0.203727072271	Henry Cohn, 2026.
22	356	0.204034193404	Henry Cohn, 2026.
22	357	0.204058215698	Henry Cohn, 2026.
22	358	0.204059171273	Henry Cohn, 2026.
22	359	0.204488589692	Henry Cohn, 2026.
22	374	0.204624019941	Henry Cohn, 2026. $911296 x^{4} - 2815904 x^{3} - 1346592 x^{2} + 246064 x + 28561$
22	375	0.205717036734	Christopher Smolen, 2026.
22	376	0.206395569430	Christopher Smolen, 2026.
22	377	0.206695193047	Christopher Smolen, 2026.
22	378	0.206882235842	Azmi C. Özgen, 2026.
22	379	0.207056804630	Azmi C. Özgen, 2026.
22	380	0.207117535113	Vadim Borisov, 2026.
22	381	0.207163540721	Azmi C. Özgen, 2026.
22	382	0.207169374827	Vadim Borisov, 2026.
22	383	0.207170039184	Vadim Borisov, 2026.
22	384	0.207170420432	Vadim Borisov, 2026.
22	385	0.207171072309	Christopher Smolen, 2026.
22	386	0.207171194623	Christopher Smolen, 2026.
22	387	0.207171348193	Christopher Smolen, 2026.
22	388	0.207171455915	Christopher Smolen, 2026.
22	389	0.207172016361	Vadim Borisov, 2026.
22	390	0.207173418366	Christopher Smolen, 2026.
22	391	0.208463126713	Christopher Smolen, 2026.
22	392	0.208815102151	Christopher Smolen, 2026.
22	393	0.209018831547	Christopher Smolen, 2026.
22	394	0.209049421422	Vadim Borisov, 2026.
22	395	0.209290942770	Azmi C. Özgen, 2026.
22	396	0.209386048822	Vadim Borisov, 2026.
22	397	0.209540882680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
22	398	0.209545632962	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
22	399	0.209554676289	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
22	400	0.209590720652	Vadim Borisov, 2026.
22	401	0.209591888735	Vadim Borisov, 2026.
22	402	0.209592657709	Vadim Borisov, 2026.
22	403	0.209595513037	Azmi C. Özgen, 2026.
22	404	0.209666940791	Azmi C. Özgen, 2026.
22	405	0.209705056029	Azmi C. Özgen, 2026.
22	415	0.209711433874	Henry Cohn, 2026.
22	416	0.209814363187	Azmi C. Özgen, 2026.
22	430	0.209817069797	Henry Cohn, 2026. $25856 x^{4} + 20288 x^{3} + 1056 x^{2} - 1120 x - 49$
22	431	0.210993089892	Henry Cohn, 2026.
22	432	0.211661635419	Henry Cohn, 2026.
22	433	0.212032690030	Christopher Smolen, 2026.
22	436	0.212148697334	Henry Cohn, 2026.
22	437	0.212406676955	Henry Cohn, 2026.
22	438	0.212505211379	Christopher Smolen, 2026.
22	442	0.212505214492	Henry Cohn, 2026.
22	451	0.212653226480	Henry Cohn, 2026.
22	452	0.213200716356	Henry Cohn, 2026. $22 x^{2} - 1$
22	487	0.225192823176	Henry Cohn, 2026. Minimal polynomial of degree 8
22	488	0.227085433996	Henry Cohn, 2026.
22	489	0.229551246103	Azmi C. Özgen, 2026.
22	505	0.229926564594	Henry Cohn, 2026.
22	506	0.231137104549	Henry Cohn, 2026.
22	529	0.233333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $30 x - 7$
22	561	0.238095238096	Henry Cohn, 2026. $21 x - 5$
22	562	0.238151335257	Azmi C. Özgen, 2026.
22	563	0.239820997726	Vadim Borisov, 2026.
22	564	0.240350502235	Vadim Borisov, 2026.
22	565	0.240513661706	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
22	566	0.240556355995	Vadim Borisov, 2026.
22	891*	0.25	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $4 x - 1$
22	1024	0.272727272728	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $11 x - 3$
23	47	0.034216857253	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $10143 x^{3} - 529 x^{2} - 23 x + 1$
23	48	0.040044232989	Henry Cohn, 2026.
23	49	0.045954913455	Henry Cohn, 2026.
23	50	0.046749604258	Henry Cohn, 2025, continuous family of codes without rattlers. $713 x^{3} + 215 x^{2} - 33 x + 1$
23	51	0.047263378257	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	52	0.047439726151	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	53	0.047577267456	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	54	0.047607601414	Arhan Canli, 2026.
23	55	0.054740716520	Henry Cohn, 2026.
23	56	0.057275984127	Henry Cohn, 2025. Minimal polynomial of degree 10
23	57	0.059898620221	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	58	0.061144993092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	59	0.065898054218	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	60	0.066268741606	Arhan Canli, 2026.
23	61	0.066446612145	Arhan Canli, 2026.
23	62	0.066544410275	Arhan Canli, 2026.
23	63	0.067249405088	Henry Cohn, 2026.
23	64	0.069716146261	Henry Cohn, 2026. Minimal polynomial of degree 14
23	65	0.073130743225	Henry Cohn, 2026.
23	66	0.075359392649	Henry Cohn, 2026.
23	67	0.076769472844	Arhan Canli, 2026.
23	68	0.076888567246	Arhan Canli, 2026.
23	69	0.077601989740	Henry Cohn, 2026.
23	70	0.077976083355	Henry Cohn, 2026.
23	71	0.079522620309	Henry Cohn, 2026.
23	72	0.080064660878	Henry Cohn, 2026.
23	73	0.081987991972	Arhan Canli, 2026.
23	74	0.082971963238	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	75	0.083232614730	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	76	0.083308124082	Arhan Canli, 2026.
23	77	0.083319986482	Arhan Canli, 2026.
23	78	0.083328526015	Christopher Smolen, 2026.
23	79	0.083331444563	Arhan Canli, 2026.
23	80	0.083332658564	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	81	0.083333004281	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	82	0.083354230263	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	83	0.087155118594	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	84	0.089247307908	Arhan Canli, 2026.
23	85	0.090369089949	Christopher Smolen, 2026.
23	86	0.090635971456	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	87	0.090845809648	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	88	0.090900526392	Christopher Smolen, 2026.
23	89	0.090909074795	Vadim Borisov, 2026.
23	90	0.090909086564	Christopher Smolen, 2026.
23	91	0.090909090666	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 12
23	92	0.090909090868	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 24
23	93	0.090909090902	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 16
23	94	0.090909090908	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 36
23	95	0.090909090909	Henry Cohn and Ilmari Vahteristo, 2026. Minimal polynomial of degree 18
23	102	0.090909090910	Code with 100 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 1$
23	103	0.094789393423	Henry Cohn, 2026. $67 x^{2} - 38 x + 3$
23	104	0.102473100453	Henry Cohn, 2026. $76221641 x^{6} - 70238210 x^{5} + 26263911 x^{4} - 5120604 x^{3} + 551799 x^{2} - 31266 x + 729$
23	106	0.109392443214	Henry Cohn, 2026. $2175 x^{2} + 210 x - 49$
23	107	0.110892215957	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	108	0.110906204507	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	109	0.111012869796	Vadim Borisov, 2026.
23	111	0.111012885634	Vadim Borisov, 2026.
23	112	0.111012946231	Christopher Smolen, 2026.
23	113	0.111034183054	Vadim Borisov, 2026.
23	114	0.111034228908	Christopher Smolen, 2026.
23	115	0.111111098510	Orthogonal union of 113 points in 22 dimensions and 2 points in 1 dimension.
23	116	0.111111109675	Henry Cohn, 2026.
23	118	0.111111111112	Kevin Li, 2026. $9 x - 1$
23	119	0.115901764548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
23	120	0.119778033286	Christopher Smolen, 2026.
23	121	0.124434126200	Arhan Canli, 2026.
23	122	0.124520867516	Arhan Canli, 2026.
23	123	0.128566662565	Azmi C. Özgen, 2026.
23	124	0.130805645392	Vadim Borisov, 2026.
23	130	0.131782945704	Henry Cohn, 2026.
23	131	0.131793350389	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	132	0.133404816895	Christopher Smolen, 2026.
23	133	0.134649685316	Vadim Borisov, 2026.
23	134	0.134991220895	Christopher Smolen, 2026.
23	135	0.135100853284	Christopher Smolen, 2026.
23	136	0.135127365162	Christopher Smolen, 2026.
23	137	0.135132968493	Christopher Smolen, 2026.
23	147	0.135135135136	Henry Cohn, 2026. $37 x - 5$
23	148	0.135243512040	Azmi C. Özgen, 2026.
23	149	0.136333149815	Henry Cohn, 2026.
23	150	0.136482882097	Henry Cohn, 2026.
23	151	0.137546592954	Azmi C. Özgen, 2026.
23	152	0.138673551832	Henry Cohn, 2026.
23	170	0.142857142858	Kevin Li, 2026. $7 x - 1$
23	171	0.144959716558	Christopher Smolen, 2026.
23	172	0.145326885183	Christopher Smolen, 2026.
23	173	0.145383795921	Henry Cohn, 2026.
23	174	0.146718972909	Christopher Smolen, 2026.
23	175	0.147421141363	Henry Cohn, 2026.
23	176	0.152489957763	Christopher Smolen, 2026.
23	177	0.152897749824	Azmi C. Özgen, 2026.
23	178	0.153820381868	Vadim Borisov, 2026.
23	179	0.154398963642	Azmi C. Özgen, 2026.
23	180	0.157012101613	Vadim Borisov, 2026.
23	181	0.158067978366	Azmi C. Özgen, 2026.
23	182	0.159230192953	Vadim Borisov, 2026.
23	183	0.160596122162	Vadim Borisov, 2026.
23	184	0.161041820616	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	208	0.161904761905	Kevin Li, 2026. $105 x - 17$
23	209	0.163284221599	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	210	0.164892646113	Vadim Borisov, 2026.
23	211	0.165233821641	Azmi C. Özgen, 2026.
23	212	0.165895335525	Vadim Borisov, 2026.
23	213	0.166449405661	Christopher Smolen, 2026.
23	214	0.166575989669	Christopher Smolen, 2026.
23	215	0.166641296691	Christopher Smolen, 2026.
23	216	0.166666666524	Henry Cohn, 2026.
23	220	0.166666666643	Henry Cohn, 2026.
23	224	0.166666666663	Henry Cohn, 2026.
23	228	0.166666666666	Henry Cohn, 2026.
23	278	0.166666666667	Henry Cohn, 2026. $6 x - 1$
23	279	0.168164328621	Henry Cohn, 2026.
23	281	0.169520847199	Kevin Li, 2026. $23 x^{2} + 2 x - 1$
23	282	0.176232422077	Azmi C. Özgen, 2026.
23	283	0.180873914011	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	284	0.184226731358	Azmi C. Özgen, 2026.
23	285	0.186028064519	Christopher Smolen, 2026.
23	286	0.187579576008	Azmi C. Özgen, 2026.
23	287	0.188048088328	Azmi C. Özgen, 2026.
23	288	0.188279870113	Azmi C. Özgen, 2026.
23	289	0.189126409936	Vadim Borisov, 2026.
23	290	0.189336797219	Vadim Borisov, 2026.
23	292	0.189437876687	Henry Cohn, 2026. $171 x^{2} - 6 x - 5$
23	293	0.189616577064	Azmi C. Özgen, 2026.
23	294	0.189647232059	Vadim Borisov, 2026.
23	295	0.189655240386	Christopher Smolen, 2026.
23	296	0.189655982900	Christopher Smolen, 2026.
23	297	0.189656051798	Vadim Borisov, 2026.
23	298	0.189656053746	Vadim Borisov, 2026.
23	299	0.189656090161	Christopher Smolen, 2026.
23	300	0.189656118505	Christopher Smolen, 2026.
23	301	0.190627934454	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	302	0.193041714029	Azmi C. Özgen, 2026.
23	303	0.194173414379	Vadim Borisov, 2026.
23	304	0.195081459092	Azmi C. Özgen, 2026.
23	305	0.195744314538	Azmi C. Özgen, 2026.
23	306	0.196406854945	Azmi C. Özgen, 2026.
23	307	0.196828785388	Azmi C. Özgen, 2026.
23	308	0.197470532558	Azmi C. Özgen, 2026.
23	309	0.197839997990	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	311	0.198231691460	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	312	0.198376741377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	313	0.198560771311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	314	0.198686269895	Christopher Smolen, 2026.
23	552*	0.2	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $5 x - 1$
23	553	0.232851959963	Henry Cohn, 2026. $11025 x^{4} - 7040 x^{3} - 3680 x^{2} + 256$
23	554	0.235338470310	Henry Cohn, 2026.
23	573	0.238095238096	Henry Cohn, 2026. $21 x - 5$
23	574	0.238840269898	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	575	0.239181373966	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	576	0.239239916252	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	577	0.239597711621	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	578	0.240178249781	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	579	0.240372540803	Vadim Borisov, 2026.
23	580	0.241124239884	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	581	0.241433614091	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	582	0.241687279309	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	583	0.242122475890	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	584	0.244158115373	Azmi C. Özgen, 2026.
23	585	0.244801747846	Azmi C. Özgen, 2026.
23	586	0.245198644315	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	587	0.245425722810	Vadim Borisov, 2026.
23	588	0.245902335053	Azmi C. Özgen, 2026.
23	589	0.246052567059	Azmi C. Özgen, 2026.
23	590	0.246102625533	Azmi C. Özgen, 2026.
23	591	0.246392626760	Azmi C. Özgen, 2026.
23	592	0.246416647593	Azmi C. Özgen, 2026.
23	593	0.246950051620	Azmi C. Özgen, 2026.
23	594	0.247144384832	Azmi C. Özgen, 2026.
23	595	0.247214788346	Azmi C. Özgen, 2026.
23	596	0.247437478574	Azmi C. Özgen, 2026.
23	597	0.247461532885	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	598	0.247604988752	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	599	0.248658464878	Azmi C. Özgen, 2026.
23	600	0.248875322703	Azmi C. Özgen, 2026.
23	601	0.249056658320	Azmi C. Özgen, 2026.
23	602	0.249258075156	Azmi C. Özgen, 2026.
23	603	0.249445000885	Azmi C. Özgen, 2026.
23	604	0.249592400286	Azmi C. Özgen, 2026.
23	605	0.249658995442	Azmi C. Özgen, 2026.
23	894	0.25	Henry Cohn, 2026. $4 x - 1$
23	897	0.25	Kevin Li, 2026. $4 x - 1$
23	898	0.251976315340	Henry Cohn, 2026. $63 x^{2} - 4$
23	899	0.251976315340	Azmi C. Özgen, 2026. $63 x^{2} - 4$
23	900	0.252103546588	Azmi C. Özgen, 2026.
23	917	0.256477368938	Kevin Li, 2026. $23 x^{2} - 2 x - 1$
23	918	0.262975083042	Azmi C. Özgen, 2026.
23	919	0.264568404137	Azmi C. Özgen, 2026.
23	920	0.266020556676	Azmi C. Özgen, 2026.
23	921	0.266627870477	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
23	949	0.269672331459	Kevin Li, 2026. $36 x^{2} - 6 x - 1$
23	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
23	4600*	0.333333333334	P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421. $3 x - 1$
24	49	0.032924519945	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11616 x^{3} - 576 x^{2} - 24 x + 1$
24	50	0.038461538462	T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114. $26 x - 1$
24	52	0.045454545455	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $22 x - 1$
24	53	0.046514918044	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. Minimal polynomial of degree 8
24	54	0.046847786762	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	55	0.047164753839	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	56	0.047426030409	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	57	0.052950643062	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	58	0.054352485457	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	59	0.057903810057	Henry Cohn, 2026.
24	60	0.059948549845	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	61	0.064086783842	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	62	0.065007675891	Christopher Smolen, 2026.
24	63	0.065461873988	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	64	0.065880378575	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	65	0.066579290387	Christopher Smolen, 2026.
24	66	0.067945380996	Christopher Smolen, 2026.
24	67	0.070762396841	Henry Cohn, 2026.
24	68	0.072116568734	Henry Cohn, 2026.
24	69	0.073247042433	Henry Cohn, 2026.
24	70	0.076518930179	Christopher Smolen, 2026.
24	71	0.076910440718	Arhan Canli, 2026.
24	72	0.077184615255	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	73	0.077724157119	Christopher Smolen, 2026.
24	74	0.077908661683	Henry Cohn, 2026.
24	75	0.078506895605	Henry Cohn, 2026.
24	76	0.078850061998	Henry Cohn, 2026. Minimal polynomial of degree 12
24	77	0.079856913447	Arhan Canli, 2026.
24	78	0.081484170718	Azmi C. Özgen, 2026.
24	79	0.083101543818	Christopher Smolen, 2026.
24	80	0.083184602029	Christopher Smolen, 2026.
24	81	0.083186497858	Christopher Smolen, 2026.
24	82	0.083237917964	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	83	0.083238079747	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	84	0.083310116889	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	85	0.083323327763	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	86	0.086097832697	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	87	0.088106043794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	88	0.089206516628	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	89	0.090039710856	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	90	0.090273268230	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	91	0.090577857062	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	92	0.090765987314	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	93	0.090813719840	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	94	0.090883656527	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	95	0.090891198506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	96	0.090899639946	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	97	0.090908237174	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	98	0.090908329446	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	99	0.090908571706	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	100	0.090908831235	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	101	0.090909045701	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	102	0.090909063963	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	103	0.090909064328	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	104	0.090909084673	Henry Cohn, 2026.
24	105	0.091455993710	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	106	0.095232453047	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	107	0.100951682978	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	108	0.105528967523	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
24	109	0.110473333697	Arhan Canli, 2026.
24	110	0.110474298888	Christopher Smolen, 2026.
24	111	0.110634495863	Christopher Smolen, 2026.
24	112	0.110644085109	Christopher Smolen, 2026.
24	113	0.110669249768	Christopher Smolen, 2026.
24	114	0.110669550663	Henry Cohn, 2026.
24	115	0.110783199442	Henry Cohn, 2026.
24	116	0.110915374731	Christopher Smolen, 2026.
24	117	0.111099537874	Vadim Borisov, 2026.
24	118	0.111099565428	Henry Cohn, 2025.
24	121	0.111111111034	Henry Cohn, 2026.
24	122	0.112090945192	Christopher Smolen, 2026.
24	123	0.116163121763	Christopher Smolen, 2026.
24	124	0.117891409262	Henry Cohn, 2026.
24	125	0.122807017544	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $57 x - 7$
24	126	0.125601748200	Christopher Smolen, 2026.
24	127	0.127015895280	Vadim Borisov, 2026.
24	128	0.131474371231	Vadim Borisov, 2026.
24	129	0.131575705030	Christopher Smolen, 2026.
24	130	0.131591568568	Azmi C. Özgen, 2026.
24	131	0.131625505945	Christopher Smolen, 2026.
24	132	0.131773832293	Christopher Smolen, 2026.
24	133	0.131777975683	Christopher Smolen, 2026.
24	134	0.131779449884	Christopher Smolen, 2026.
24	135	0.131782782154	Christopher Smolen, 2026.
24	136	0.132188937263	Christopher Smolen, 2026.
24	137	0.132479495970	Christopher Smolen, 2026.
24	138	0.133244241757	Christopher Smolen, 2026.
24	139	0.134127899004	Vadim Borisov, 2026.
24	140	0.134373132799	Vadim Borisov, 2026.
24	141	0.134507762835	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	142	0.134520245499	Christopher Smolen, 2026.
24	143	0.134808772144	Vadim Borisov, 2026.
24	144	0.134945801270	Vadim Borisov, 2026.
24	145	0.134984745788	Christopher Smolen, 2026.
24	146	0.135079613305	Christopher Smolen, 2026.
24	147	0.135098858258	Christopher Smolen, 2026.
24	148	0.135109130340	Christopher Smolen, 2026.
24	149	0.135124488253	Christopher Smolen, 2026.
24	150	0.135128951944	Christopher Smolen, 2026.
24	151	0.135131223233	Christopher Smolen, 2026.
24	152	0.135135135074	Henry Cohn, 2026.
24	154	0.135854426726	Henry Cohn, 2026.
24	155	0.136174662682	Henry Cohn, 2026.
24	156	0.137040776891	Henry Cohn, 2026.
24	157	0.140964714895	Azmi C. Özgen, 2026.
24	158	0.142856457697	Christopher Smolen, 2026.
24	160	0.142856599586	Christopher Smolen, 2026.
24	161	0.142856767353	Vadim Borisov, 2026.
24	162	0.142856775455	Vadim Borisov, 2026.
24	163	0.142856778936	Christopher Smolen, 2026.
24	164	0.142856864065	Christopher Smolen, 2026.
24	165	0.142856874528	Christopher Smolen, 2026.
24	166	0.142856961628	Christopher Smolen, 2026.
24	167	0.142856964817	Christopher Smolen, 2026.
24	168	0.142857006901	Christopher Smolen, 2026.
24	169	0.142857059025	Christopher Smolen, 2026.
24	170	0.142857081896	Christopher Smolen, 2026.
24	171	0.142857104984	Christopher Smolen, 2026.
24	172	0.142857119767	Christopher Smolen, 2026.
24	174	0.142857142847	Henry Cohn, 2026.
24	175	0.143365672004	Christopher Smolen, 2026.
24	176	0.145030687242	Henry Cohn, 2026.
24	177	0.145780442033	Vadim Borisov, 2026.
24	178	0.145845617860	Christopher Smolen, 2026.
24	179	0.146016112364	Christopher Smolen, 2026.
24	180	0.146018032582	Christopher Smolen, 2026.
24	181	0.146018032655	Henry Cohn, 2026.
24	182	0.147761648217	Vadim Borisov, 2026.
24	183	0.147761650701	Christopher Smolen, 2026.
24	184	0.148170959627	Henry Cohn, 2026.
24	186	0.148688022031	Azmi C. Özgen, 2026.
24	187	0.152027450678	Azmi C. Özgen, 2026.
24	188	0.152027517150	Azmi C. Özgen, 2026.
24	189	0.152169621132	Henry Cohn, 2026.
24	191	0.153010121900	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	192	0.153098386869	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	193	0.154970908153	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	195	0.155187839306	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	196	0.156088187082	Azmi C. Özgen, 2026.
24	197	0.157137677392	Henry Cohn, 2026.
24	198	0.158433040527	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	199	0.159195918051	Christopher Smolen, 2026.
24	200	0.160061678636	Christopher Smolen, 2026.
24	201	0.161123410791	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	202	0.161494838254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	214	0.161904761885	Henry Cohn, 2026.
24	215	0.162111881127	Vadim Borisov, 2026.
24	216	0.162840675585	Christopher Smolen, 2026.
24	217	0.163159804006	Vadim Borisov, 2026.
24	218	0.164131480214	Christopher Smolen, 2026.
24	219	0.164593864515	Vadim Borisov, 2026.
24	220	0.164973718388	Christopher Smolen, 2026.
24	221	0.165294099228	Christopher Smolen, 2026.
24	222	0.165826885519	Vadim Borisov, 2026.
24	223	0.166128387976	Azmi C. Özgen, 2026.
24	224	0.166395979801	Christopher Smolen, 2026.
24	226	0.166666666663	Orthogonal union of 224 points in 23 dimensions and 2 points in 1 dimension.
24	230	0.166666666666	Orthogonal union of 228 points in 23 dimensions and 2 points in 1 dimension.
24	283	0.166666666667	Henry Cohn, 2026. $6 x - 1$
24	284	0.166790646363	Azmi C. Özgen, 2026.
24	285	0.169965156174	Vadim Borisov, 2026.
24	286	0.171282395301	Vadim Borisov, 2026.
24	287	0.174936225018	Azmi C. Özgen, 2026.
24	288	0.177013607848	Christopher Smolen, 2026.
24	289	0.179218162061	Vadim Borisov, 2026.
24	290	0.181572809694	Vadim Borisov, 2026.
24	297	0.181818181819	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 2$
24	314	0.181818181819	Henry Cohn, 2026. $11 x - 2$
24	315	0.186360420192	Pavlos Moros, 2026.
24	316	0.188619149989	Pavlos Moros, 2026.
24	317	0.190672505800	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	318	0.191959319848	Azmi C. Özgen, 2026.
24	330	0.193548387097	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $31 x - 6$
24	331	0.199999432649	Vadim Borisov, 2026.
24	332	0.199999727529	Vadim Borisov, 2026.
24	333	0.199999827177	Vadim Borisov, 2026.
24	334	0.199999897984	Henry Cohn, 2026.
24	338	0.199999993679	Christopher Smolen, 2026.
24	342	0.199999998003	Christopher Smolen, 2026.
24	347	0.199999999698	Henry Cohn, 2026.
24	352	0.199999999924	Henry Cohn, 2026.
24	357	0.199999999986	Henry Cohn, 2026.
24	555	0.2	Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233. $5 x - 1$
24	556	0.200001288486	Christopher Smolen, 2026.
24	557	0.206704233680	Azmi C. Özgen, 2026.
24	559	0.210852996458	Kevin Li, 2026. $71 x^{2} + 4 x - 4$
24	561	0.215410109214	Kevin Li, 2026. $1056 x^{2} - 49$
24	562	0.222581893725	Vadim Borisov, 2026.
24	563	0.224090062898	Azmi C. Özgen, 2026.
24	564	0.225307077162	Azmi C. Özgen, 2026.
24	565	0.226543269887	Azmi C. Özgen, 2026.
24	566	0.228186672416	Azmi C. Özgen, 2026.
24	567	0.229098073800	Vadim Borisov, 2026.
24	568	0.230483507269	Azmi C. Özgen, 2026.
24	569	0.231609114952	Azmi C. Özgen, 2026.
24	570	0.231648486738	Azmi C. Özgen, 2026.
24	571	0.232151214355	Azmi C. Özgen, 2026.
24	572	0.232346061997	Vadim Borisov, 2026.
24	573	0.232782520995	Azmi C. Özgen, 2026.
24	574	0.233292301752	Azmi C. Özgen, 2026.
24	581	0.233711730709	Vadim Borisov, 2026. $160 x^{2} - 16 x - 5$
24	627	0.233711730709	Kevin Li, 2026. $160 x^{2} - 16 x - 5$
24	628	0.241934794934	Azmi C. Özgen, 2026.
24	629	0.243313805799	Azmi C. Özgen, 2026.
24	630	0.244270970205	Azmi C. Özgen, 2026.
24	631	0.245060422244	Azmi C. Özgen, 2026.
24	632	0.245722579319	Azmi C. Özgen, 2026.
24	633	0.246438326819	Azmi C. Özgen, 2026.
24	634	0.247469500704	Azmi C. Özgen, 2026.
24	635	0.247961902201	Vadim Borisov, 2026.
24	636	0.248625985655	Vadim Borisov, 2026.
24	903	0.25	Kevin Li, 2026. $4 x - 1$
24	904	0.25	Henry Cohn, 2026. $4 x - 1$
24	905	0.250031006680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	906	0.250032666429	Azmi C. Özgen, 2026.
24	907	0.250092745270	Vadim Borisov, 2026.
24	908	0.250150373587	Azmi C. Özgen, 2026.
24	909	0.250725336713	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	910	0.250917885509	Azmi C. Özgen, 2026.
24	911	0.254054080034	Azmi C. Özgen, 2026.
24	912	0.255028664447	Vadim Borisov, 2026.
24	913	0.255514745536	Azmi C. Özgen, 2026.
24	914	0.255926073210	Azmi C. Özgen, 2026.
24	915	0.256441853459	Vadim Borisov, 2026.
24	916	0.256459938336	Henry Cohn, 2026.
24	917	0.256467925517	Vadim Borisov, 2026.
24	918	0.256473256912	Henry Cohn, 2026.
24	925	0.256477368938	Henry Cohn, 2026. $23 x^{2} - 2 x - 1$
24	943	0.259843574332	Henry Cohn, 2026. $167 x^{2} - 28 x - 4$
24	952	0.262071551239	Azmi C. Özgen, 2026.
24	953	0.263902885390	Azmi C. Özgen, 2026.
24	954	0.264347637656	Vadim Borisov, 2026.
24	955	0.264799130194	Azmi C. Özgen, 2026.
24	956	0.264993962535	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	957	0.266381724558	Azmi C. Özgen, 2026.
24	958	0.266442659220	Azmi C. Özgen, 2026.
24	959	0.266856039679	Vadim Borisov, 2026.
24	960	0.269074052008	Vadim Borisov, 2026.
24	961	0.269081634205	Vadim Borisov, 2026.
24	962	0.269093317833	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
24	963	0.269111687339	Vadim Borisov, 2026.
24	964	0.269121589928	Vadim Borisov, 2026.
24	965	0.269360590659	Vadim Borisov, 2026.
24	966	0.269392778484	Vadim Borisov, 2026.
24	967	0.269411060958	Vadim Borisov, 2026.
24	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
24	196560*	0.5	J. Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267, doi:10.4153/CJM-1967-017-0; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8. $2 x - 1$
25	51	0.031729360276	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $13225 x^{3} - 625 x^{2} - 25 x + 1$
25	52	0.037067969154	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	55	0.04	Henry Cohn, 2026. $25 x - 1$
25	56	0.046191273933	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $79 x^{2} + 18 x - 1$
25	57	0.046461733282	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	58	0.046851360412	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	59	0.050704072647	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	64	0.051797462893	Pavlos Moros, 2026.
25	65	0.064022037337	Arhan Canli, 2026.
25	66	0.065031929033	Arhan Canli, 2026.
25	67	0.066199317959	Arhan Canli, 2026.
25	68	0.066373627960	Arhan Canli, 2026.
25	69	0.068627707329	Henry Cohn, 2026.
25	70	0.071055411990	Henry Cohn, 2026.
25	71	0.071656872324	Christopher Smolen, 2026.
25	72	0.073123875608	Christopher Smolen, 2026.
25	73	0.076149158372	Azmi C. Özgen, 2026.
25	74	0.076464357938	Christopher Smolen, 2026.
25	75	0.076914972932	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	76	0.076915868124	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	77	0.077464853239	Azmi C. Özgen, 2026.
25	78	0.077915089938	Henry Cohn, 2026.
25	79	0.078439938519	Arhan Canli, 2026.
25	80	0.078628000041	Azmi C. Özgen, 2026.
25	81	0.078744959714	Antoine Jay, 2026.
25	82	0.079706101579	Arhan Canli, 2026.
25	83	0.082630411304	Christopher Smolen, 2026.
25	84	0.082778817215	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	85	0.082997587773	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	86	0.083068688870	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	87	0.083249586073	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	88	0.083267079002	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	89	0.084850884056	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	90	0.085255453742	Henry Cohn, 2026.
25	91	0.086622600059	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	92	0.088535148068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	93	0.089394011575	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	94	0.089885207915	Arhan Canli, 2026.
25	95	0.090206950611	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	96	0.090436733307	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	97	0.090613279716	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	98	0.090736690899	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	99	0.090776899944	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	100	0.090823896794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	101	0.090828568778	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	102	0.090855790338	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	103	0.090876943997	Vadim Borisov, 2026.
25	104	0.090876998927	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	105	0.090889352940	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	106	0.090893337254	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	107	0.090907480979	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	108	0.090909088928	Henry Cohn, 2026.
25	109	0.095541162917	Arhan Canli, 2026.
25	110	0.099492679872	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	111	0.102579822133	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	112	0.104990242023	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
25	117	0.105319726475	Henry Cohn, 2026. $375 x^{2} - 30 x - 1$
25	118	0.107204836568	Henry Cohn, 2026.
25	119	0.108423923134	Azmi C. Özgen, 2026.
25	120	0.108641454648	Christopher Smolen, 2026.
25	121	0.109261196489	Azmi C. Özgen, 2026.
25	122	0.109442179556	Azmi C. Özgen, 2026.
25	123	0.109783869010	Vadim Borisov, 2026.
25	124	0.110987308530	Christopher Smolen, 2026.
25	125	0.111106833591	Christopher Smolen, 2026.
25	126	0.111110416551	Christopher Smolen, 2026.
25	127	0.111126148142	Christopher Smolen, 2026.
25	128	0.111220371822	Antoine Jay, 2026.
25	129	0.116897996838	Antoine Jay, 2026.
25	130	0.119668023632	Antoine Jay, 2026.
25	131	0.121758124746	Vadim Borisov, 2026.
25	132	0.122921236688	Antoine Jay, 2026.
25	133	0.123990095504	Vadim Borisov, 2026.
25	134	0.126240477414	Christopher Smolen, 2026.
25	135	0.128140169712	Antoine Jay, 2026.
25	136	0.129664270518	Antoine Jay, 2026.
25	137	0.130956644451	Vadim Borisov, 2026.
25	138	0.131021467623	Azmi C. Özgen, 2026.
25	139	0.131038639078	Christopher Smolen, 2026.
25	140	0.131210772027	Vadim Borisov, 2026.
25	141	0.131432591986	Vadim Borisov, 2026.
25	142	0.131575501418	Christopher Smolen, 2026.
25	143	0.132709964091	Christopher Smolen, 2026.
25	156	0.133333333334	Henry Cohn, 2023. In Ericson and Zinoviev's notation, this code is the union of a code constructed by CW₂ from C : (26,6,8,130) and -S₂₅ by CW₂. $15 x - 2$
25	157	0.135151741337	Vadim Borisov, 2026.
25	158	0.136221254777	Antoine Jay, 2026.
25	159	0.136916037356	Antoine Jay, 2026.
25	160	0.138850733698	Antoine Jay, 2026.
25	161	0.140761009797	Antoine Jay, 2026.
25	162	0.142795032582	Christopher Smolen, 2026.
25	163	0.142818001183	Christopher Smolen, 2026.
25	164	0.142821654418	Christopher Smolen, 2026.
25	165	0.142828471296	Christopher Smolen, 2026.
25	166	0.142830686901	Christopher Smolen, 2026.
25	167	0.142833714119	Christopher Smolen, 2026.
25	168	0.142840622946	Christopher Smolen, 2026.
25	169	0.142843249322	Christopher Smolen, 2026.
25	170	0.142844494679	Christopher Smolen, 2026.
25	171	0.142846020063	Christopher Smolen, 2026.
25	172	0.142847923715	Christopher Smolen, 2026.
25	173	0.142851706692	Vadim Borisov, 2026.
25	174	0.142851801992	Christopher Smolen, 2026.
25	175	0.142852194265	Christopher Smolen, 2026.
25	176	0.142852926354	Christopher Smolen, 2026.
25	179	0.142857142858	Kevin Li, 2026. $7 x - 1$
25	182	0.142857142858	Henry Cohn and Ilmari Vahteristo, 2026. $7 x - 1$
25	183	0.145378350853	Vadim Borisov, 2026.
25	184	0.145378421351	Christopher Smolen, 2026.
25	185	0.145952338482	Christopher Smolen, 2026.
25	186	0.145954290919	Christopher Smolen, 2026.
25	187	0.146196063009	Christopher Smolen, 2026.
25	188	0.146507915996	Christopher Smolen, 2026.
25	194	0.147102976680	Henry Cohn, 2026. $87 x^{2} - 6 x - 1$
25	195	0.148455095256	Christopher Smolen, 2026.
25	204	0.151215950898	Azmi C. Özgen, 2026.
25	208	0.154168072141	Azmi C. Özgen, 2026.
25	209	0.154264661068	Christopher Smolen, 2026.
25	210	0.154558574527	Azmi C. Özgen, 2026.
25	211	0.155911569106	Christopher Smolen, 2026.
25	212	0.157260787450	Azmi C. Özgen, 2026.
25	213	0.158145438254	Azmi C. Özgen, 2026.
25	214	0.158448269799	Christopher Smolen, 2026.
25	215	0.158850106125	Vadim Borisov, 2026.
25	216	0.159795656989	Christopher Smolen, 2026.
25	217	0.159851861686	Christopher Smolen, 2026.
25	218	0.159990615801	Christopher Smolen, 2026.
25	219	0.160821562503	Christopher Smolen, 2026.
25	220	0.161315541645	Christopher Smolen, 2026.
25	221	0.161906493732	Vadim Borisov, 2026.
25	222	0.161908558925	Christopher Smolen, 2026.
25	223	0.162150058803	Vadim Borisov, 2026.
25	224	0.162612517841	Vadim Borisov, 2026.
25	225	0.162716187259	Azmi C. Özgen, 2026.
25	226	0.163498333861	Vadim Borisov, 2026.
25	227	0.164248289114	Vadim Borisov, 2026.
25	228	0.164648127585	Azmi C. Özgen, 2026.
25	229	0.165025506094	Azmi C. Özgen, 2026.
25	230	0.165315804293	Vadim Borisov, 2026.
25	231	0.165748826564	Vadim Borisov, 2026.
25	232	0.165767786763	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	233	0.165959281836	Vadim Borisov, 2026.
25	234	0.166057645607	Christopher Smolen, 2026.
25	235	0.166184999478	Vadim Borisov, 2026.
25	236	0.166260326030	Vadim Borisov, 2026.
25	237	0.166351139303	Christopher Smolen, 2026.
25	238	0.166526440589	Vadim Borisov, 2026.
25	239	0.166565658505	Vadim Borisov, 2026.
25	240	0.166597149027	Vadim Borisov, 2026.
25	241	0.166601104215	Christopher Smolen, 2026.
25	242	0.166627160975	Azmi C. Özgen, 2026.
25	287	0.166666666667	Kevin Li, 2026. $6 x - 1$
25	290	0.166666666667	Henry Cohn, 2026. $6 x - 1$
25	291	0.167578879624	Azmi C. Özgen, 2026.
25	292	0.169427584131	Vadim Borisov, 2026.
25	293	0.169994436136	Vadim Borisov, 2026.
25	294	0.172043223002	Christopher Smolen, 2026.
25	295	0.173769252893	Azmi C. Özgen, 2026.
25	296	0.175848730218	Azmi C. Özgen, 2026.
25	297	0.177323641292	Vadim Borisov, 2026.
25	298	0.178904575051	Azmi C. Özgen, 2026.
25	299	0.180411746247	Vadim Borisov, 2026.
25	321	0.181818181819	Henry Cohn, 2026. $11 x - 2$
25	322	0.182385230966	Christopher Smolen, 2026.
25	323	0.183705653610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	324	0.185379262420	Vadim Borisov, 2026.
25	325	0.186934434969	Vadim Borisov, 2026.
25	326	0.187733586630	Vadim Borisov, 2026.
25	327	0.189440712101	Vadim Borisov, 2026.
25	328	0.191111093791	Azmi C. Özgen, 2026.
25	329	0.192016457064	Azmi C. Özgen, 2026.
25	335	0.193548387097	Henry Cohn, 2026. $31 x - 6$
25	340	0.194120819402	Henry Cohn, 2026.
25	341	0.196567225284	Christopher Smolen, 2026.
25	342	0.198063664565	Azmi C. Özgen, 2026.
25	343	0.199508841430	Azmi C. Özgen, 2026.
25	344	0.199999998003	Orthogonal union of 342 points in 24 dimensions and 2 points in 1 dimension.
25	349	0.199999999698	Orthogonal union of 347 points in 24 dimensions and 2 points in 1 dimension.
25	354	0.199999999924	Orthogonal union of 352 points in 24 dimensions and 2 points in 1 dimension.
25	359	0.199999999986	Orthogonal union of 357 points in 24 dimensions and 2 points in 1 dimension.
25	559	0.2	Kevin Li, 2026. $5 x - 1$
25	562	0.2	Henry Cohn, 2026. $5 x - 1$
25	563	0.200016072171	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	564	0.201323098524	Azmi C. Özgen, 2026.
25	565	0.203187111218	Vadim Borisov, 2026.
25	566	0.206757855395	Azmi C. Özgen, 2026.
25	567	0.209530159355	Vadim Borisov, 2026.
25	568	0.211645757075	Azmi C. Özgen, 2026.
25	569	0.214201482948	Vadim Borisov, 2026.
25	570	0.216221850225	Vadim Borisov, 2026.
25	571	0.217582517083	Azmi C. Özgen, 2026.
25	572	0.219159586577	Azmi C. Özgen, 2026.
25	573	0.221147027387	Azmi C. Özgen, 2026.
25	574	0.221934145700	Azmi C. Özgen, 2026.
25	575	0.223484747454	Azmi C. Özgen, 2026.
25	576	0.224109722850	Azmi C. Özgen, 2026.
25	577	0.225436425353	Azmi C. Özgen, 2026.
25	578	0.225901804103	Vadim Borisov, 2026.
25	579	0.226660892071	Azmi C. Özgen, 2026.
25	580	0.227928938154	Azmi C. Özgen, 2026.
25	581	0.228810525521	Azmi C. Özgen, 2026.
25	582	0.229313927844	Vadim Borisov, 2026.
25	583	0.230158334598	Azmi C. Özgen, 2026.
25	584	0.231385145238	Azmi C. Özgen, 2026.
25	585	0.231763010245	Azmi C. Özgen, 2026.
25	586	0.232604700070	Azmi C. Özgen, 2026.
25	587	0.233191844115	Christopher Smolen, 2026.
25	630	0.233711730709	Kevin Li, 2026. $160 x^{2} - 16 x - 5$
25	634	0.233711730709	Henry Cohn, 2026. $160 x^{2} - 16 x - 5$
25	635	0.233770912193	Azmi C. Özgen, 2026.
25	636	0.234781503027	Vadim Borisov, 2026.
25	637	0.235106777107	Azmi C. Özgen, 2026.
25	638	0.235951140580	Azmi C. Özgen, 2026.
25	639	0.237527275868	Azmi C. Özgen, 2026.
25	640	0.237897863456	Azmi C. Özgen, 2026.
25	641	0.238818446039	Azmi C. Özgen, 2026.
25	642	0.239252144406	Vadim Borisov, 2026.
25	644	0.239323913109	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	645	0.239827660626	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	646	0.240224869325	Vadim Borisov, 2026.
25	647	0.240764390264	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	648	0.240960378322	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	649	0.241207987187	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	650	0.241598782958	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	651	0.242645633674	Vadim Borisov, 2026.
25	652	0.243241836654	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	653	0.244218874168	Vadim Borisov, 2026.
25	654	0.248988580136	Azmi C. Özgen, 2026.
25	655	0.249054039496	Azmi C. Özgen, 2026.
25	656	0.249083586675	Vadim Borisov, 2026.
25	657	0.249122422912	Azmi C. Özgen, 2026.
25	658	0.249194899621	Azmi C. Özgen, 2026.
25	659	0.249259904861	Azmi C. Özgen, 2026.
25	660	0.249302840648	Vadim Borisov, 2026.
25	661	0.249338608093	Azmi C. Özgen, 2026.
25	662	0.249354961237	Vadim Borisov, 2026.
25	663	0.249370347100	Azmi C. Özgen, 2026.
25	664	0.249498390079	Azmi C. Özgen, 2026.
25	665	0.249526764276	Azmi C. Özgen, 2026.
25	666	0.249553966032	Azmi C. Özgen, 2026.
25	667	0.249609099752	Azmi C. Özgen, 2026.
25	668	0.249637437278	Azmi C. Özgen, 2026.
25	669	0.249678605590	Azmi C. Özgen, 2026.
25	670	0.249708724133	Vadim Borisov, 2026.
25	671	0.249719061558	Azmi C. Özgen, 2026.
25	672	0.249738031449	Azmi C. Özgen, 2026.
25	673	0.249776093066	Vadim Borisov, 2026.
25	674	0.249795745248	Vadim Borisov, 2026.
25	675	0.249809824189	Vadim Borisov, 2026.
25	676	0.249814275246	Vadim Borisov, 2026.
25	677	0.249850279376	Azmi C. Özgen, 2026.
25	900	0.25	Henry Cohn, 2025. $4 x - 1$
25	915	0.25	Kevin Li, 2026. $4 x - 1$
25	920	0.25	Henry Cohn, 2026. $4 x - 1$
25	921	0.250006944988	Christopher Smolen, 2026.
25	922	0.250316877481	Azmi C. Özgen, 2026.
25	924	0.250338417403	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	925	0.250400626432	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	926	0.250428061103	Vadim Borisov, 2026.
25	927	0.250435311233	Henry Cohn, 2026.
25	928	0.251084127841	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	929	0.251425060729	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	930	0.252062161357	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	931	0.252510863004	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	932	0.253048816935	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	933	0.253449393693	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	934	0.253509571367	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	935	0.255851237231	Azmi C. Özgen, 2026.
25	936	0.256442082319	Azmi C. Özgen, 2026.
25	937	0.257004919013	Vadim Borisov, 2026.
25	938	0.257355720901	Azmi C. Özgen, 2026.
25	939	0.257785773554	Vadim Borisov, 2026.
25	940	0.258295030973	Azmi C. Özgen, 2026.
25	941	0.258906048254	Azmi C. Özgen, 2026.
25	942	0.259532302167	Azmi C. Özgen, 2026.
25	970	0.259843574332	Henry Cohn, 2026. $167 x^{2} - 28 x - 4$
25	971	0.261522913133	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	972	0.261837876088	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	973	0.262071541055	Vadim Borisov, 2026.
25	974	0.262071541997	Vadim Borisov, 2026.
25	979	0.262072716471	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	980	0.262158058934	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	981	0.263299848396	Vadim Borisov, 2026.
25	982	0.263472019369	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	983	0.263495248455	Vadim Borisov, 2026.
25	984	0.263835740339	Vadim Borisov, 2026.
25	985	0.264333484828	Azmi C. Özgen, 2026.
25	986	0.264363979434	Azmi C. Özgen, 2026.
25	988	0.264585234307	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	989	0.264867066087	Azmi C. Özgen, 2026.
25	990	0.265891405724	Azmi C. Özgen, 2026.
25	991	0.265926296363	Azmi C. Özgen, 2026.
25	992	0.266256603165	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	993	0.266386717798	Vadim Borisov, 2026.
25	994	0.266491724095	Vadim Borisov, 2026.
25	995	0.267447805705	Vadim Borisov, 2026.
25	996	0.267789437440	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	997	0.268585798824	Vadim Borisov, 2026.
25	998	0.268887273946	Vadim Borisov, 2026.
25	999	0.269374015777	Vadim Borisov, 2026.
25	1000	0.269763876387	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
25	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
26	53	0.030620650808	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $14976 x^{3} - 676 x^{2} - 26 x + 1$
26	54	0.035745276453	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	55	0.039989097282	Henry Cohn and Ilmari Vahteristo, 2026. $3073536 x^{6} - 3835776 x^{5} + 845088 x^{4} - 81288 x^{3} + 4012 x^{2} - 100 x + 1$
26	56	0.039998149037	Henry Cohn and Ilmari Vahteristo, 2026. $9024 x^{4} - 10336 x^{3} + 1374 x^{2} - 64 x + 1$
26	57	0.039999833812	Henry Cohn, 2026.
26	58	0.045359447519	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	59	0.046102308738	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	60	0.046283677257	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $4416 x^{4} + 1568 x^{3} - 376 x^{2} - 8 x + 1$
26	61	0.049129792958	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	62	0.051287179678	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	63	0.051797462004	Christopher Smolen, 2026.
26	64	0.051797462312	Christopher Smolen, 2026.
26	65	0.051797462476	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	66	0.051797462893	Henry Cohn, 2026.
26	67	0.062956992866	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	68	0.063556368253	Arhan Canli, 2026.
26	69	0.064912218612	Arhan Canli, 2026.
26	70	0.065284154370	Antoine Jay, 2026.
26	71	0.066596080786	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	72	0.068273741076	Azmi C. Özgen, 2026.
26	73	0.070914846165	Azmi C. Özgen, 2026.
26	74	0.072330351047	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	75	0.073787223453	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	76	0.074793892629	Henry Cohn, 2026.
26	77	0.076164644906	Christopher Smolen, 2026.
26	78	0.076811974001	Arhan Canli, 2026.
26	79	0.076900357844	Arhan Canli, 2026.
26	80	0.076921124041	Christopher Smolen, 2026.
26	81	0.077479700080	Azmi C. Özgen, 2026.
26	82	0.077780939193	Antoine Jay, 2026.
26	83	0.078078829779	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
26	84	0.078378290833	Henry Cohn, 2026.
26	85	0.078745852280	Azmi C. Özgen, 2026.
26	86	0.079365417880	Arhan Canli, 2026.
26	94	0.080685003328	Henry Cohn, 2026. $575 x^{2} - 34 x - 1$
26	95	0.082971677910	Azmi C. Özgen, 2026.
26	96	0.085847998571	Arhan Canli, 2026.
26	97	0.088468883242	Antoine Jay, 2026.
26	98	0.089067272832	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	99	0.089810706241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	100	0.089956641908	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	101	0.090012514903	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	102	0.090089091244	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	103	0.090587751393	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	104	0.090594197257	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	105	0.090731677093	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	106	0.090784057884	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	107	0.090800963061	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	108	0.090818338987	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	109	0.090874595241	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	110	0.090892781501	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	111	0.091344182233	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	112	0.093659256061	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	113	0.097014195010	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	114	0.099595293563	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	115	0.101947711863	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
26	120	0.103125332235	Henry Cohn, 2026. $191 x^{2} - 10 x - 1$
26	121	0.103331682647	Christopher Smolen, 2026.
26	122	0.105387312689	Henry Cohn, 2026.
26	123	0.106168303620	Antoine Jay, 2026.
26	124	0.107051332941	Christopher Smolen, 2026.
26	125	0.107634500492	Azmi C. Özgen, 2026.
26	126	0.108089982947	Christopher Smolen, 2026.
26	127	0.109062127261	Azmi C. Özgen, 2026.
26	128	0.110958151203	Christopher Smolen, 2026.
26	129	0.110972654148	Christopher Smolen, 2026.
26	130	0.110993705386	Christopher Smolen, 2026.
26	131	0.111080399791	Christopher Smolen, 2026.
26	132	0.112365906423	Antoine Jay, 2026.
26	133	0.114496656910	Vadim Borisov, 2026.
26	134	0.115169971547	Antoine Jay, 2026.
26	135	0.116265420267	Antoine Jay, 2026.
26	136	0.116444830934	Christopher Smolen, 2026.
26	137	0.117067110014	Azmi C. Özgen, 2026.
26	138	0.118373761796	Christopher Smolen, 2026.
26	139	0.122022891999	Antoine Jay, 2026.
26	140	0.125192513736	Antoine Jay, 2026.
26	141	0.127774629719	Antoine Jay, 2026.
26	142	0.130142063299	Vadim Borisov, 2026.
26	143	0.130623528896	Vadim Borisov, 2026.
26	144	0.130643040776	Vadim Borisov, 2026.
26	145	0.130953723201	Vadim Borisov, 2026.
26	146	0.130964980818	Vadim Borisov, 2026.
26	147	0.131772592840	Vadim Borisov, 2026.
26	148	0.131987140072	Vadim Borisov, 2026.
26	149	0.132301584621	Vadim Borisov, 2026.
26	150	0.132815713979	Azmi C. Özgen, 2026.
26	159	0.133333333294	Henry Cohn, 2026.
26	160	0.134514548843	Vadim Borisov, 2026.
26	161	0.135119010132	Vadim Borisov, 2026.
26	162	0.135261082852	Vadim Borisov, 2026.
26	163	0.136014979469	Azmi C. Özgen, 2026.
26	164	0.136321564726	Azmi C. Özgen, 2026.
26	165	0.136775921790	Vadim Borisov, 2026.
26	166	0.138763379714	Vadim Borisov, 2026.
26	167	0.139906466140	Vadim Borisov, 2026.
26	168	0.140983718254	Vadim Borisov, 2026.
26	169	0.142590826048	Antoine Jay, 2026.
26	170	0.142637034425	Vadim Borisov, 2026.
26	171	0.142684668267	Pavlos Moros, 2026.
26	172	0.142706839250	Christopher Smolen, 2026.
26	173	0.142717325620	Vadim Borisov, 2026.
26	174	0.142726976838	Vadim Borisov, 2026.
26	175	0.142741675152	Christopher Smolen, 2026.
26	176	0.142751071800	Christopher Smolen, 2026.
26	177	0.142758332479	Christopher Smolen, 2026.
26	178	0.142771252938	Christopher Smolen, 2026.
26	179	0.142787741922	Vadim Borisov, 2026.
26	180	0.142799571843	Christopher Smolen, 2026.
26	181	0.142811283467	Christopher Smolen, 2026.
26	182	0.142815778992	Christopher Smolen, 2026.
26	183	0.142822595612	Christopher Smolen, 2026.
26	184	0.142830822811	Christopher Smolen, 2026.
26	187	0.142857142834	Henry Cohn, 2026.
26	188	0.143137772032	Christopher Smolen, 2026.
26	189	0.144434997516	Christopher Smolen, 2026.
26	190	0.145441149933	Christopher Smolen, 2026.
26	191	0.145476334107	Vadim Borisov, 2026.
26	192	0.145628624083	Vadim Borisov, 2026.
26	193	0.145855572794	Vadim Borisov, 2026.
26	194	0.146583005437	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	195	0.146646652142	Vadim Borisov, 2026.
26	196	0.146654100956	Vadim Borisov, 2026.
26	197	0.146655049873	Azmi C. Özgen, 2026.
26	198	0.146949453500	Christopher Smolen, 2026.
26	199	0.147104902132	Christopher Smolen, 2026.
26	200	0.147110646151	Christopher Smolen, 2026.
26	201	0.147397461755	Vadim Borisov, 2026.
26	202	0.147397462626	Vadim Borisov, 2026.
26	203	0.147397612440	Vadim Borisov, 2026.
26	204	0.147397808695	Christopher Smolen, 2026.
26	207	0.149210652613	Azmi C. Özgen, 2026.
26	218	0.149321963531	Henry Cohn, 2026. $152 x^{2} - 16 x - 1$
26	219	0.150452042765	Christopher Smolen, 2026.
26	220	0.152424755789	Christopher Smolen, 2026.
26	221	0.153832021786	Christopher Smolen, 2026.
26	222	0.154181702034	Vadim Borisov, 2026.
26	223	0.154609207153	Christopher Smolen, 2026.
26	224	0.155088725532	Christopher Smolen, 2026.
26	225	0.155236180801	Christopher Smolen, 2026.
26	226	0.155237686036	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	227	0.155883484808	Christopher Smolen, 2026.
26	228	0.156647504598	Azmi C. Özgen, 2026.
26	229	0.158435841986	Christopher Smolen, 2026.
26	230	0.159324773965	Azmi C. Özgen, 2026.
26	231	0.160231894797	Azmi C. Özgen, 2026.
26	232	0.161906668953	Christopher Smolen, 2026.
26	233	0.162032589512	Azmi C. Özgen, 2026.
26	234	0.162272293730	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	235	0.162302319416	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	236	0.162693556544	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	237	0.162984704251	Azmi C. Özgen, 2026.
26	238	0.163782862567	Azmi C. Özgen, 2026.
26	239	0.163966065262	Azmi C. Özgen, 2026.
26	240	0.164507231391	Azmi C. Özgen, 2026.
26	241	0.164942560921	Vadim Borisov, 2026.
26	242	0.165092111244	Vadim Borisov, 2026.
26	243	0.165419136540	Vadim Borisov, 2026.
26	244	0.165782422203	Vadim Borisov, 2026.
26	245	0.165890947308	Azmi C. Özgen, 2026.
26	246	0.166154672470	Azmi C. Özgen, 2026.
26	247	0.166244970384	Vadim Borisov, 2026.
26	248	0.166257652471	Vadim Borisov, 2026.
26	249	0.166307495061	Vadim Borisov, 2026.
26	250	0.166369963003	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	251	0.166389623877	Vadim Borisov, 2026.
26	252	0.166451776554	Vadim Borisov, 2026.
26	253	0.166488702381	Vadim Borisov, 2026.
26	254	0.166514342066	Vadim Borisov, 2026.
26	255	0.166531514739	Christopher Smolen, 2026.
26	256	0.166561527311	Christopher Smolen, 2026.
26	257	0.166572653461	Christopher Smolen, 2026.
26	258	0.166604840185	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	297	0.166666666667	Kevin Li, 2026. $6 x - 1$
26	298	0.167286219797	Azmi C. Özgen, 2026.
26	299	0.168415502303	Azmi C. Özgen, 2026.
26	300	0.169882803922	Vadim Borisov, 2026.
26	301	0.170947894707	Vadim Borisov, 2026.
26	302	0.172021093115	Vadim Borisov, 2026.
26	303	0.173587716533	Azmi C. Özgen, 2026.
26	304	0.175344018097	Azmi C. Özgen, 2026.
26	305	0.176258428955	Azmi C. Özgen, 2026.
26	306	0.176911078628	Christopher Smolen, 2026.
26	307	0.179384837183	Vadim Borisov, 2026.
26	308	0.180025236707	Azmi C. Özgen, 2026.
26	330	0.181818181819	Henry Cohn, 2026. $11 x - 2$
26	331	0.182011894343	Azmi C. Özgen, 2026.
26	332	0.182499589037	Azmi C. Özgen, 2026.
26	333	0.183962788450	Azmi C. Özgen, 2026.
26	334	0.184951431812	Azmi C. Özgen, 2026.
26	335	0.185609752723	Vadim Borisov, 2026.
26	336	0.185976387566	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	337	0.187775224954	Azmi C. Özgen, 2026.
26	338	0.188611318571	Vadim Borisov, 2026.
26	339	0.189940749156	Vadim Borisov, 2026.
26	340	0.190248638004	Azmi C. Özgen, 2026.
26	341	0.191993080448	Azmi C. Özgen, 2026.
26	342	0.192419090429	Azmi C. Özgen, 2026.
26	343	0.193040909588	Azmi C. Özgen, 2026.
26	344	0.194275551682	Azmi C. Özgen, 2026.
26	345	0.195111498511	Azmi C. Özgen, 2026.
26	346	0.196255138341	Azmi C. Özgen, 2026.
26	347	0.196378360194	Azmi C. Özgen, 2026.
26	348	0.196470140971	Vadim Borisov, 2026.
26	349	0.196624798777	Azmi C. Özgen, 2026.
26	350	0.196836506071	Azmi C. Özgen, 2026.
26	351	0.196941831097	Azmi C. Özgen, 2026.
26	352	0.196962964486	Azmi C. Özgen, 2026.
26	353	0.197130458777	Azmi C. Özgen, 2026.
26	354	0.197238215120	Azmi C. Özgen, 2026.
26	355	0.197318050400	Azmi C. Özgen, 2026.
26	356	0.197386101955	Azmi C. Özgen, 2026.
26	357	0.197672706856	Azmi C. Özgen, 2026.
26	358	0.197763451075	Azmi C. Özgen, 2026.
26	359	0.197833343197	Azmi C. Özgen, 2026.
26	360	0.198036620692	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	361	0.198054761668	Azmi C. Özgen, 2026.
26	362	0.198107034786	Azmi C. Özgen, 2026.
26	363	0.198183142033	Azmi C. Özgen, 2026.
26	364	0.198251489160	Azmi C. Özgen, 2026.
26	365	0.198365598023	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	366	0.198408487145	Vadim Borisov, 2026.
26	367	0.198410163921	Vadim Borisov, 2026.
26	368	0.198449971038	Christopher Smolen, 2026.
26	369	0.198666900655	Azmi C. Özgen, 2026.
26	370	0.198779367728	Azmi C. Özgen, 2026.
26	371	0.198923100315	Azmi C. Özgen, 2026.
26	372	0.199002828925	Azmi C. Özgen, 2026.
26	373	0.199027141227	Azmi C. Özgen, 2026.
26	374	0.199100550191	Azmi C. Özgen, 2026.
26	375	0.199119996716	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	376	0.199220206741	Hamzah Asyrani Sulaiman, 2026.
26	377	0.199277505068	Azmi C. Özgen, 2026.
26	378	0.199291572086	Vadim Borisov, 2026.
26	379	0.199291644706	Vadim Borisov, 2026.
26	380	0.199291739433	Vadim Borisov, 2026.
26	381	0.199291764268	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	382	0.199468456506	Vadim Borisov, 2026.
26	383	0.199498395092	Azmi C. Özgen, 2026.
26	384	0.199519246991	Azmi C. Özgen, 2026.
26	385	0.199567500344	Vadim Borisov, 2026.
26	386	0.199605179907	Azmi C. Özgen, 2026.
26	387	0.199645045707	Azmi C. Özgen, 2026.
26	388	0.199669363463	Vadim Borisov, 2026.
26	389	0.199699173959	Azmi C. Özgen, 2026.
26	390	0.199743950340	Vadim Borisov, 2026.
26	391	0.199753976561	Vadim Borisov, 2026.
26	392	0.199762481407	Vadim Borisov, 2026.
26	393	0.199772486922	Azmi C. Özgen, 2026.
26	394	0.199798897797	Azmi C. Özgen, 2026.
26	395	0.199800747463	Azmi C. Özgen, 2026.
26	396	0.199834823805	Azmi C. Özgen, 2026.
26	397	0.199863731571	Azmi C. Özgen, 2026.
26	398	0.199874276945	Azmi C. Özgen, 2026.
26	399	0.199878414712	Vadim Borisov, 2026.
26	400	0.199878466785	Vadim Borisov, 2026.
26	401	0.199884076927	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	402	0.199887229306	Christopher Smolen, 2026.
26	403	0.199924568743	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	404	0.199937576768	Christopher Smolen, 2026.
26	405	0.199956987334	Vadim Borisov, 2026.
26	406	0.199958508219	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	407	0.199960595244	Christopher Smolen, 2026.
26	571	0.2	Henry Cohn, 2026. $5 x - 1$
26	572	0.200446447522	Azmi C. Özgen, 2026.
26	573	0.200818231583	Azmi C. Özgen, 2026.
26	574	0.202132386740	Azmi C. Özgen, 2026.
26	575	0.203797882374	Azmi C. Özgen, 2026.
26	576	0.205231167054	Azmi C. Özgen, 2026.
26	577	0.207865588090	Azmi C. Özgen, 2026.
26	578	0.208888496527	Vadim Borisov, 2026.
26	579	0.209082486370	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	580	0.211844028581	Azmi C. Özgen, 2026.
26	581	0.212551136728	Azmi C. Özgen, 2026.
26	582	0.213681418759	Azmi C. Özgen, 2026.
26	583	0.214446486256	Azmi C. Özgen, 2026.
26	584	0.217158642608	Vadim Borisov, 2026.
26	585	0.218078714483	Azmi C. Özgen, 2026.
26	586	0.218696323273	Azmi C. Özgen, 2026.
26	587	0.219783852271	Azmi C. Özgen, 2026.
26	588	0.220986042242	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	589	0.221287360828	Azmi C. Özgen, 2026.
26	590	0.221961466093	Azmi C. Özgen, 2026.
26	591	0.223037159176	Azmi C. Özgen, 2026.
26	592	0.223770397691	Azmi C. Özgen, 2026.
26	593	0.224533762573	Vadim Borisov, 2026.
26	594	0.225092176279	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	595	0.225311637543	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	596	0.225600595108	Azmi C. Özgen, 2026.
26	597	0.226287405847	Azmi C. Özgen, 2026.
26	598	0.226820201950	Vadim Borisov, 2026.
26	599	0.227327967477	Azmi C. Özgen, 2026.
26	600	0.227835236964	Vadim Borisov, 2026.
26	601	0.228664153617	Vadim Borisov, 2026.
26	633	0.233711730709	Kevin Li, 2026. $160 x^{2} - 16 x - 5$
26	649	0.233711730709	Henry Cohn, 2026. $160 x^{2} - 16 x - 5$
26	650	0.233886487983	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
26	651	0.234176858030	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	652	0.234436494830	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	653	0.235079458635	Azmi C. Özgen, 2026.
26	654	0.235186797244	Azmi C. Özgen, 2026.
26	655	0.235471824619	Azmi C. Özgen, 2026.
26	656	0.236705136527	Azmi C. Özgen, 2026.
26	657	0.237309249320	Vadim Borisov, 2026.
26	658	0.237821944886	Azmi C. Özgen, 2026.
26	659	0.238390780498	Vadim Borisov, 2026.
26	660	0.238817840158	Vadim Borisov, 2026.
26	661	0.239185896831	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	662	0.239589560746	Vadim Borisov, 2026.
26	663	0.239733391919	Vadim Borisov, 2026.
26	664	0.240245350573	Vadim Borisov, 2026.
26	665	0.240345998729	Azmi C. Özgen, 2026.
26	666	0.241212963984	Azmi C. Özgen, 2026.
26	667	0.241614388758	Azmi C. Özgen, 2026.
26	668	0.241962691129	Azmi C. Özgen, 2026.
26	669	0.242551473289	Vadim Borisov, 2026.
26	670	0.243003181612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	671	0.243429985084	Vadim Borisov, 2026.
26	672	0.247866710347	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	673	0.247985289487	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	674	0.248065175293	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	675	0.248132855894	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	676	0.248235117922	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	677	0.248301280419	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	678	0.248305259612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	679	0.248389033911	Vadim Borisov, 2026.
26	680	0.248391895520	Vadim Borisov, 2026.
26	681	0.248573451555	Azmi C. Özgen, 2026.
26	682	0.248644775053	Vadim Borisov, 2026.
26	683	0.248736672316	Vadim Borisov, 2026.
26	684	0.248747602729	Azmi C. Özgen, 2026.
26	685	0.248782665964	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	686	0.248788153390	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	687	0.248789443183	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	688	0.248843527666	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	689	0.248885400993	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	690	0.248932295776	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	691	0.248991131932	Vadim Borisov, 2026.
26	692	0.249034507877	Vadim Borisov, 2026.
26	693	0.249038867483	Vadim Borisov, 2026.
26	694	0.249069559979	Vadim Borisov, 2026.
26	695	0.249097907534	Vadim Borisov, 2026.
26	696	0.249112841999	Azmi C. Özgen, 2026.
26	697	0.249157509714	Azmi C. Özgen, 2026.
26	698	0.249196578825	Azmi C. Özgen, 2026.
26	699	0.249257190594	Vadim Borisov, 2026.
26	700	0.249259583330	Azmi C. Özgen, 2026.
26	701	0.249342546041	Azmi C. Özgen, 2026.
26	702	0.249375944803	Azmi C. Özgen, 2026.
26	703	0.249407433136	Azmi C. Özgen, 2026.
26	704	0.249422964492	Azmi C. Özgen, 2026.
26	705	0.249460801585	Azmi C. Özgen, 2026.
26	706	0.249478785089	Azmi C. Özgen, 2026.
26	707	0.249542723358	Azmi C. Özgen, 2026.
26	708	0.249562977890	Azmi C. Özgen, 2026.
26	709	0.249585052873	Azmi C. Özgen, 2026.
26	710	0.249606753765	Azmi C. Özgen, 2026.
26	711	0.249635946419	Azmi C. Özgen, 2026.
26	712	0.249649067030	Azmi C. Özgen, 2026.
26	713	0.249661229236	Vadim Borisov, 2026.
26	714	0.249664796546	Azmi C. Özgen, 2026.
26	715	0.249699947058	Azmi C. Özgen, 2026.
26	716	0.249721659830	Azmi C. Özgen, 2026.
26	717	0.249736863985	Azmi C. Özgen, 2026.
26	718	0.249742898198	Azmi C. Özgen, 2026.
26	719	0.249763533383	Azmi C. Özgen, 2026.
26	720	0.249773886429	Azmi C. Özgen, 2026.
26	721	0.249779315544	Azmi C. Özgen, 2026.
26	722	0.249802153604	Azmi C. Özgen, 2026.
26	723	0.249810752636	Azmi C. Özgen, 2026.
26	939	0.25	Kevin Li, 2026. $4 x - 1$
26	940	0.250137506384	Vadim Borisov, 2026.
26	941	0.250140138838	Vadim Borisov, 2026.
26	942	0.250143017033	Vadim Borisov, 2026.
26	943	0.250143072939	Vadim Borisov, 2026.
26	944	0.250833613660	Vadim Borisov, 2026.
26	945	0.250986354585	Azmi C. Özgen, 2026.
26	946	0.251642014227	Vadim Borisov, 2026.
26	947	0.251980744464	Azmi C. Özgen, 2026.
26	949	0.252208937671	Vadim Borisov, 2026.
26	950	0.252244460997	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	951	0.252394457918	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	952	0.252635779084	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	953	0.252758769148	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	954	0.254630281407	Azmi C. Özgen, 2026.
26	956	0.254767778138	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	957	0.254949188772	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	958	0.255115663849	Henry Cohn, 2026.
26	959	0.255296501616	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	960	0.255875912616	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	961	0.255944175659	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	962	0.256036676918	Christopher Smolen, 2026.
26	963	0.257319750506	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	964	0.258263045235	Azmi C. Özgen, 2026.
26	965	0.258365741423	Vadim Borisov, 2026.
26	966	0.258649645643	Azmi C. Özgen, 2026.
26	967	0.259054001306	Vadim Borisov, 2026.
26	968	0.259288845391	Azmi C. Özgen, 2026.
26	969	0.259742618171	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	970	0.259745382068	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	971	0.259767392733	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	972	0.259779753126	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	973	0.259786509356	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	974	0.259795997434	Vadim Borisov, 2026.
26	975	0.259802931493	Vadim Borisov, 2026.
26	976	0.259813700354	Vadim Borisov, 2026.
26	977	0.259839837472	Vadim Borisov, 2026.
26	978	0.259872343398	Vadim Borisov, 2026.
26	979	0.261868240813	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	980	0.261875451541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	981	0.261883901095	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	982	0.261889073893	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
26	983	0.261891204172	Vadim Borisov, 2026.
26	984	0.261893597623	Vadim Borisov, 2026.
26	985	0.261897551162	Vadim Borisov, 2026.
26	986	0.261900239289	Vadim Borisov, 2026.
26	987	0.261902797366	Vadim Borisov, 2026.
26	988	0.261904486067	Vadim Borisov, 2026.
26	989	0.261906909840	Vadim Borisov, 2026.
26	990	0.261914596574	Vadim Borisov, 2026.
26	1024	0.263299316186	Henry Cohn, 2026. $60 x^{2} - 12 x - 1$
27	55	0.029589200879	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $16875 x^{3} - 729 x^{2} - 27 x + 1$
27	56	0.034509985004	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	57	0.039736901877	Henry Cohn and Ilmari Vahteristo, 2026. $21 x^{2} - 26 x + 1$
27	58	0.039896802692	Henry Cohn, 2026.
27	59	0.039966730086	Arhan Canli, 2026.
27	60	0.044785718794	Henry Cohn, 2026.
27	61	0.045201033609	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	62	0.046029514076	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	63	0.047652441689	Henry Cohn, 2026.
27	64	0.050067815256	Henry Cohn, 2026.
27	65	0.051788044767	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	66	0.051789238416	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	67	0.051790451534	Christopher Smolen, 2026.
27	68	0.051797462893	Orthogonal union of 66 points in 26 dimensions and 2 points in 1 dimension.
27	69	0.060739236420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	70	0.062920317502	Arhan Canli, 2026.
27	71	0.063925985794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	72	0.064129336813	Arhan Canli, 2026.
27	73	0.065313966371	Vadim Borisov, 2026.
27	74	0.066292883716	Arhan Canli, 2026.
27	75	0.067691814168	Arhan Canli, 2026.
27	76	0.069936420540	Azmi C. Özgen, 2026.
27	77	0.072325076926	Arhan Canli, 2026.
27	78	0.073947774097	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	79	0.075140154489	Azmi C. Özgen, 2026.
27	80	0.075856049710	Arhan Canli, 2026.
27	81	0.076553087415	Christopher Smolen, 2026.
27	82	0.076766679649	Arhan Canli, 2026.
27	83	0.076786159334	Arhan Canli, 2026.
27	84	0.076814431150	Arhan Canli, 2026.
27	85	0.077360412549	Vadim Borisov, 2026.
27	86	0.077581191382	Azmi C. Özgen, 2026.
27	87	0.078052817711	Azmi C. Özgen, 2026.
27	88	0.078607188885	Azmi C. Özgen, 2026.
27	89	0.079013113833	Vadim Borisov, 2026.
27	90	0.079464011841	Henry Cohn, 2026.
27	91	0.079742562003	Arhan Canli, 2026.
27	92	0.080374198772	Azmi C. Özgen, 2026.
27	93	0.080603514329	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	94	0.080669972109	Christopher Smolen, 2026.
27	95	0.080684131783	Christopher Smolen, 2026.
27	98	0.080685003328	Henry Cohn, 2026. $575 x^{2} - 34 x - 1$
27	99	0.084112452017	Christopher Smolen, 2026.
27	100	0.086219405988	Christopher Smolen, 2026.
27	101	0.088058365505	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	102	0.088748226794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	103	0.088777315935	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	104	0.089035400332	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	105	0.089444154229	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	106	0.089638585526	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	107	0.089640909289	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	108	0.089811748515	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	109	0.090395199106	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	110	0.090552603681	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	111	0.090617926233	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	112	0.090741401878	Henry Cohn, 2026.
27	113	0.090777212437	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	114	0.090903863888	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	115	0.092274494633	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	116	0.094743840358	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	117	0.097019128086	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	118	0.099760980934	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	119	0.101957515806	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	120	0.102640923748	Christopher Smolen, 2026.
27	121	0.102992246528	Christopher Smolen, 2026.
27	122	0.103076746230	Christopher Smolen, 2026.
27	125	0.103125332235	Henry Cohn, 2026. $191 x^{2} - 10 x - 1$
27	126	0.104298235960	Arhan Canli, 2026.
27	127	0.104909208197	Christopher Smolen, 2026.
27	128	0.105445244718	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	129	0.106436976434	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	130	0.107449669907	Christopher Smolen, 2026.
27	131	0.108074871224	Christopher Smolen, 2026.
27	132	0.109177240697	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
27	133	0.110537517482	Christopher Smolen, 2026.
27	134	0.110994083420	Christopher Smolen, 2026.
27	135	0.111000410688	Christopher Smolen, 2026.
27	136	0.111380921475	Vadim Borisov, 2026.
27	137	0.112837132464	Azmi C. Özgen, 2026.
27	138	0.114218687677	Vadim Borisov, 2026.
27	139	0.114819729936	Vadim Borisov, 2026.
27	140	0.115205045571	Vadim Borisov, 2026.
27	141	0.116264806911	Vadim Borisov, 2026.
27	142	0.117401271390	Vadim Borisov, 2026.
27	143	0.119084394809	Vadim Borisov, 2026.
27	144	0.120835686954	Christopher Smolen, 2026.
27	145	0.123117112226	Vadim Borisov, 2026.
27	146	0.125352760963	Vadim Borisov, 2026.
27	147	0.127226475354	Vadim Borisov, 2026.
27	148	0.128555481017	Azmi C. Özgen, 2026.
27	149	0.129942622575	Vadim Borisov, 2026.
27	150	0.131226193004	Vadim Borisov, 2026.
27	151	0.131309464136	Vadim Borisov, 2026.
27	152	0.131534366009	Vadim Borisov, 2026.
27	153	0.131732420335	Vadim Borisov, 2026.
27	154	0.131835717356	Vadim Borisov, 2026.
27	155	0.131843499649	Vadim Borisov, 2026.
27	156	0.132190647056	Vadim Borisov, 2026.
27	157	0.132438686070	Vadim Borisov, 2026.
27	158	0.132498634996	Christopher Smolen, 2026.
27	159	0.132747464422	Christopher Smolen, 2026.
27	160	0.133264282545	Christopher Smolen, 2026.
27	161	0.133298174888	Christopher Smolen, 2026.
27	162	0.133314267888	Christopher Smolen, 2026.
27	163	0.133326848766	Vadim Borisov, 2026.
27	164	0.133448514227	Vadim Borisov, 2026.
27	165	0.134770532153	Christopher Smolen, 2026.
27	166	0.134795112262	Vadim Borisov, 2026.
27	167	0.134891781018	Vadim Borisov, 2026.
27	168	0.135115136581	Vadim Borisov, 2026.
27	169	0.135200328552	Vadim Borisov, 2026.
27	170	0.135761409868	Vadim Borisov, 2026.
27	171	0.136197085699	Christopher Smolen, 2026.
27	172	0.137270389939	Vadim Borisov, 2026.
27	173	0.138865770305	Azmi C. Özgen, 2026.
27	174	0.139035628822	Henry Cohn, 2026.
27	175	0.140936148404	Vadim Borisov, 2026.
27	176	0.142236717229	Vadim Borisov, 2026.
27	177	0.142270435220	Vadim Borisov, 2026.
27	178	0.142341189181	Vadim Borisov, 2026.
27	179	0.142387625775	Vadim Borisov, 2026.
27	180	0.142480708023	Christopher Smolen, 2026.
27	181	0.142504802115	Vadim Borisov, 2026.
27	182	0.142525266072	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	183	0.142533183871	Vadim Borisov, 2026.
27	184	0.142536818368	Vadim Borisov, 2026.
27	185	0.142544610217	Christopher Smolen, 2026.
27	186	0.142608389491	Vadim Borisov, 2026.
27	187	0.142636013756	Vadim Borisov, 2026.
27	188	0.142681906881	Christopher Smolen, 2026.
27	189	0.142745007362	Christopher Smolen, 2026.
27	190	0.142749448155	Christopher Smolen, 2026.
27	191	0.142798438598	Vadim Borisov, 2026.
27	195	0.142857142846	Henry Cohn, 2026.
27	196	0.142889658744	Azmi C. Özgen, 2026.
27	197	0.145248199564	Vadim Borisov, 2026.
27	198	0.145314877911	Vadim Borisov, 2026.
27	199	0.145418614626	Vadim Borisov, 2026.
27	200	0.145633970755	Vadim Borisov, 2026.
27	201	0.146045660042	Vadim Borisov, 2026.
27	202	0.146156559451	Vadim Borisov, 2026.
27	203	0.146443215404	Vadim Borisov, 2026.
27	204	0.146749414665	Christopher Smolen, 2026.
27	205	0.146838831324	Vadim Borisov, 2026.
27	206	0.146919233894	Christopher Smolen, 2026.
27	208	0.147138925543	Vadim Borisov, 2026.
27	209	0.147139041111	Christopher Smolen, 2026.
27	210	0.147377745258	Christopher Smolen, 2026.
27	211	0.147377894607	Christopher Smolen, 2026.
27	212	0.147451487596	Christopher Smolen, 2026.
27	215	0.147651517511	Henry Cohn, 2026. $1655 x^{2} - 136 x - 16$
27	216	0.147715266256	Vadim Borisov, 2026.
27	217	0.147954630668	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	218	0.148095404799	Vadim Borisov, 2026.
27	219	0.149263707174	Christopher Smolen, 2026.
27	220	0.149297195239	Christopher Smolen, 2026.
27	229	0.149321963531	Henry Cohn, 2026. $152 x^{2} - 16 x - 1$
27	230	0.149527091429	Christopher Smolen, 2026.
27	231	0.150269997256	Vadim Borisov, 2026.
27	232	0.150270166359	Vadim Borisov, 2026.
27	233	0.150279534416	Vadim Borisov, 2026.
27	234	0.150279547060	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	235	0.152350883900	Azmi C. Özgen, 2026.
27	236	0.153592690587	Azmi C. Özgen, 2026.
27	237	0.153783615867	Vadim Borisov, 2026.
27	238	0.154753181423	Christopher Smolen, 2026.
27	239	0.157700400121	Azmi C. Özgen, 2026.
27	240	0.158830979234	Azmi C. Özgen, 2026.
27	241	0.159645475191	Azmi C. Özgen, 2026.
27	242	0.160373266080	Azmi C. Özgen, 2026.
27	243	0.161433046867	Christopher Smolen, 2026.
27	245	0.161909649268	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	246	0.162399949068	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	247	0.162501373323	Vadim Borisov, 2026.
27	248	0.162583296074	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	249	0.162594500376	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	250	0.162664008617	Azmi C. Özgen, 2026.
27	251	0.163591164319	Vadim Borisov, 2026.
27	252	0.163743343084	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	253	0.163860021954	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	254	0.164010760650	Vadim Borisov, 2026.
27	255	0.164440242504	Christopher Smolen, 2026.
27	256	0.164601947455	Christopher Smolen, 2026.
27	257	0.164737814450	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	258	0.164981727841	Azmi C. Özgen, 2026.
27	259	0.165073971544	Christopher Smolen, 2026.
27	260	0.165192097022	Vadim Borisov, 2026.
27	261	0.165323501240	Christopher Smolen, 2026.
27	262	0.165458217422	Vadim Borisov, 2026.
27	263	0.165542075630	Christopher Smolen, 2026.
27	264	0.165674288671	Vadim Borisov, 2026.
27	265	0.165747915277	Christopher Smolen, 2026.
27	266	0.165808168189	Christopher Smolen, 2026.
27	267	0.165876839066	Christopher Smolen, 2026.
27	268	0.165935004093	Vadim Borisov, 2026.
27	269	0.166015595600	Vadim Borisov, 2026.
27	270	0.166124931818	Christopher Smolen, 2026.
27	271	0.166241186375	Christopher Smolen, 2026.
27	272	0.166284739031	Vadim Borisov, 2026.
27	273	0.166307881242	Vadim Borisov, 2026.
27	274	0.166340565879	Vadim Borisov, 2026.
27	275	0.166346581548	Vadim Borisov, 2026.
27	276	0.166379479125	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	277	0.166474895692	Vadim Borisov, 2026.
27	278	0.166483209347	Vadim Borisov, 2026.
27	279	0.166494764115	Vadim Borisov, 2026.
27	280	0.166526026013	Vadim Borisov, 2026.
27	281	0.166568073436	Christopher Smolen, 2026.
27	305	0.166666666667	Kevin Li, 2026. $6 x - 1$
27	306	0.166737827825	Azmi C. Özgen, 2026.
27	307	0.167235530306	Azmi C. Özgen, 2026.
27	308	0.168001365842	Azmi C. Özgen, 2026.
27	309	0.169297209191	Vadim Borisov, 2026.
27	310	0.169868042463	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	311	0.171422426659	Vadim Borisov, 2026.
27	312	0.172731758651	Vadim Borisov, 2026.
27	313	0.173614132690	Azmi C. Özgen, 2026.
27	314	0.174631083513	Azmi C. Özgen, 2026.
27	315	0.175873170490	Azmi C. Özgen, 2026.
27	316	0.177267227356	Azmi C. Özgen, 2026.
27	317	0.177639322535	Vadim Borisov, 2026.
27	318	0.178859956499	Azmi C. Özgen, 2026.
27	319	0.179292325991	Vadim Borisov, 2026.
27	320	0.180405021116	Vadim Borisov, 2026.
27	321	0.180806283521	Vadim Borisov, 2026.
27	322	0.180808872225	Vadim Borisov, 2026.
27	323	0.181010601007	Vadim Borisov, 2026.
27	324	0.181171929129	Vadim Borisov, 2026.
27	325	0.181292141645	Vadim Borisov, 2026.
27	326	0.181377086072	Vadim Borisov, 2026.
27	327	0.181437542682	Vadim Borisov, 2026.
27	328	0.181443525490	Azmi C. Özgen, 2026.
27	329	0.181600739808	Vadim Borisov, 2026.
27	330	0.181645263714	Vadim Borisov, 2026.
27	331	0.181665097891	Vadim Borisov, 2026.
27	332	0.181690672587	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	333	0.181737996154	Vadim Borisov, 2026.
27	334	0.181757545979	Vadim Borisov, 2026.
27	335	0.181779644543	Vadim Borisov, 2026.
27	336	0.181782165459	Vadim Borisov, 2026.
27	337	0.181809603126	Vadim Borisov, 2026.
27	338	0.181822009683	Vadim Borisov, 2026.
27	339	0.181828806717	Christopher Smolen, 2026.
27	340	0.182142283980	Vadim Borisov, 2026.
27	341	0.182652913245	Azmi C. Özgen, 2026.
27	342	0.183375790877	Azmi C. Özgen, 2026.
27	343	0.183964142828	Azmi C. Özgen, 2026.
27	344	0.184441266419	Azmi C. Özgen, 2026.
27	345	0.185413682483	Azmi C. Özgen, 2026.
27	346	0.186190828713	Azmi C. Özgen, 2026.
27	347	0.186513535747	Azmi C. Özgen, 2026.
27	348	0.187153578078	Azmi C. Özgen, 2026.
27	349	0.188014992822	Azmi C. Özgen, 2026.
27	350	0.188471974679	Azmi C. Özgen, 2026.
27	351	0.189168676915	Vadim Borisov, 2026.
27	352	0.189964569595	Christopher Smolen, 2026.
27	353	0.190790002651	Azmi C. Özgen, 2026.
27	354	0.191677887470	Azmi C. Özgen, 2026.
27	355	0.192475401306	Azmi C. Özgen, 2026.
27	356	0.193114584865	Azmi C. Özgen, 2026.
27	357	0.193769154166	Azmi C. Özgen, 2026.
27	358	0.193810836134	Azmi C. Özgen, 2026.
27	359	0.193968763059	Azmi C. Özgen, 2026.
27	360	0.194431094140	Azmi C. Özgen, 2026.
27	361	0.195427850368	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	362	0.195709562385	Azmi C. Özgen, 2026.
27	363	0.195849591115	Azmi C. Özgen, 2026.
27	364	0.195996925879	Vadim Borisov, 2026.
27	365	0.196010616170	Azmi C. Özgen, 2026.
27	366	0.196095430777	Vadim Borisov, 2026.
27	367	0.196095589086	Vadim Borisov, 2026.
27	368	0.196095600667	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	369	0.196433241078	Azmi C. Özgen, 2026.
27	370	0.196506535811	Vadim Borisov, 2026.
27	371	0.196659101262	Azmi C. Özgen, 2026.
27	372	0.196702004818	Azmi C. Özgen, 2026.
27	373	0.196823837970	Azmi C. Özgen, 2026.
27	374	0.196942999286	Azmi C. Özgen, 2026.
27	375	0.197050069465	Azmi C. Özgen, 2026.
27	376	0.197125768065	Azmi C. Özgen, 2026.
27	377	0.197315911157	Azmi C. Özgen, 2026.
27	378	0.197436145100	Azmi C. Özgen, 2026.
27	379	0.197550234655	Vadim Borisov, 2026.
27	380	0.197638412440	Azmi C. Özgen, 2026.
27	381	0.197849924115	Azmi C. Özgen, 2026.
27	382	0.197878932232	Azmi C. Özgen, 2026.
27	383	0.198003614971	Vadim Borisov, 2026.
27	384	0.198016292319	Azmi C. Özgen, 2026.
27	385	0.198135895187	Vadim Borisov, 2026.
27	386	0.198273380100	Azmi C. Özgen, 2026.
27	387	0.198304974564	Azmi C. Özgen, 2026.
27	388	0.198430177717	Azmi C. Özgen, 2026.
27	389	0.198517425661	Azmi C. Özgen, 2026.
27	390	0.198581359821	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	391	0.198706115693	Azmi C. Özgen, 2026.
27	392	0.198734371815	Azmi C. Özgen, 2026.
27	393	0.198800212949	Pavlos Moros, 2026.
27	394	0.198885689043	Vadim Borisov, 2026.
27	395	0.198980764165	Azmi C. Özgen, 2026.
27	396	0.199004971910	Vadim Borisov, 2026.
27	397	0.199017307804	Vadim Borisov, 2026.
27	398	0.199029389007	Azmi C. Özgen, 2026.
27	399	0.199086446245	Azmi C. Özgen, 2026.
27	400	0.199177068218	Vadim Borisov, 2026.
27	401	0.199186332517	Azmi C. Özgen, 2026.
27	402	0.199212413123	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	403	0.199212616033	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	404	0.199213508491	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	405	0.199333114125	Vadim Borisov, 2026.
27	406	0.199333115676	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	407	0.199400789813	Azmi C. Özgen, 2026.
27	408	0.199467170128	Azmi C. Özgen, 2026.
27	409	0.199513622976	Azmi C. Özgen, 2026.
27	410	0.199523434579	Azmi C. Özgen, 2026.
27	411	0.199541727077	Azmi C. Özgen, 2026.
27	412	0.199602289048	Azmi C. Özgen, 2026.
27	413	0.199603719054	Azmi C. Özgen, 2026.
27	414	0.199619770907	Azmi C. Özgen, 2026.
27	415	0.199640015695	Azmi C. Özgen, 2026.
27	416	0.199668168628	Vadim Borisov, 2026.
27	417	0.199668170398	Christopher Smolen, 2026.
27	418	0.199740733935	Vadim Borisov, 2026.
27	419	0.199744072428	Azmi C. Özgen, 2026.
27	420	0.199781493337	Azmi C. Özgen, 2026.
27	421	0.199816588359	Azmi C. Özgen, 2026.
27	422	0.199818077330	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	423	0.199824091777	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	424	0.199829151503	Vadim Borisov, 2026.
27	425	0.199837549910	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	426	0.199841894513	Vadim Borisov, 2026.
27	427	0.199845427103	Vadim Borisov, 2026.
27	428	0.199850501121	Christopher Smolen, 2026.
27	429	0.199925132935	Vadim Borisov, 2026.
27	430	0.199928958333	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	570	0.2	Kevin Li, 2026. $5 x - 1$
27	580	0.2	Henry Cohn, 2026. $5 x - 1$
27	581	0.200124129663	Azmi C. Özgen, 2026.
27	582	0.200659300140	Vadim Borisov, 2026.
27	583	0.200926831450	Vadim Borisov, 2026.
27	584	0.202068866938	Vadim Borisov, 2026.
27	585	0.202421119398	Azmi C. Özgen, 2026.
27	586	0.203475102079	Azmi C. Özgen, 2026.
27	587	0.204308228137	Azmi C. Özgen, 2026.
27	588	0.204787550590	Azmi C. Özgen, 2026.
27	589	0.205476042671	Azmi C. Özgen, 2026.
27	590	0.208015380416	Azmi C. Özgen, 2026.
27	591	0.208991195865	Azmi C. Özgen, 2026.
27	592	0.209970308009	Azmi C. Özgen, 2026.
27	593	0.211319157217	Azmi C. Özgen, 2026.
27	594	0.211330406876	Azmi C. Özgen, 2026.
27	596	0.212151286139	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	597	0.212825609503	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	598	0.213111120204	Christopher Smolen, 2026.
27	599	0.214513098540	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	600	0.214644822456	Henry Cohn, 2026.
27	601	0.217218906811	Azmi C. Özgen, 2026.
27	603	0.217961806178	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	604	0.218462393664	Vadim Borisov, 2026.
27	605	0.219130142680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	606	0.219131527991	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	607	0.219180174774	Christopher Smolen, 2026.
27	608	0.220702581302	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	609	0.220968646376	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	610	0.221075145964	Christopher Smolen, 2026.
27	611	0.225359034563	Vadim Borisov, 2026.
27	612	0.225897436745	Vadim Borisov, 2026.
27	639	0.233711730709	Kevin Li, 2026. $160 x^{2} - 16 x - 5$
27	666	0.233711730709	Henry Cohn, 2026. $160 x^{2} - 16 x - 5$
27	667	0.233729528325	Vadim Borisov, 2026.
27	668	0.233912546512	Azmi C. Özgen, 2026.
27	669	0.234020924902	Vadim Borisov, 2026.
27	670	0.234021038394	Azmi C. Özgen, 2026.
27	671	0.234148327840	Azmi C. Özgen, 2026.
27	672	0.234382684143	Vadim Borisov, 2026.
27	673	0.234786603643	Azmi C. Özgen, 2026.
27	674	0.235121596471	Azmi C. Özgen, 2026.
27	675	0.235551191151	Vadim Borisov, 2026.
27	676	0.235649707299	Azmi C. Özgen, 2026.
27	677	0.236189484899	Azmi C. Özgen, 2026.
27	678	0.236656320027	Vadim Borisov, 2026.
27	679	0.237127934837	Vadim Borisov, 2026.
27	680	0.237335190342	Vadim Borisov, 2026.
27	681	0.238049838849	Vadim Borisov, 2026.
27	682	0.239476920526	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	683	0.239477095650	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	684	0.240004483231	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	685	0.240478502235	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	686	0.240922586738	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	687	0.241846177306	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	688	0.241887854348	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	689	0.242454732776	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	690	0.242932030237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	691	0.243294945259	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	692	0.243531139410	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	693	0.243874968948	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	694	0.244429471725	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	695	0.245127862960	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	696	0.245142027326	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	697	0.245422488933	Azmi C. Özgen, 2026.
27	698	0.245524113192	Azmi C. Özgen, 2026.
27	699	0.245691856955	Azmi C. Özgen, 2026.
27	700	0.246006044341	Azmi C. Özgen, 2026.
27	701	0.246199665480	Azmi C. Özgen, 2026.
27	702	0.246300837159	Azmi C. Özgen, 2026.
27	703	0.246341345252	Azmi C. Özgen, 2026.
27	704	0.246500836086	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	705	0.246578411713	Vadim Borisov, 2026.
27	706	0.246665553849	Vadim Borisov, 2026.
27	707	0.246750577225	Azmi C. Özgen, 2026.
27	708	0.247017418668	Azmi C. Özgen, 2026.
27	709	0.247094626516	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	710	0.247106438558	Azmi C. Özgen, 2026.
27	711	0.247240686925	Azmi C. Özgen, 2026.
27	712	0.247282298821	Azmi C. Özgen, 2026.
27	713	0.247394964496	Azmi C. Özgen, 2026.
27	714	0.247430370450	Azmi C. Özgen, 2026.
27	715	0.247459363596	Azmi C. Özgen, 2026.
27	716	0.247668410867	Vadim Borisov, 2026.
27	717	0.247687124923	Azmi C. Özgen, 2026.
27	718	0.247716925714	Vadim Borisov, 2026.
27	719	0.247746710864	Azmi C. Özgen, 2026.
27	720	0.247806373231	Azmi C. Özgen, 2026.
27	721	0.247906929563	Azmi C. Özgen, 2026.
27	722	0.248003974146	Azmi C. Özgen, 2026.
27	723	0.248111703537	Azmi C. Özgen, 2026.
27	724	0.248216975729	Vadim Borisov, 2026.
27	725	0.248235547946	Azmi C. Özgen, 2026.
27	726	0.248340083339	Azmi C. Özgen, 2026.
27	727	0.248377305194	Vadim Borisov, 2026.
27	728	0.248412774561	Azmi C. Özgen, 2026.
27	729	0.248510295160	Azmi C. Özgen, 2026.
27	730	0.248549328868	Azmi C. Özgen, 2026.
27	731	0.248640381256	Azmi C. Özgen, 2026.
27	732	0.248657665271	Azmi C. Özgen, 2026.
27	733	0.248731174998	Azmi C. Özgen, 2026.
27	734	0.248792992135	Azmi C. Özgen, 2026.
27	735	0.248885213496	Vadim Borisov, 2026.
27	736	0.248890357066	Azmi C. Özgen, 2026.
27	737	0.248948732426	Azmi C. Özgen, 2026.
27	738	0.249002950534	Azmi C. Özgen, 2026.
27	739	0.249087728571	Azmi C. Özgen, 2026.
27	740	0.249093179174	Azmi C. Özgen, 2026.
27	741	0.249126825207	Azmi C. Özgen, 2026.
27	742	0.249184707811	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	743	0.249226989816	Vadim Borisov, 2026.
27	744	0.249243578134	Vadim Borisov, 2026.
27	745	0.249244299670	Vadim Borisov, 2026.
27	746	0.249257767987	Vadim Borisov, 2026.
27	747	0.249272472081	Vadim Borisov, 2026.
27	748	0.249277647541	Azmi C. Özgen, 2026.
27	749	0.249308620534	Azmi C. Özgen, 2026.
27	750	0.249332428596	Azmi C. Özgen, 2026.
27	751	0.249367562646	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	752	0.249370203384	Azmi C. Özgen, 2026.
27	753	0.249393666920	Azmi C. Özgen, 2026.
27	754	0.249456592371	Azmi C. Özgen, 2026.
27	755	0.249484426334	Azmi C. Özgen, 2026.
27	756	0.249526651955	Azmi C. Özgen, 2026.
27	757	0.249535790086	Vadim Borisov, 2026.
27	758	0.249542275727	Vadim Borisov, 2026.
27	759	0.249611604599	Vadim Borisov, 2026.
27	760	0.249624218432	Vadim Borisov, 2026.
27	761	0.249628478260	Vadim Borisov, 2026.
27	762	0.249651186498	Azmi C. Özgen, 2026.
27	763	0.249668759149	Azmi C. Özgen, 2026.
27	764	0.249696525416	Azmi C. Özgen, 2026.
27	971	0.25	Kevin Li, 2026. $4 x - 1$
27	974	0.251528314296	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	975	0.251922205188	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	976	0.252416917704	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	977	0.252468695325	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	978	0.253351065362	Vadim Borisov, 2026.
27	979	0.253446820490	Vadim Borisov, 2026.
27	980	0.253763161615	Vadim Borisov, 2026.
27	981	0.253778474393	Christopher Smolen, 2026.
27	982	0.254560908190	Azmi C. Özgen, 2026.
27	983	0.254907288716	Azmi C. Özgen, 2026.
27	984	0.255101835599	Vadim Borisov, 2026.
27	985	0.255680341001	Vadim Borisov, 2026.
27	986	0.255815536748	Vadim Borisov, 2026.
27	987	0.255821619084	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	988	0.255888055860	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	989	0.255907746035	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	990	0.257420592621	Azmi C. Özgen, 2026.
27	991	0.258119005301	Azmi C. Özgen, 2026.
27	992	0.258228063020	Azmi C. Özgen, 2026.
27	993	0.258614028972	Vadim Borisov, 2026.
27	994	0.258633869132	Azmi C. Özgen, 2026.
27	995	0.259013708841	Azmi C. Özgen, 2026.
27	996	0.259460897832	Azmi C. Özgen, 2026.
27	997	0.259760345990	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
27	998	0.259812042058	Azmi C. Özgen, 2026.
27	999	0.260339191605	Azmi C. Özgen, 2026.
27	1000	0.260614014369	Azmi C. Özgen, 2026.
27	1001	0.261145914873	Vadim Borisov, 2026.
27	1002	0.261710087109	Azmi C. Özgen, 2026.
27	1003	0.262141039376	Azmi C. Özgen, 2026.
27	1004	0.262451070614	Vadim Borisov, 2026.
27	1024	0.263299316186	Code with 1024 points in 26 dimensions. $60 x^{2} - 12 x - 1$
28	57	0.028627089329	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $18928 x^{3} - 784 x^{2} - 28 x + 1$
28	58	0.033333333334	H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $30 x - 1$
28	59	0.039154654935	Christopher Smolen, 2026.
28	60	0.039703378844	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988. $584 x^{2} + 2 x - 1$
28	61	0.039748128111	Henry Cohn, 2026. Minimal polynomial of degree 8
28	62	0.044085881575	Vadim Borisov, 2026.
28	63	0.044845027070	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	64	0.045330588014	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	65	0.046120041619	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	66	0.047264906913	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	67	0.051619283330	Christopher Smolen, 2026.
28	68	0.051755035493	Vadim Borisov, 2026.
28	69	0.051759500978	Christopher Smolen, 2026.
28	70	0.051797462893	Orthogonal union of 66 points in 26 dimensions and 4 points in 2 dimensions.
28	71	0.059062187940	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	72	0.060835023563	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	73	0.061831527379	Christopher Smolen, 2026.
28	74	0.062695841141	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	75	0.064280936077	Arhan Canli, 2026.
28	76	0.064711721886	Arhan Canli, 2026.
28	77	0.065629121675	Christopher Smolen, 2026.
28	78	0.067202592064	Azmi C. Özgen, 2026.
28	79	0.069465959676	Azmi C. Özgen, 2026.
28	80	0.070903831678	Azmi C. Özgen, 2026.
28	81	0.072590685434	Azmi C. Özgen, 2026.
28	82	0.074337691888	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	83	0.074820220286	Christopher Smolen, 2026.
28	84	0.075879337659	Christopher Smolen, 2026.
28	85	0.076580366303	Arhan Canli, 2026.
28	86	0.076701065570	Christopher Smolen, 2026.
28	87	0.076797346653	Christopher Smolen, 2026.
28	88	0.076838325964	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	89	0.077191917895	Azmi C. Özgen, 2026.
28	90	0.077489902465	Arhan Canli, 2026.
28	91	0.078281564565	Azmi C. Özgen, 2026.
28	92	0.078666583173	Azmi C. Özgen, 2026.
28	93	0.079137814351	Christopher Smolen, 2026.
28	94	0.079364966766	Arhan Canli, 2026.
28	95	0.079648557741	Arhan Canli, 2026.
28	96	0.079960999470	Arhan Canli, 2026.
28	97	0.080129735758	Azmi C. Özgen, 2026.
28	98	0.080355952691	Christopher Smolen, 2026.
28	99	0.080627421332	Christopher Smolen, 2026.
28	101	0.080685003240	Henry Cohn, 2026.
28	102	0.080895834154	Henry Cohn, 2026.
28	103	0.083579218232	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	104	0.084602848281	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	105	0.085794626217	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	106	0.085822290111	Arhan Canli, 2026.
28	107	0.088553810157	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	108	0.088787490784	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	109	0.088932605003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	110	0.089385419801	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	111	0.089487708662	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	112	0.089534762217	Henry Cohn, 2026.
28	113	0.089790721709	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	114	0.089906129091	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	115	0.089948882583	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	116	0.090010904560	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	117	0.090758781032	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	118	0.090951875753	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	119	0.093149287430	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	120	0.095104870948	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	121	0.097103226846	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	122	0.098858918619	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	123	0.100616606620	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	124	0.102120218982	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
28	125	0.102410089927	Christopher Smolen, 2026.
28	127	0.102484734546	Henry Cohn, 2026. $3356 x^{2} - 100 x - 25$
28	128	0.102994874275	Christopher Smolen, 2026.
28	129	0.103072299524	Christopher Smolen, 2026.
28	130	0.103117898785	Christopher Smolen, 2026.
28	131	0.103961344555	Christopher Smolen, 2026.
28	132	0.105273429676	Christopher Smolen, 2026.
28	133	0.106243056782	Christopher Smolen, 2026.
28	134	0.107678880227	Vadim Borisov, 2026.
28	135	0.108052911152	Vadim Borisov, 2026.
28	136	0.108958640265	Azmi C. Özgen, 2026.
28	137	0.109642501925	Christopher Smolen, 2026.
28	138	0.110639592313	Christopher Smolen, 2026.
28	139	0.110884923380	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	140	0.110890096880	Christopher Smolen, 2026.
28	150	0.111111111112	Henry Cohn, 2026. $9 x - 1$
28	151	0.111556075883	Henry Cohn, 2026. $73 x^{2} - 44 x + 4$
28	152	0.116948610781	Henry Cohn, 2026.
28	153	0.119601952761	Christopher Smolen, 2026.
28	154	0.120288372404	Christopher Smolen, 2026.
28	155	0.123978770370	Vadim Borisov, 2026.
28	156	0.126303484086	Christopher Smolen, 2026.
28	157	0.127118102266	Christopher Smolen, 2026.
28	158	0.127596613178	Vadim Borisov, 2026.
28	159	0.127946105365	Christopher Smolen, 2026.
28	182	0.128238684469	Henry Cohn, 2026. $92 x^{2} - 4 x - 1$
28	183	0.130665724291	Henry Cohn, 2026. $676 x^{4} - 108 x^{3} - 56 x^{2} + 1$
28	184	0.141516456815	Vadim Borisov, 2026.
28	185	0.142085262957	Vadim Borisov, 2026.
28	186	0.142104699946	Vadim Borisov, 2026.
28	187	0.142126209519	Vadim Borisov, 2026.
28	188	0.142149724161	Vadim Borisov, 2026.
28	189	0.142159567935	Vadim Borisov, 2026.
28	190	0.142202340895	Vadim Borisov, 2026.
28	191	0.142210492106	Vadim Borisov, 2026.
28	192	0.142300749441	Vadim Borisov, 2026.
28	193	0.142365430189	Vadim Borisov, 2026.
28	194	0.142396125135	Vadim Borisov, 2026.
28	195	0.142484965009	Christopher Smolen, 2026.
28	196	0.142617345335	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	197	0.142627152210	Christopher Smolen, 2026.
28	198	0.142762614233	Christopher Smolen, 2026.
28	203	0.142857142848	Henry Cohn, 2026.
28	204	0.143492346348	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	205	0.144198374388	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	206	0.145526911490	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	207	0.145834159532	Vadim Borisov, 2026.
28	208	0.145917030312	Vadim Borisov, 2026.
28	209	0.145943572781	Vadim Borisov, 2026.
28	210	0.146046643253	Vadim Borisov, 2026.
28	211	0.146205027488	Vadim Borisov, 2026.
28	212	0.146373420998	Christopher Smolen, 2026.
28	213	0.146808654473	Vadim Borisov, 2026.
28	214	0.146955465513	Vadim Borisov, 2026.
28	215	0.147003850339	Vadim Borisov, 2026.
28	216	0.147081019891	Vadim Borisov, 2026.
28	217	0.147168235591	Vadim Borisov, 2026.
28	218	0.147275194133	Vadim Borisov, 2026.
28	219	0.147281862616	Vadim Borisov, 2026.
28	220	0.147294709381	Christopher Smolen, 2026.
28	221	0.147306346483	Christopher Smolen, 2026.
28	222	0.147503869242	Vadim Borisov, 2026.
28	223	0.147506737501	Christopher Smolen, 2026.
28	224	0.147518344648	Christopher Smolen, 2026.
28	226	0.147664433105	Azmi C. Özgen, 2026.
28	227	0.147682567538	Christopher Smolen, 2026.
28	228	0.147852503451	Christopher Smolen, 2026.
28	229	0.148206757601	Christopher Smolen, 2026.
28	230	0.148857876732	Christopher Smolen, 2026.
28	231	0.148995119500	Christopher Smolen, 2026.
28	232	0.148995668011	Christopher Smolen, 2026.
28	233	0.149188717789	Christopher Smolen, 2026.
28	234	0.149236291737	Christopher Smolen, 2026.
28	235	0.149281129592	Christopher Smolen, 2026.
28	236	0.149321967301	Vadim Borisov, 2026.
28	237	0.149321969781	Christopher Smolen, 2026.
28	238	0.149322069009	Christopher Smolen, 2026.
28	239	0.149335194275	Christopher Smolen, 2026.
28	240	0.149904213247	Vadim Borisov, 2026.
28	241	0.150628392356	Vadim Borisov, 2026.
28	242	0.151537550865	Christopher Smolen, 2026.
28	243	0.152477106444	Vadim Borisov, 2026.
28	244	0.154123890473	Azmi C. Özgen, 2026.
28	245	0.155214389571	Azmi C. Özgen, 2026.
28	246	0.156190341669	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	247	0.156450678152	Christopher Smolen, 2026.
28	248	0.157615585154	Azmi C. Özgen, 2026.
28	249	0.158605799459	Azmi C. Özgen, 2026.
28	250	0.159501389307	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	251	0.161221111463	Azmi C. Özgen, 2026.
28	252	0.161998686369	Christopher Smolen, 2026.
28	253	0.162021158557	Christopher Smolen, 2026.
28	254	0.162029737100	Christopher Smolen, 2026.
28	255	0.162126395554	Christopher Smolen, 2026.
28	256	0.162312067898	Christopher Smolen, 2026.
28	257	0.162617872962	Azmi C. Özgen, 2026.
28	258	0.162855678022	Christopher Smolen, 2026.
28	259	0.163013029953	Christopher Smolen, 2026.
28	260	0.163197022833	Christopher Smolen, 2026.
28	261	0.163551056279	Vadim Borisov, 2026.
28	262	0.163553036312	Christopher Smolen, 2026.
28	263	0.163799309768	Christopher Smolen, 2026.
28	264	0.164015931084	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	266	0.164037656337	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	267	0.164410897084	Christopher Smolen, 2026.
28	268	0.164574882695	Azmi C. Özgen, 2026.
28	269	0.164681392779	Vadim Borisov, 2026.
28	270	0.164791601284	Vadim Borisov, 2026.
28	271	0.164844231279	Azmi C. Özgen, 2026.
28	272	0.165004817006	Vadim Borisov, 2026.
28	273	0.165092889349	Vadim Borisov, 2026.
28	274	0.165188460000	Vadim Borisov, 2026.
28	275	0.165248080841	Vadim Borisov, 2026.
28	276	0.165384213995	Vadim Borisov, 2026.
28	277	0.165433814707	Christopher Smolen, 2026.
28	278	0.165511654888	Vadim Borisov, 2026.
28	279	0.165577352470	Christopher Smolen, 2026.
28	280	0.165621075501	Christopher Smolen, 2026.
28	281	0.165651273879	Christopher Smolen, 2026.
28	282	0.165695940149	Christopher Smolen, 2026.
28	283	0.165771056339	Vadim Borisov, 2026.
28	284	0.165818563361	Christopher Smolen, 2026.
28	285	0.165857111139	Christopher Smolen, 2026.
28	286	0.165979921343	Azmi C. Özgen, 2026.
28	287	0.166011762730	Vadim Borisov, 2026.
28	288	0.166111516557	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	289	0.166201164364	Vadim Borisov, 2026.
28	290	0.166206778355	Vadim Borisov, 2026.
28	291	0.166251981530	Vadim Borisov, 2026.
28	292	0.166276695101	Vadim Borisov, 2026.
28	293	0.166322188502	Azmi C. Özgen, 2026.
28	294	0.166355169267	Vadim Borisov, 2026.
28	295	0.166359133921	Vadim Borisov, 2026.
28	296	0.166371640270	Vadim Borisov, 2026.
28	297	0.166419800890	Vadim Borisov, 2026.
28	298	0.166449695097	Vadim Borisov, 2026.
28	299	0.166477069741	Christopher Smolen, 2026.
28	300	0.166488703211	Vadim Borisov, 2026.
28	301	0.166521450611	Vadim Borisov, 2026.
28	302	0.166546070698	Azmi C. Özgen, 2026.
28	303	0.166659994041	Vadim Borisov, 2026.
28	304	0.166660352865	Vadim Borisov, 2026.
28	305	0.166660734387	Vadim Borisov, 2026.
28	306	0.166661208143	Vadim Borisov, 2026.
28	307	0.166661782357	Vadim Borisov, 2026.
28	315	0.166666666667	Kevin Li, 2026. $6 x - 1$
28	330	0.166666666667	Henry Cohn, 2026. $6 x - 1$
28	331	0.168653785328	Azmi C. Özgen, 2026.
28	332	0.168926831424	Azmi C. Özgen, 2026.
28	333	0.169773282701	Vadim Borisov, 2026.
28	334	0.171222607443	Vadim Borisov, 2026.
28	335	0.171346423533	Vadim Borisov, 2026.
28	336	0.171393525850	Azmi C. Özgen, 2026.
28	337	0.171413912419	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	338	0.171549018101	Vadim Borisov, 2026.
28	339	0.171811153956	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	340	0.172209889993	Vadim Borisov, 2026.
28	341	0.175169077551	Vadim Borisov, 2026.
28	342	0.177242294281	Vadim Borisov, 2026.
28	343	0.179289299612	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	344	0.180672878891	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	345	0.181538784184	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	346	0.181646950507	Vadim Borisov, 2026.
28	347	0.181647668199	Vadim Borisov, 2026.
28	348	0.181756128505	Vadim Borisov, 2026.
28	349	0.181814918154	Vadim Borisov, 2026.
28	350	0.181834439656	Vadim Borisov, 2026.
28	351	0.181944239478	Azmi C. Özgen, 2026.
28	352	0.182229538717	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	353	0.182530654855	Azmi C. Özgen, 2026.
28	354	0.183446061712	Azmi C. Özgen, 2026.
28	355	0.183958006115	Vadim Borisov, 2026.
28	356	0.184505361743	Azmi C. Özgen, 2026.
28	357	0.184964355075	Azmi C. Özgen, 2026.
28	358	0.185208339229	Christopher Smolen, 2026.
28	359	0.185935236467	Azmi C. Özgen, 2026.
28	360	0.186352747532	Azmi C. Özgen, 2026.
28	361	0.187033530950	Azmi C. Özgen, 2026.
28	362	0.187552135977	Christopher Smolen, 2026.
28	363	0.188204017274	Vadim Borisov, 2026.
28	364	0.188442805091	Christopher Smolen, 2026.
28	365	0.190766642856	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	366	0.192169384678	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	367	0.192400234773	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	368	0.192743635491	Azmi C. Özgen, 2026.
28	369	0.193062675463	Azmi C. Özgen, 2026.
28	370	0.193143092011	Azmi C. Özgen, 2026.
28	371	0.193297369143	Vadim Borisov, 2026.
28	372	0.193331563941	Vadim Borisov, 2026.
28	373	0.193331631261	Christopher Smolen, 2026.
28	374	0.193622822412	Christopher Smolen, 2026.
28	375	0.194092097905	Azmi C. Özgen, 2026.
28	376	0.194224041541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	377	0.194247902137	Christopher Smolen, 2026.
28	378	0.194680128659	Azmi C. Özgen, 2026.
28	379	0.194788684032	Azmi C. Özgen, 2026.
28	380	0.195011496989	Azmi C. Özgen, 2026.
28	381	0.195228937545	Azmi C. Özgen, 2026.
28	382	0.195437573586	Azmi C. Özgen, 2026.
28	383	0.195680642511	Azmi C. Özgen, 2026.
28	384	0.195772288271	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	385	0.195879501160	Azmi C. Özgen, 2026.
28	386	0.195933771275	Azmi C. Özgen, 2026.
28	387	0.196137833011	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	388	0.196138147135	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	389	0.196138549811	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	390	0.196139246770	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	391	0.196674121989	Vadim Borisov, 2026.
28	392	0.196717399505	Azmi C. Özgen, 2026.
28	393	0.196834840776	Azmi C. Özgen, 2026.
28	394	0.197030709039	Azmi C. Özgen, 2026.
28	395	0.197078241232	Azmi C. Özgen, 2026.
28	396	0.197100350850	Vadim Borisov, 2026.
28	397	0.197160175663	Azmi C. Özgen, 2026.
28	398	0.197254960424	Azmi C. Özgen, 2026.
28	399	0.197372461273	Azmi C. Özgen, 2026.
28	400	0.197490306022	Azmi C. Özgen, 2026.
28	401	0.197634147869	Azmi C. Özgen, 2026.
28	402	0.197721678275	Vadim Borisov, 2026.
28	403	0.197831564913	Azmi C. Özgen, 2026.
28	404	0.197891534624	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	405	0.197943375540	Vadim Borisov, 2026.
28	406	0.197963916367	Azmi C. Özgen, 2026.
28	407	0.198095006688	Azmi C. Özgen, 2026.
28	408	0.198172839122	Vadim Borisov, 2026.
28	410	0.198173159334	Vadim Borisov, 2026.
28	411	0.198387491146	Vadim Borisov, 2026.
28	412	0.198405900355	Vadim Borisov, 2026.
28	413	0.198447141751	Azmi C. Özgen, 2026.
28	414	0.198530760499	Vadim Borisov, 2026.
28	415	0.198530760602	Vadim Borisov, 2026.
28	416	0.198530865254	Vadim Borisov, 2026.
28	417	0.198530866539	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	418	0.198782215860	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	419	0.198796629848	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	420	0.198819212320	Vadim Borisov, 2026.
28	421	0.198825802791	Vadim Borisov, 2026.
28	422	0.198827718152	Vadim Borisov, 2026.
28	423	0.198827719095	Vadim Borisov, 2026.
28	424	0.198827720787	Christopher Smolen, 2026.
28	425	0.198948945736	Christopher Smolen, 2026.
28	426	0.199086777551	Vadim Borisov, 2026.
28	427	0.199086778560	Christopher Smolen, 2026.
28	428	0.199228242153	Azmi C. Özgen, 2026.
28	429	0.199247176429	Azmi C. Özgen, 2026.
28	430	0.199306836174	Azmi C. Özgen, 2026.
28	431	0.199354483576	Azmi C. Özgen, 2026.
28	432	0.199390588815	Vadim Borisov, 2026.
28	433	0.199396039987	Azmi C. Özgen, 2026.
28	434	0.199445998890	Azmi C. Özgen, 2026.
28	437	0.199457346794	Vadim Borisov, 2026.
28	438	0.199457400545	Christopher Smolen, 2026.
28	439	0.199575696559	Vadim Borisov, 2026.
28	440	0.199592084537	Vadim Borisov, 2026.
28	441	0.199614372023	Azmi C. Özgen, 2026.
28	442	0.199633402592	Azmi C. Özgen, 2026.
28	443	0.199650027172	Vadim Borisov, 2026.
28	444	0.199654861579	Azmi C. Özgen, 2026.
28	445	0.199674792714	Azmi C. Özgen, 2026.
28	446	0.199717057296	Azmi C. Özgen, 2026.
28	447	0.199747323184	Vadim Borisov, 2026.
28	448	0.199750049837	Azmi C. Özgen, 2026.
28	449	0.199786135952	Azmi C. Özgen, 2026.
28	450	0.199798263043	Azmi C. Özgen, 2026.
28	451	0.199803158734	Azmi C. Özgen, 2026.
28	452	0.199812704540	Vadim Borisov, 2026.
28	453	0.199812748400	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	454	0.199824084480	Azmi C. Özgen, 2026.
28	455	0.199838405551	Vadim Borisov, 2026.
28	456	0.199848164781	Azmi C. Özgen, 2026.
28	457	0.199858860372	Azmi C. Özgen, 2026.
28	458	0.199861596508	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	459	0.199863039230	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	460	0.199864106651	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	461	0.199894519094	Azmi C. Özgen, 2026.
28	462	0.199908204542	Vadim Borisov, 2026.
28	577	0.2	Kevin Li, 2026. $5 x - 1$
28	591	0.2	Henry Cohn, 2026. $5 x - 1$
28	592	0.200113770833	Henry Cohn, 2026.
28	593	0.200525376669	Vadim Borisov, 2026.
28	594	0.200746032971	Azmi C. Özgen, 2026.
28	595	0.201142787426	Azmi C. Özgen, 2026.
28	596	0.201271203391	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	597	0.201296353800	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	598	0.202635224001	Azmi C. Özgen, 2026.
28	599	0.203268293161	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	600	0.203398929298	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	601	0.204561425332	Azmi C. Özgen, 2026.
28	602	0.205577464115	Azmi C. Özgen, 2026.
28	603	0.205922459390	Vadim Borisov, 2026.
28	604	0.206717354413	Azmi C. Özgen, 2026.
28	605	0.207225358236	Azmi C. Özgen, 2026.
28	606	0.207827747559	Vadim Borisov, 2026.
28	607	0.208660444240	Vadim Borisov, 2026.
28	608	0.209670856646	Azmi C. Özgen, 2026.
28	609	0.210619907400	Azmi C. Özgen, 2026.
28	610	0.211006319399	Azmi C. Özgen, 2026.
28	611	0.211566619678	Azmi C. Özgen, 2026.
28	612	0.212408534343	Azmi C. Özgen, 2026.
28	613	0.212977021679	Azmi C. Özgen, 2026.
28	614	0.213825465816	Azmi C. Özgen, 2026.
28	615	0.214612644846	Azmi C. Özgen, 2026.
28	616	0.215380315598	Azmi C. Özgen, 2026.
28	617	0.216036610717	Azmi C. Özgen, 2026.
28	618	0.216584769921	Azmi C. Özgen, 2026.
28	620	0.217187143205	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	621	0.217297703570	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	622	0.217728666563	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	623	0.218267405791	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	624	0.218607332779	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	625	0.218762504423	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	626	0.218838790048	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	627	0.219363694753	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	628	0.219453929829	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	629	0.219945743805	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	630	0.219951816756	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	631	0.220028737536	Christopher Smolen, 2026.
28	632	0.222355130036	Vadim Borisov, 2026.
28	633	0.222573935928	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	634	0.222982838755	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	635	0.222994436604	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	636	0.223125518185	Vadim Borisov, 2026.
28	637	0.223127551173	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	638	0.224042202018	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	639	0.224222442939	Vadim Borisov, 2026.
28	640	0.224224869563	Christopher Smolen, 2026.
28	641	0.226243826192	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	642	0.226634242709	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	643	0.226753827053	Vadim Borisov, 2026.
28	644	0.226766042658	Vadim Borisov, 2026.
28	645	0.226766099188	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	646	0.228448803855	Azmi C. Özgen, 2026.
28	647	0.228931912920	Azmi C. Özgen, 2026.
28	648	0.229346218389	Azmi C. Özgen, 2026.
28	649	0.229767219719	Azmi C. Özgen, 2026.
28	650	0.229989034196	Azmi C. Özgen, 2026.
28	651	0.230310190205	Azmi C. Özgen, 2026.
28	652	0.230578286105	Azmi C. Özgen, 2026.
28	653	0.230849806465	Azmi C. Özgen, 2026.
28	654	0.231079649344	Azmi C. Özgen, 2026.
28	655	0.231385029530	Azmi C. Özgen, 2026.
28	656	0.231693052400	Azmi C. Özgen, 2026.
28	657	0.232003787410	Azmi C. Özgen, 2026.
28	658	0.232289620124	Azmi C. Özgen, 2026.
28	659	0.232480922114	Vadim Borisov, 2026.
28	660	0.232722935587	Azmi C. Özgen, 2026.
28	661	0.232959238529	Azmi C. Özgen, 2026.
28	662	0.233204903258	Azmi C. Özgen, 2026.
28	663	0.233709932874	Vadim Borisov, 2026.
28	664	0.233710067021	Vadim Borisov, 2026.
28	665	0.233710250870	Vadim Borisov, 2026.
28	666	0.233710323426	Vadim Borisov, 2026.
28	667	0.233710441896	Vadim Borisov, 2026.
28	668	0.233710739971	Vadim Borisov, 2026.
28	669	0.233710887537	Vadim Borisov, 2026.
28	670	0.233710902047	Vadim Borisov, 2026.
28	671	0.233710902603	Vadim Borisov, 2026.
28	672	0.233711005862	Vadim Borisov, 2026.
28	673	0.233711231436	Vadim Borisov, 2026.
28	674	0.233711285465	Vadim Borisov, 2026.
28	675	0.233711370625	Vadim Borisov, 2026.
28	676	0.233711403431	Vadim Borisov, 2026.
28	677	0.233711438434	Vadim Borisov, 2026.
28	678	0.233711484816	Vadim Borisov, 2026.
28	679	0.233711540586	Vadim Borisov, 2026.
28	680	0.233711553065	Vadim Borisov, 2026.
28	681	0.233711577683	Vadim Borisov, 2026.
28	682	0.233711606799	Vadim Borisov, 2026.
28	683	0.233711622584	Vadim Borisov, 2026.
28	684	0.233711651927	Vadim Borisov, 2026.
28	685	0.233711681056	Vadim Borisov, 2026.
28	686	0.233711699106	Vadim Borisov, 2026.
28	687	0.233711714468	Vadim Borisov, 2026.
28	688	0.233711727747	Vadim Borisov, 2026.
28	689	0.233711730622	Henry Cohn, 2026.
28	690	0.233752316718	Vadim Borisov, 2026.
28	691	0.233771198581	Vadim Borisov, 2026.
28	692	0.233832065035	Vadim Borisov, 2026.
28	693	0.233908548151	Azmi C. Özgen, 2026.
28	694	0.234113472037	Vadim Borisov, 2026.
28	695	0.234311063413	Vadim Borisov, 2026.
28	696	0.234516659706	Vadim Borisov, 2026.
28	697	0.234712067752	Vadim Borisov, 2026.
28	698	0.239552450680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	699	0.239609243620	Vadim Borisov, 2026.
28	700	0.239921053530	Vadim Borisov, 2026.
28	701	0.239970684663	Vadim Borisov, 2026.
28	702	0.240078702220	Vadim Borisov, 2026.
28	703	0.240254560579	Vadim Borisov, 2026.
28	704	0.240366683494	Azmi C. Özgen, 2026.
28	705	0.240583068164	Azmi C. Özgen, 2026.
28	706	0.240815575469	Azmi C. Özgen, 2026.
28	707	0.240893284391	Vadim Borisov, 2026.
28	708	0.241025186772	Vadim Borisov, 2026.
28	709	0.241065138876	Azmi C. Özgen, 2026.
28	710	0.241229938876	Azmi C. Özgen, 2026.
28	711	0.241645209514	Vadim Borisov, 2026.
28	712	0.241973623896	Azmi C. Özgen, 2026.
28	713	0.242153977553	Azmi C. Özgen, 2026.
28	714	0.242325821877	Azmi C. Özgen, 2026.
28	715	0.242404112939	Vadim Borisov, 2026.
28	716	0.242532565586	Azmi C. Özgen, 2026.
28	717	0.242639788633	Azmi C. Özgen, 2026.
28	718	0.242859486555	Azmi C. Özgen, 2026.
28	719	0.243052844133	Azmi C. Özgen, 2026.
28	720	0.243123545068	Vadim Borisov, 2026.
28	721	0.243161939433	Vadim Borisov, 2026.
28	722	0.243665520054	Azmi C. Özgen, 2026.
28	723	0.243842137828	Vadim Borisov, 2026.
28	724	0.244051529365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	725	0.244144127130	Vadim Borisov, 2026.
28	726	0.247180251350	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	727	0.247186664041	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	728	0.247235636084	Vadim Borisov, 2026.
28	729	0.247246060256	Vadim Borisov, 2026.
28	730	0.247252422647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	731	0.247259961883	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	732	0.247273351585	Vadim Borisov, 2026.
28	733	0.247275755183	Vadim Borisov, 2026.
28	734	0.247275827851	Vadim Borisov, 2026.
28	735	0.247283352031	Vadim Borisov, 2026.
28	736	0.247283360617	Vadim Borisov, 2026.
28	739	0.247283367265	Vadim Borisov, 2026.
28	740	0.247283438049	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	741	0.247877932428	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	742	0.247882905098	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	744	0.247889080785	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	746	0.247890862357	Vadim Borisov, 2026.
28	747	0.247905245933	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	748	0.248298572904	Azmi C. Özgen, 2026.
28	749	0.248363300676	Azmi C. Özgen, 2026.
28	750	0.248412505396	Vadim Borisov, 2026.
28	751	0.248461597137	Vadim Borisov, 2026.
28	752	0.248503431474	Vadim Borisov, 2026.
28	753	0.248530797250	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	754	0.248548206882	Vadim Borisov, 2026.
28	755	0.248548238871	Vadim Borisov, 2026.
28	756	0.248549707495	Vadim Borisov, 2026.
28	757	0.248549740054	Vadim Borisov, 2026.
28	758	0.248549821389	Vadim Borisov, 2026.
28	759	0.248549842928	Christopher Smolen, 2026.
28	760	0.248778777197	Azmi C. Özgen, 2026.
28	761	0.248832076836	Azmi C. Özgen, 2026.
28	762	0.248855742659	Vadim Borisov, 2026.
28	763	0.248865257983	Vadim Borisov, 2026.
28	764	0.248865498715	Vadim Borisov, 2026.
28	765	0.248865499301	Vadim Borisov, 2026.
28	766	0.248865589965	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	767	0.249030010261	Vadim Borisov, 2026.
28	768	0.249050759763	Vadim Borisov, 2026.
28	769	0.249078188785	Vadim Borisov, 2026.
28	770	0.249084727939	Vadim Borisov, 2026.
28	771	0.249086357553	Azmi C. Özgen, 2026.
28	772	0.249128499973	Vadim Borisov, 2026.
28	773	0.249168136638	Azmi C. Özgen, 2026.
28	774	0.249190746415	Vadim Borisov, 2026.
28	775	0.249198774466	Vadim Borisov, 2026.
28	776	0.249223871530	Vadim Borisov, 2026.
28	777	0.249246427634	Vadim Borisov, 2026.
28	779	0.249249374330	Vadim Borisov, 2026.
28	781	0.249249374335	Vadim Borisov, 2026.
28	782	0.249249376417	Henry Cohn, 2026.
28	783	0.249358364498	Vadim Borisov, 2026.
28	784	0.249376153068	Vadim Borisov, 2026.
28	786	0.249386390890	Vadim Borisov, 2026.
28	787	0.249387771346	Vadim Borisov, 2026.
28	788	0.249410408294	Vadim Borisov, 2026.
28	790	0.249423775611	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	791	0.249429231295	Vadim Borisov, 2026.
28	792	0.249430875219	Christopher Smolen, 2026.
28	793	0.249461140833	Vadim Borisov, 2026.
28	794	0.249498729743	Vadim Borisov, 2026.
28	795	0.249509945034	Vadim Borisov, 2026.
28	796	0.249513492483	Vadim Borisov, 2026.
28	797	0.249530302739	Vadim Borisov, 2026.
28	798	0.249550967278	Vadim Borisov, 2026.
28	799	0.249551073892	Vadim Borisov, 2026.
28	800	0.249569120632	Vadim Borisov, 2026.
28	801	0.249569138456	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	802	0.249583429055	Vadim Borisov, 2026.
28	803	0.249592684093	Vadim Borisov, 2026.
28	804	0.249594075776	Vadim Borisov, 2026.
28	805	0.249624833059	Vadim Borisov, 2026.
28	806	0.249624865912	Vadim Borisov, 2026.
28	807	0.249647211296	Vadim Borisov, 2026.
28	808	0.249647619038	Vadim Borisov, 2026.
28	809	0.249647638520	Vadim Borisov, 2026.
28	810	0.249662075448	Vadim Borisov, 2026.
28	811	0.249675054780	Azmi C. Özgen, 2026.
28	812	0.249693421692	Vadim Borisov, 2026.
28	813	0.249696877845	Vadim Borisov, 2026.
28	814	0.249697423125	Vadim Borisov, 2026.
28	815	0.249697485894	Vadim Borisov, 2026.
28	816	0.249713874432	Azmi C. Özgen, 2026.
28	817	0.249739806334	Vadim Borisov, 2026.
28	818	0.249739860269	Vadim Borisov, 2026.
28	819	0.249741618049	Vadim Borisov, 2026.
28	820	0.249741629160	Vadim Borisov, 2026.
28	821	0.249752627589	Vadim Borisov, 2026.
28	822	0.249770853606	Azmi C. Özgen, 2026.
28	823	0.249783006828	Vadim Borisov, 2026.
28	824	0.249790983371	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
28	825	0.249791066832	Azmi C. Özgen, 2026.
28	1011	0.25	Kevin Li, 2026. $4 x - 1$
28	1012	0.250630262395	Azmi C. Özgen, 2026.
28	1013	0.250870123776	Vadim Borisov, 2026.
28	1014	0.251109421896	Azmi C. Özgen, 2026.
28	1015	0.251218129136	Vadim Borisov, 2026.
28	1016	0.251563349832	Azmi C. Özgen, 2026.
28	1017	0.251818521401	Azmi C. Özgen, 2026.
28	1018	0.252172717551	Azmi C. Özgen, 2026.
28	1019	0.252491616657	Azmi C. Özgen, 2026.
28	1020	0.252783949336	Vadim Borisov, 2026.
28	1021	0.252907056259	Azmi C. Özgen, 2026.
28	1022	0.253022605225	Azmi C. Özgen, 2026.
28	1023	0.253312246071	Vadim Borisov, 2026.
28	1024	0.253626800027	Azmi C. Özgen, 2026.
29	59	0.027727451354	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $21141 x^{3} - 841 x^{2} - 29 x + 1$
29	60	0.032282791684	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	61	0.038068703280	Christopher Smolen, 2026.
29	62	0.038918955727	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	63	0.039552183365	Henry Cohn, 2026. $224624 x^{4} + 24312 x^{3} + 287 x^{2} - 38 x - 1$
29	64	0.043272075045	Henry Cohn, 2026.
29	65	0.044519815142	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	66	0.044587130463	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	67	0.044624391459	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	68	0.046023717623	Henry Cohn, 2026.
29	69	0.049612366106	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	70	0.049845182464	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	71	0.051511066992	Christopher Smolen, 2026.
29	72	0.051797462893	Azmi C. Özgen, 2026.
29	73	0.057482024267	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	74	0.058935627645	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	75	0.060441863195	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	76	0.061466497280	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	77	0.063060596375	Vadim Borisov, 2026.
29	78	0.063546098480	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	79	0.063943801621	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	80	0.065656892089	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	81	0.066913334526	Azmi C. Özgen, 2026.
29	82	0.068320284700	Christopher Smolen, 2026.
29	83	0.070354694071	Arhan Canli, 2026.
29	84	0.072118320579	Azmi C. Özgen, 2026.
29	85	0.073285636207	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	86	0.074201966329	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	87	0.075178073621	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	88	0.075900458381	Christopher Smolen, 2026.
29	89	0.076413965694	Arhan Canli, 2026.
29	90	0.076725233813	Azmi C. Özgen, 2026.
29	91	0.076947824055	Christopher Smolen, 2026.
29	92	0.077121856059	Christopher Smolen, 2026.
29	93	0.077122850502	Christopher Smolen, 2026.
29	94	0.077501588340	Christopher Smolen, 2026.
29	95	0.077852555786	Christopher Smolen, 2026.
29	96	0.078168008709	Azmi C. Özgen, 2026.
29	97	0.078407847971	Christopher Smolen, 2026.
29	98	0.078644893126	Christopher Smolen, 2026.
29	99	0.079076875051	Azmi C. Özgen, 2026.
29	100	0.079319387986	Christopher Smolen, 2026.
29	101	0.079949696225	Christopher Smolen, 2026.
29	102	0.080258065036	Christopher Smolen, 2026.
29	103	0.080511494869	Vadim Borisov, 2026.
29	104	0.080511595116	Christopher Smolen, 2026.
29	105	0.080684994016	Christopher Smolen, 2026.
29	106	0.081926015734	Vadim Borisov, 2026.
29	107	0.082605775561	Christopher Smolen, 2026.
29	108	0.084632504185	Christopher Smolen, 2026.
29	112	0.086333380579	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Example 5.10.1. $111 x^{2} + 2 x - 1$
29	113	0.088700086956	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	114	0.088769592974	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	115	0.089056602041	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	116	0.089320330169	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	117	0.089469667450	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	118	0.089902841268	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	119	0.090203625496	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	120	0.090311537242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	121	0.090767006340	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	122	0.091041620068	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	123	0.092780735218	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	124	0.093674902246	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	125	0.095723876548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	126	0.096277841521	Christopher Smolen, 2026.
29	127	0.096361171803	Christopher Smolen, 2026.
29	128	0.097360563242	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	129	0.098306729618	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	130	0.098418299395	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	131	0.098487059083	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	132	0.098677369824	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	133	0.100095680417	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	134	0.100127442523	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	135	0.101944715003	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	136	0.102653973962	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
29	137	0.105085480771	Christopher Smolen, 2026.
29	138	0.106235105962	Vadim Borisov, 2026.
29	139	0.107319181796	Vadim Borisov, 2026.
29	140	0.107979953593	Vadim Borisov, 2026.
29	141	0.108019141859	Henry Cohn, 2026.
29	142	0.109372108157	Vadim Borisov, 2026.
29	143	0.110082236861	Azmi C. Özgen, 2026.
29	144	0.110674224357	Vadim Borisov, 2026.
29	145	0.110695253434	Christopher Smolen, 2026.
29	146	0.111106237305	Christopher Smolen, 2026.
29	147	0.111106907044	Christopher Smolen, 2026.
29	148	0.111109118400	Christopher Smolen, 2026.
29	149	0.111110139116	Christopher Smolen, 2026.
29	150	0.111110329291	Christopher Smolen, 2026.
29	154	0.111111110872	Henry Cohn, 2026.
29	155	0.112078746700	Vadim Borisov, 2026.
29	156	0.113915478067	Vadim Borisov, 2026.
29	157	0.117782249815	Vadim Borisov, 2026.
29	158	0.118504107468	Vadim Borisov, 2026.
29	159	0.120572060793	Christopher Smolen, 2026.
29	160	0.121289593223	Vadim Borisov, 2026.
29	161	0.122322143018	Christopher Smolen, 2026.
29	162	0.124194495332	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	163	0.125217184633	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	164	0.126052620518	Vadim Borisov, 2026.
29	165	0.126264962334	Christopher Smolen, 2026.
29	166	0.128052551765	Christopher Smolen, 2026.
29	185	0.128238684469	Henry Cohn, 2026. $92 x^{2} - 4 x - 1$
29	186	0.128682367501	Vadim Borisov, 2026.
29	188	0.128682367823	Vadim Borisov, 2026.
29	189	0.130514099529	Vadim Borisov, 2026.
29	200	0.131426074480	Azmi C. Özgen, 2026.
29	201	0.134386064640	Azmi C. Özgen, 2026.
29	202	0.137810584870	Azmi C. Özgen, 2026.
29	203	0.140551571157	Vadim Borisov, 2026.
29	204	0.142415111141	Vadim Borisov, 2026.
29	205	0.142511317208	Vadim Borisov, 2026.
29	206	0.142562270472	Vadim Borisov, 2026.
29	207	0.142841086693	Vadim Borisov, 2026.
29	209	0.142857142858	Kevin Li, 2026. $7 x - 1$
29	210	0.142857142858	Henry Cohn, 2026. $7 x - 1$
29	212	0.142857142858	Henry Cohn and Ilmari Vahteristo, 2026. $7 x - 1$
29	213	0.145040709078	Vadim Borisov, 2026.
29	214	0.145200548732	Christopher Smolen, 2026.
29	215	0.145458331805	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	216	0.145541319742	Christopher Smolen, 2026.
29	217	0.145644952375	Vadim Borisov, 2026.
29	218	0.145859364295	Vadim Borisov, 2026.
29	219	0.146015407843	Vadim Borisov, 2026.
29	220	0.146150718647	Vadim Borisov, 2026.
29	221	0.146355494583	Vadim Borisov, 2026.
29	222	0.146545287808	Vadim Borisov, 2026.
29	223	0.146664842711	Christopher Smolen, 2026.
29	224	0.146718909545	Vadim Borisov, 2026.
29	225	0.146862366885	Christopher Smolen, 2026.
29	235	0.147102976680	Henry Cohn, 2026. $87 x^{2} - 6 x - 1$
29	236	0.147786985656	Christopher Smolen, 2026.
29	237	0.147845803445	Vadim Borisov, 2026.
29	238	0.147845827028	Azmi C. Özgen, 2026.
29	240	0.147982610080	Henry Cohn, 2026. $2831 x^{2} - 250 x - 25$
29	241	0.148117730477	Christopher Smolen, 2026.
29	242	0.148370007718	Christopher Smolen, 2026.
29	243	0.148704819835	Christopher Smolen, 2026.
29	244	0.148916916375	Christopher Smolen, 2026.
29	245	0.149341786460	Christopher Smolen, 2026.
29	246	0.149951175135	Vadim Borisov, 2026.
29	247	0.150217875748	Vadim Borisov, 2026.
29	248	0.150522057684	Vadim Borisov, 2026.
29	249	0.150692836435	Christopher Smolen, 2026.
29	250	0.151712376392	Azmi C. Özgen, 2026.
29	251	0.152154593694	Azmi C. Özgen, 2026.
29	252	0.153198388867	Vadim Borisov, 2026.
29	253	0.153811492540	Azmi C. Özgen, 2026.
29	254	0.155171390233	Azmi C. Özgen, 2026.
29	255	0.156018913037	Azmi C. Özgen, 2026.
29	256	0.156507588836	Azmi C. Özgen, 2026.
29	257	0.157386225753	Azmi C. Özgen, 2026.
29	258	0.158214176586	Azmi C. Özgen, 2026.
29	259	0.158731489320	Vadim Borisov, 2026.
29	260	0.158979342122	Vadim Borisov, 2026.
29	261	0.159863759758	Azmi C. Özgen, 2026.
29	262	0.160793533620	Azmi C. Özgen, 2026.
29	263	0.161796270115	Azmi C. Özgen, 2026.
29	264	0.162183138183	Vadim Borisov, 2026.
29	265	0.162214452442	Christopher Smolen, 2026.
29	266	0.162308450878	Vadim Borisov, 2026.
29	267	0.162359508171	Christopher Smolen, 2026.
29	268	0.162370373500	Christopher Smolen, 2026.
29	269	0.162503682252	Vadim Borisov, 2026.
29	270	0.162545393272	Vadim Borisov, 2026.
29	271	0.162545485318	Christopher Smolen, 2026.
29	272	0.162851163898	Christopher Smolen, 2026.
29	273	0.163257182158	Christopher Smolen, 2026.
29	274	0.163348304882	Christopher Smolen, 2026.
29	275	0.163490054712	Christopher Smolen, 2026.
29	276	0.163561786919	Christopher Smolen, 2026.
29	277	0.163641038746	Christopher Smolen, 2026.
29	278	0.163759843618	Christopher Smolen, 2026.
29	279	0.163866024591	Christopher Smolen, 2026.
29	280	0.163948076178	Christopher Smolen, 2026.
29	281	0.164067058006	Christopher Smolen, 2026.
29	282	0.164292829121	Christopher Smolen, 2026.
29	283	0.164428428400	Christopher Smolen, 2026.
29	284	0.164529874675	Christopher Smolen, 2026.
29	285	0.164583591111	Christopher Smolen, 2026.
29	286	0.164630883988	Christopher Smolen, 2026.
29	287	0.164718782494	Christopher Smolen, 2026.
29	288	0.164863891844	Vadim Borisov, 2026.
29	289	0.164968324155	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	290	0.164992734516	Christopher Smolen, 2026.
29	291	0.165050914421	Christopher Smolen, 2026.
29	292	0.165085243921	Vadim Borisov, 2026.
29	293	0.165154633435	Christopher Smolen, 2026.
29	294	0.165199686862	Christopher Smolen, 2026.
29	295	0.165204615804	Christopher Smolen, 2026.
29	296	0.165248661677	Christopher Smolen, 2026.
29	297	0.165293609910	Christopher Smolen, 2026.
29	298	0.165331807665	Christopher Smolen, 2026.
29	299	0.165394752439	Vadim Borisov, 2026.
29	300	0.165516849498	Christopher Smolen, 2026.
29	301	0.165546776982	Azmi C. Özgen, 2026.
29	302	0.165620696239	Vadim Borisov, 2026.
29	303	0.165695269218	Azmi C. Özgen, 2026.
29	304	0.165768820104	Azmi C. Özgen, 2026.
29	305	0.165806022484	Vadim Borisov, 2026.
29	306	0.165852882380	Vadim Borisov, 2026.
29	307	0.165934451065	Azmi C. Özgen, 2026.
29	308	0.166049020940	Vadim Borisov, 2026.
29	309	0.166064765586	Vadim Borisov, 2026.
29	310	0.166229001370	Vadim Borisov, 2026.
29	311	0.166234543347	Azmi C. Özgen, 2026.
29	312	0.166245704669	Vadim Borisov, 2026.
29	313	0.166356214707	Vadim Borisov, 2026.
29	314	0.166408648929	Vadim Borisov, 2026.
29	315	0.166497686254	Vadim Borisov, 2026.
29	316	0.166636219263	Vadim Borisov, 2026.
29	317	0.166643548470	Vadim Borisov, 2026.
29	318	0.166648961485	Vadim Borisov, 2026.
29	319	0.166650610631	Vadim Borisov, 2026.
29	345	0.166666666667	Kevin Li, 2026. $6 x - 1$
29	346	0.167120327688	Azmi C. Özgen, 2026.
29	347	0.167164052162	Azmi C. Özgen, 2026.
29	348	0.167340117913	Azmi C. Özgen, 2026.
29	349	0.167503514778	Vadim Borisov, 2026.
29	350	0.168281043467	Vadim Borisov, 2026.
29	351	0.168294340695	Vadim Borisov, 2026.
29	352	0.169008208044	Vadim Borisov, 2026.
29	353	0.171340974159	Vadim Borisov, 2026.
29	354	0.174214163152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	355	0.175628850435	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	356	0.176967843450	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	357	0.177999367164	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	358	0.180505961230	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	359	0.180635691232	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	360	0.181395233240	Azmi C. Özgen, 2026.
29	361	0.181603281995	Azmi C. Özgen, 2026.
29	362	0.181674707665	Azmi C. Özgen, 2026.
29	363	0.181911564500	Azmi C. Özgen, 2026.
29	364	0.182334181865	Vadim Borisov, 2026.
29	366	0.183912425522	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	368	0.185343537147	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	369	0.186078020516	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	371	0.187227387509	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	372	0.188025834988	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	373	0.188583507754	Azmi C. Özgen, 2026.
29	374	0.188857134977	Azmi C. Özgen, 2026.
29	375	0.189052847215	Vadim Borisov, 2026.
29	376	0.189163116114	Azmi C. Özgen, 2026.
29	377	0.189693186374	Azmi C. Özgen, 2026.
29	378	0.189716785820	Christopher Smolen, 2026.
29	379	0.190124840413	Azmi C. Özgen, 2026.
29	380	0.190473675888	Azmi C. Özgen, 2026.
29	381	0.190733993922	Azmi C. Özgen, 2026.
29	382	0.190916674606	Azmi C. Özgen, 2026.
29	383	0.191293013478	Vadim Borisov, 2026.
29	384	0.191345009832	Azmi C. Özgen, 2026.
29	385	0.191636248996	Azmi C. Özgen, 2026.
29	386	0.191906262718	Azmi C. Özgen, 2026.
29	387	0.192014907572	Azmi C. Özgen, 2026.
29	388	0.192145749641	Azmi C. Özgen, 2026.
29	389	0.192247407323	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	390	0.192269480446	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	391	0.192861470882	Azmi C. Özgen, 2026.
29	392	0.193240949812	Azmi C. Özgen, 2026.
29	393	0.193462952778	Vadim Borisov, 2026.
29	394	0.193507248248	Christopher Smolen, 2026.
29	395	0.193918710291	Azmi C. Özgen, 2026.
29	396	0.194044055589	Azmi C. Özgen, 2026.
29	451	0.194630872484	Henry Cohn, 2026. $149 x - 29$
29	452	0.196026504946	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	453	0.196981965735	Vadim Borisov, 2026.
29	454	0.199123772855	Azmi C. Özgen, 2026.
29	455	0.199140830074	Azmi C. Özgen, 2026.
29	456	0.199186352492	Vadim Borisov, 2026.
29	457	0.199193987089	Vadim Borisov, 2026.
29	458	0.199207317214	Vadim Borisov, 2026.
29	459	0.199219544028	Vadim Borisov, 2026.
29	460	0.199228991704	Vadim Borisov, 2026.
29	461	0.199234054557	Azmi C. Özgen, 2026.
29	462	0.199271208353	Azmi C. Özgen, 2026.
29	463	0.199322700597	Azmi C. Özgen, 2026.
29	464	0.199343839161	Azmi C. Özgen, 2026.
29	465	0.199404240733	Azmi C. Özgen, 2026.
29	466	0.199438387088	Vadim Borisov, 2026.
29	467	0.199442338225	Azmi C. Özgen, 2026.
29	468	0.199452556544	Azmi C. Özgen, 2026.
29	469	0.199474154766	Azmi C. Özgen, 2026.
29	470	0.199512544200	Azmi C. Özgen, 2026.
29	471	0.199531135347	Vadim Borisov, 2026.
29	472	0.199534551276	Vadim Borisov, 2026.
29	473	0.199580957805	Vadim Borisov, 2026.
29	474	0.199585423715	Azmi C. Özgen, 2026.
29	475	0.199609007857	Vadim Borisov, 2026.
29	476	0.199612859245	Vadim Borisov, 2026.
29	477	0.199613773743	Azmi C. Özgen, 2026.
29	478	0.199627580626	Vadim Borisov, 2026.
29	479	0.199656801887	Azmi C. Özgen, 2026.
29	480	0.199662588159	Vadim Borisov, 2026.
29	481	0.199663070464	Azmi C. Özgen, 2026.
29	482	0.199690816032	Azmi C. Özgen, 2026.
29	483	0.199694758317	Azmi C. Özgen, 2026.
29	484	0.199718439702	Azmi C. Özgen, 2026.
29	485	0.199745409429	Vadim Borisov, 2026.
29	486	0.199749262347	Vadim Borisov, 2026.
29	487	0.199754075059	Azmi C. Özgen, 2026.
29	488	0.199773356449	Vadim Borisov, 2026.
29	489	0.199782539071	Azmi C. Özgen, 2026.
29	490	0.199793733697	Azmi C. Özgen, 2026.
29	491	0.199804003759	Vadim Borisov, 2026.
29	492	0.199826204948	Vadim Borisov, 2026.
29	493	0.199826519574	Vadim Borisov, 2026.
29	494	0.199832198219	Azmi C. Özgen, 2026.
29	495	0.199844756381	Azmi C. Özgen, 2026.
29	496	0.199853516172	Azmi C. Özgen, 2026.
29	497	0.199862239918	Vadim Borisov, 2026.
29	587	0.2	Kevin Li, 2026. $5 x - 1$
29	605	0.2	Henry Cohn, 2026. $5 x - 1$
29	606	0.200260225331	Azmi C. Özgen, 2026.
29	607	0.200351252637	Vadim Borisov, 2026.
29	608	0.200682652880	Vadim Borisov, 2026.
29	609	0.200854690521	Vadim Borisov, 2026.
29	610	0.201045508563	Vadim Borisov, 2026.
29	611	0.201409383891	Azmi C. Özgen, 2026.
29	612	0.201736192767	Azmi C. Özgen, 2026.
29	613	0.202178222924	Vadim Borisov, 2026.
29	614	0.202323198171	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	615	0.202928627997	Azmi C. Özgen, 2026.
29	616	0.203647782961	Azmi C. Özgen, 2026.
29	617	0.204530155188	Vadim Borisov, 2026.
29	618	0.204693983179	Vadim Borisov, 2026.
29	619	0.205328688403	Azmi C. Özgen, 2026.
29	620	0.205767887240	Azmi C. Özgen, 2026.
29	622	0.206425290996	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	623	0.206660846489	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	624	0.206771092042	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	625	0.206955160807	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	626	0.209188517394	Azmi C. Özgen, 2026.
29	627	0.209600703948	Azmi C. Özgen, 2026.
29	628	0.209661337403	Vadim Borisov, 2026.
29	629	0.209706801503	Vadim Borisov, 2026.
29	630	0.209708139525	Christopher Smolen, 2026.
29	631	0.211847803870	Azmi C. Özgen, 2026.
29	632	0.212226217792	Azmi C. Özgen, 2026.
29	633	0.212681509216	Azmi C. Özgen, 2026.
29	634	0.213119513561	Azmi C. Özgen, 2026.
29	635	0.213511935090	Azmi C. Özgen, 2026.
29	636	0.213960234785	Azmi C. Özgen, 2026.
29	637	0.214394639750	Azmi C. Özgen, 2026.
29	638	0.214886848579	Azmi C. Özgen, 2026.
29	639	0.215540738694	Azmi C. Özgen, 2026.
29	640	0.216097859539	Azmi C. Özgen, 2026.
29	641	0.216635647263	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	642	0.216635773711	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	643	0.216701658448	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	644	0.216753584673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	645	0.216755299683	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	646	0.218970186080	Azmi C. Özgen, 2026.
29	647	0.219432007755	Azmi C. Özgen, 2026.
29	648	0.219857558502	Azmi C. Özgen, 2026.
29	649	0.220228718938	Azmi C. Özgen, 2026.
29	651	0.220648280541	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	652	0.220778833720	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	653	0.221026441771	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	654	0.221281726867	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	655	0.221431291628	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	656	0.221578129588	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	657	0.221751172216	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	658	0.221821461246	Christopher Smolen, 2026.
29	660	0.222225469177	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	661	0.222247205414	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	662	0.224137861498	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	663	0.224463319941	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	664	0.224552168988	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	665	0.224566089120	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	666	0.224575226536	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	667	0.228695984558	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	668	0.228953857120	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	669	0.229149829242	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	670	0.229449307328	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	671	0.229638934725	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	672	0.229772940839	Vadim Borisov, 2026.
29	673	0.229876174366	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	674	0.230105618220	Vadim Borisov, 2026.
29	675	0.230296710360	Vadim Borisov, 2026.
29	676	0.230318032850	Vadim Borisov, 2026.
29	677	0.230363039136	Vadim Borisov, 2026.
29	678	0.230363116430	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	679	0.231782167538	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	680	0.231922889479	Vadim Borisov, 2026.
29	681	0.231983921912	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	682	0.232014406381	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	683	0.232019241195	Vadim Borisov, 2026.
29	684	0.232029742701	Vadim Borisov, 2026.
29	685	0.233333440227	Vadim Borisov, 2026.
29	686	0.233340918767	Azmi C. Özgen, 2026.
29	687	0.233362420260	Azmi C. Özgen, 2026.
29	688	0.233397350669	Vadim Borisov, 2026.
29	689	0.233454393327	Vadim Borisov, 2026.
29	690	0.233454616435	Vadim Borisov, 2026.
29	691	0.233472334254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	692	0.233482243557	Vadim Borisov, 2026.
29	693	0.233497636338	Vadim Borisov, 2026.
29	694	0.233512054147	Vadim Borisov, 2026.
29	695	0.233556366773	Azmi C. Özgen, 2026.
29	696	0.233586797433	Vadim Borisov, 2026.
29	697	0.233594502402	Vadim Borisov, 2026.
29	698	0.233597454617	Vadim Borisov, 2026.
29	699	0.233610152801	Azmi C. Özgen, 2026.
29	700	0.233616795854	Vadim Borisov, 2026.
29	701	0.233648643600	Vadim Borisov, 2026.
29	702	0.233667531860	Vadim Borisov, 2026.
29	703	0.233670809199	Vadim Borisov, 2026.
29	704	0.233673405022	Vadim Borisov, 2026.
29	705	0.233677004458	Vadim Borisov, 2026.
29	706	0.233679217454	Vadim Borisov, 2026.
29	707	0.233682483016	Vadim Borisov, 2026.
29	708	0.233684744417	Vadim Borisov, 2026.
29	709	0.233687196079	Vadim Borisov, 2026.
29	710	0.233688416494	Vadim Borisov, 2026.
29	711	0.233694632896	Vadim Borisov, 2026.
29	712	0.233701464230	Vadim Borisov, 2026.
29	713	0.233710792408	Vadim Borisov, 2026.
29	714	0.233710812238	Henry Cohn, 2026.
29	715	0.233759282719	Azmi C. Özgen, 2026.
29	716	0.233798318314	Vadim Borisov, 2026.
29	717	0.233837240254	Vadim Borisov, 2026.
29	718	0.234095349759	Vadim Borisov, 2026.
29	719	0.234185817334	Vadim Borisov, 2026.
29	720	0.234816262059	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	725	0.236139737260	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	727	0.236502273812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	729	0.237032715347	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	732	0.237482385581	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	733	0.237758787772	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	734	0.237889933968	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	737	0.238654087337	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	738	0.238857389947	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	739	0.239709992105	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	740	0.239710596673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	741	0.240084269022	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	742	0.240179064396	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	743	0.240215164450	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	744	0.240420609599	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	747	0.241530689826	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	748	0.241641263465	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	749	0.242122836170	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	751	0.242351633401	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	753	0.242439953418	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	754	0.242755820680	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	755	0.243000471843	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	756	0.243195081518	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	757	0.243295516863	Vadim Borisov, 2026.
29	758	0.243448570430	Vadim Borisov, 2026.
29	759	0.243455984503	Azmi C. Özgen, 2026.
29	760	0.243590745363	Vadim Borisov, 2026.
29	761	0.243732549142	Azmi C. Özgen, 2026.
29	762	0.243914447438	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	763	0.243951988115	Azmi C. Özgen, 2026.
29	764	0.244080907191	Azmi C. Özgen, 2026.
29	765	0.244238459920	Vadim Borisov, 2026.
29	766	0.244252901381	Azmi C. Özgen, 2026.
29	767	0.244451627974	Azmi C. Özgen, 2026.
29	768	0.244606948089	Azmi C. Özgen, 2026.
29	769	0.244810125413	Vadim Borisov, 2026.
29	770	0.244822262288	Azmi C. Özgen, 2026.
29	771	0.244990636914	Azmi C. Özgen, 2026.
29	772	0.245110094258	Azmi C. Özgen, 2026.
29	773	0.245223227929	Azmi C. Özgen, 2026.
29	774	0.245356945864	Vadim Borisov, 2026.
29	775	0.245385391342	Vadim Borisov, 2026.
29	776	0.245441957081	Vadim Borisov, 2026.
29	777	0.245465969294	Vadim Borisov, 2026.
29	778	0.245585782337	Azmi C. Özgen, 2026.
29	779	0.245660151023	Azmi C. Özgen, 2026.
29	780	0.245689311815	Vadim Borisov, 2026.
29	781	0.245742738228	Vadim Borisov, 2026.
29	782	0.245792673462	Vadim Borisov, 2026.
29	783	0.245806744228	Azmi C. Özgen, 2026.
29	784	0.245920303041	Azmi C. Özgen, 2026.
29	785	0.245952653854	Azmi C. Özgen, 2026.
29	786	0.246006789322	Vadim Borisov, 2026.
29	787	0.246145860732	Vadim Borisov, 2026.
29	788	0.246246477802	Azmi C. Özgen, 2026.
29	789	0.246287847977	Vadim Borisov, 2026.
29	790	0.246358592595	Vadim Borisov, 2026.
29	791	0.246432048579	Azmi C. Özgen, 2026.
29	792	0.246452051576	Azmi C. Özgen, 2026.
29	793	0.246487346212	Azmi C. Özgen, 2026.
29	794	0.246565289053	Azmi C. Özgen, 2026.
29	795	0.246591256517	Vadim Borisov, 2026.
29	796	0.246674364505	Azmi C. Özgen, 2026.
29	797	0.246846355611	Vadim Borisov, 2026.
29	798	0.246908275576	Vadim Borisov, 2026.
29	799	0.247037194077	Vadim Borisov, 2026.
29	800	0.247097735400	Vadim Borisov, 2026.
29	801	0.247104360275	Vadim Borisov, 2026.
29	802	0.247105461755	Vadim Borisov, 2026.
29	803	0.247147521096	Azmi C. Özgen, 2026.
29	804	0.247243769487	Vadim Borisov, 2026.
29	805	0.247257593918	Vadim Borisov, 2026.
29	806	0.247303830989	Azmi C. Özgen, 2026.
29	807	0.247384758590	Vadim Borisov, 2026.
29	808	0.247466941847	Vadim Borisov, 2026.
29	809	0.247498120184	Vadim Borisov, 2026.
29	810	0.247536518969	Vadim Borisov, 2026.
29	811	0.247571545322	Vadim Borisov, 2026.
29	812	0.247589763021	Vadim Borisov, 2026.
29	813	0.247595416826	Vadim Borisov, 2026.
29	814	0.247598411505	Vadim Borisov, 2026.
29	815	0.247693360063	Vadim Borisov, 2026.
29	816	0.247716348005	Azmi C. Özgen, 2026.
29	817	0.247730608282	Vadim Borisov, 2026.
29	818	0.247747862894	Azmi C. Özgen, 2026.
29	819	0.247854602781	Vadim Borisov, 2026.
29	820	0.247860500015	Azmi C. Özgen, 2026.
29	821	0.247919775158	Azmi C. Özgen, 2026.
29	822	0.247952777622	Azmi C. Özgen, 2026.
29	823	0.247974971670	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	824	0.247987720231	Vadim Borisov, 2026.
29	825	0.248029374713	Vadim Borisov, 2026.
29	826	0.248104450199	Vadim Borisov, 2026.
29	827	0.248147824924	Azmi C. Özgen, 2026.
29	828	0.248185307099	Vadim Borisov, 2026.
29	829	0.248193245788	Vadim Borisov, 2026.
29	830	0.248252029395	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	831	0.248281865059	Vadim Borisov, 2026.
29	832	0.248301983867	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	833	0.248312795670	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	834	0.248332012378	Vadim Borisov, 2026.
29	835	0.248337479407	Vadim Borisov, 2026.
29	836	0.248351190325	Vadim Borisov, 2026.
29	837	0.248352956385	Vadim Borisov, 2026.
29	838	0.248356135247	Vadim Borisov, 2026.
29	839	0.248366096405	Vadim Borisov, 2026.
29	840	0.248400930167	Vadim Borisov, 2026.
29	841	0.248424091133	Vadim Borisov, 2026.
29	842	0.248454728991	Vadim Borisov, 2026.
29	843	0.248512001956	Vadim Borisov, 2026.
29	844	0.248514207666	Vadim Borisov, 2026.
29	845	0.248562348520	Vadim Borisov, 2026.
29	846	0.248606221591	Vadim Borisov, 2026.
29	847	0.248635237849	Vadim Borisov, 2026.
29	848	0.248671113464	Vadim Borisov, 2026.
29	849	0.248725628786	Vadim Borisov, 2026.
29	850	0.248735923784	Vadim Borisov, 2026.
29	851	0.248779510684	Azmi C. Özgen, 2026.
29	852	0.248827464582	Vadim Borisov, 2026.
29	853	0.248829703622	Vadim Borisov, 2026.
29	854	0.248843171738	Azmi C. Özgen, 2026.
29	855	0.248876203188	Vadim Borisov, 2026.
29	856	0.248968925938	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	857	0.248975417324	Vadim Borisov, 2026.
29	858	0.248985790219	Vadim Borisov, 2026.
29	859	0.248994048381	Vadim Borisov, 2026.
29	860	0.248999863775	Vadim Borisov, 2026.
29	861	0.249007113069	Vadim Borisov, 2026.
29	862	0.249010087415	Vadim Borisov, 2026.
29	863	0.249056275396	Vadim Borisov, 2026.
29	864	0.249084649391	Vadim Borisov, 2026.
29	865	0.249092468494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	866	0.249092639289	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	867	0.249107751741	Vadim Borisov, 2026.
29	868	0.249135315640	Vadim Borisov, 2026.
29	869	0.249166385227	Vadim Borisov, 2026.
29	870	0.249287324002	Vadim Borisov, 2026.
29	872	0.249291603900	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	873	0.249294228631	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	874	0.249307294072	Vadim Borisov, 2026.
29	875	0.249311960911	Vadim Borisov, 2026.
29	876	0.249312151042	Vadim Borisov, 2026.
29	877	0.249321188862	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	878	0.249328802490	Vadim Borisov, 2026.
29	879	0.249328962340	Azmi C. Özgen, 2026.
29	880	0.249348615703	Vadim Borisov, 2026.
29	881	0.249373032724	Vadim Borisov, 2026.
29	882	0.249377710628	Vadim Borisov, 2026.
29	883	0.249380261251	Vadim Borisov, 2026.
29	884	0.249395918267	Vadim Borisov, 2026.
29	885	0.249402948660	Vadim Borisov, 2026.
29	886	0.249430624469	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	887	0.249438587658	Vadim Borisov, 2026.
29	888	0.249439463918	Vadim Borisov, 2026.
29	889	0.249448112353	Vadim Borisov, 2026.
29	890	0.249462011657	Vadim Borisov, 2026.
29	891	0.249475315654	Azmi C. Özgen, 2026.
29	892	0.249487933906	Vadim Borisov, 2026.
29	893	0.249490868599	Vadim Borisov, 2026.
29	894	0.249491486920	Vadim Borisov, 2026.
29	895	0.249536213728	Vadim Borisov, 2026.
29	896	0.249536821124	Vadim Borisov, 2026.
29	897	0.249538190685	Azmi C. Özgen, 2026.
29	898	0.249559651647	Vadim Borisov, 2026.
29	899	0.249559794483	Vadim Borisov, 2026.
29	900	0.249571312835	Vadim Borisov, 2026.
29	901	0.249572067460	Azmi C. Özgen, 2026.
29	902	0.249605834133	Vadim Borisov, 2026.
29	903	0.249606239428	Vadim Borisov, 2026.
29	904	0.249611553077	Azmi C. Özgen, 2026.
29	905	0.249652667642	Azmi C. Özgen, 2026.
29	909	0.249764610945	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	910	0.249804134327	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	917	0.249819266148	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
29	918	0.249965301119	Vadim Borisov, 2026.
29	919	0.249965407705	Vadim Borisov, 2026.
29	920	0.249965424992	Vadim Borisov, 2026.
29	921	0.249967321733	Vadim Borisov, 2026.
29	922	0.249967655305	Vadim Borisov, 2026.
29	923	0.249967723591	Vadim Borisov, 2026.
29	924	0.249971470717	Vadim Borisov, 2026.
29	925	0.249972832930	Vadim Borisov, 2026.
29	926	0.249974248646	Vadim Borisov, 2026.
29	927	0.249975730325	Vadim Borisov, 2026.
29	928	0.249976425335	Vadim Borisov, 2026.
29	929	0.249977009396	Vadim Borisov, 2026.
29	930	0.249977030834	Vadim Borisov, 2026.
29	931	0.249977096611	Vadim Borisov, 2026.
29	932	0.249977324555	Vadim Borisov, 2026.
29	933	0.249977419728	Vadim Borisov, 2026.
29	934	0.249977533008	Vadim Borisov, 2026.
29	935	0.249977610984	Vadim Borisov, 2026.
29	936	0.249977655594	Vadim Borisov, 2026.
29	937	0.249980491981	Vadim Borisov, 2026.
29	938	0.249981884616	Vadim Borisov, 2026.
29	939	0.249981976764	Vadim Borisov, 2026.
29	940	0.249982064484	Vadim Borisov, 2026.
29	941	0.249982598415	Vadim Borisov, 2026.
29	942	0.249984189623	Vadim Borisov, 2026.
29	943	0.249984640922	Vadim Borisov, 2026.
29	944	0.249985230843	Vadim Borisov, 2026.
29	945	0.249985326307	Vadim Borisov, 2026.
29	946	0.249985694777	Vadim Borisov, 2026.
29	947	0.249985862817	Vadim Borisov, 2026.
29	948	0.249985898055	Vadim Borisov, 2026.
29	949	0.249987765594	Vadim Borisov, 2026.
29	950	0.249987950857	Vadim Borisov, 2026.
29	951	0.249987953436	Vadim Borisov, 2026.
29	952	0.249987971051	Vadim Borisov, 2026.
29	953	0.249988189568	Vadim Borisov, 2026.
29	954	0.249988517420	Vadim Borisov, 2026.
29	955	0.249988682572	Vadim Borisov, 2026.
29	956	0.249988717433	Vadim Borisov, 2026.
29	957	0.249988754256	Vadim Borisov, 2026.
29	958	0.249988818006	Vadim Borisov, 2026.
29	959	0.249990687917	Vadim Borisov, 2026.
29	960	0.249990744094	Vadim Borisov, 2026.
29	961	0.249990858068	Vadim Borisov, 2026.
29	962	0.249991381251	Vadim Borisov, 2026.
29	963	0.249992308317	Vadim Borisov, 2026.
29	964	0.249992369278	Vadim Borisov, 2026.
29	965	0.249992540236	Vadim Borisov, 2026.
29	966	0.249992678640	Vadim Borisov, 2026.
29	967	0.249992781174	Vadim Borisov, 2026.
29	968	0.249992922183	Vadim Borisov, 2026.
29	969	0.249992993995	Vadim Borisov, 2026.
29	970	0.249993800441	Vadim Borisov, 2026.
29	971	0.249993942391	Vadim Borisov, 2026.
29	972	0.249994071018	Vadim Borisov, 2026.
29	973	0.249994143447	Vadim Borisov, 2026.
29	974	0.249994260096	Vadim Borisov, 2026.
29	975	0.249994333014	Vadim Borisov, 2026.
29	976	0.249994396622	Vadim Borisov, 2026.
29	977	0.249994849241	Vadim Borisov, 2026.
29	978	0.249994878258	Vadim Borisov, 2026.
29	979	0.249995054357	Vadim Borisov, 2026.
29	980	0.249995104237	Vadim Borisov, 2026.
29	981	0.249995130548	Vadim Borisov, 2026.
29	982	0.249995251824	Vadim Borisov, 2026.
29	983	0.249995322919	Vadim Borisov, 2026.
29	984	0.249995409249	Vadim Borisov, 2026.
29	985	0.249995435790	Vadim Borisov, 2026.
29	986	0.249995546339	Vadim Borisov, 2026.
29	987	0.249995608742	Vadim Borisov, 2026.
29	988	0.249995690440	Vadim Borisov, 2026.
29	1024	0.25	Kevin Li, 2026. $4 x - 1$
30	61	0.026884307091	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $23520 x^{3} - 900 x^{2} - 30 x + 1$
30	62	0.031273236170	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	63	0.037664488335	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	64	0.038215865894	Henry Cohn, 2026.
30	65	0.038479664975	Henry Cohn, 2026.
30	66	0.042414064849	Vadim Borisov, 2026.
30	67	0.043279205049	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	68	0.043439510039	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	69	0.044560014147	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	70	0.044757397041	Henry Cohn, 2026.
30	71	0.048412928398	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	72	0.048641450299	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	73	0.051199435059	Christopher Smolen, 2026.
30	74	0.051797462893	Azmi C. Özgen, 2026.
30	75	0.054797544714	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	76	0.057087952356	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	77	0.058597722669	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	78	0.059643158367	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	79	0.061207737623	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	80	0.062312551227	Arhan Canli, 2026.
30	81	0.062820061220	Azmi C. Özgen, 2026.
30	82	0.063356335671	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	83	0.064957683937	Christopher Smolen, 2026.
30	84	0.065918799395	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	85	0.067987812023	Azmi C. Özgen, 2026.
30	86	0.069405995944	Christopher Smolen, 2026.
30	87	0.070863439339	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	88	0.072090236813	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	89	0.073008015101	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	90	0.073967459792	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	91	0.074668858657	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	92	0.075599010506	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	93	0.076084547316	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	94	0.076863926727	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	95	0.076919778279	Christopher Smolen, 2026.
30	96	0.076995708594	Christopher Smolen, 2026.
30	97	0.077147159419	Christopher Smolen, 2026.
30	98	0.077263015354	Azmi C. Özgen, 2026.
30	99	0.077331294674	Christopher Smolen, 2026.
30	100	0.077767754150	Christopher Smolen, 2026.
30	101	0.077920423335	Azmi C. Özgen, 2026.
30	102	0.078028644595	Azmi C. Özgen, 2026.
30	103	0.078512247025	Arhan Canli, 2026.
30	104	0.079109515268	Christopher Smolen, 2026.
30	105	0.079589565165	Christopher Smolen, 2026.
30	106	0.080474845706	Christopher Smolen, 2026.
30	107	0.080659539020	Christopher Smolen, 2026.
30	108	0.080811709429	Christopher Smolen, 2026.
30	109	0.081493485203	Azmi C. Özgen, 2026.
30	110	0.081788172307	Vadim Borisov, 2026.
30	111	0.082299452590	Christopher Smolen, 2026.
30	112	0.083252343684	Christopher Smolen, 2026.
30	113	0.085098649839	Vadim Borisov, 2026.
30	114	0.086226873135	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	115	0.086231940230	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	116	0.086342733194	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	117	0.086387915001	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	118	0.087524493996	Henry Cohn, 2026.
30	119	0.088427485433	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	120	0.088883206097	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	121	0.089320513875	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	122	0.089823054295	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	123	0.089952384550	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	124	0.090024426794	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	125	0.090501567432	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	126	0.091016634078	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	127	0.091865045275	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	128	0.092778117720	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	129	0.094290613320	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	130	0.095659806385	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	131	0.096867091437	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	132	0.097540004115	Vadim Borisov, 2026.
30	133	0.097806237462	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	134	0.098032829539	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	135	0.098435413984	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	136	0.098800919945	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	137	0.099186673656	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	138	0.099803711723	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	139	0.099884660588	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	140	0.099961780842	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	141	0.100178741787	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	142	0.100736369093	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	143	0.101021245719	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	144	0.103078993329	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	145	0.103330591792	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
30	146	0.107643185871	Azmi C. Özgen, 2026.
30	147	0.108248970538	Christopher Smolen, 2026.
30	148	0.109053170997	Vadim Borisov, 2026.
30	149	0.109582305422	Vadim Borisov, 2026.
30	150	0.109833302157	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	151	0.109872227849	Christopher Smolen, 2026.
30	152	0.111070290940	Christopher Smolen, 2026.
30	153	0.111085433659	Christopher Smolen, 2026.
30	154	0.111090468539	Christopher Smolen, 2026.
30	155	0.111091822837	Vadim Borisov, 2026.
30	156	0.111104713467	Christopher Smolen, 2026.
30	157	0.111111128191	Henry Cohn, 2026.
30	158	0.111111129841	Christopher Smolen, 2026.
30	159	0.112245275179	Vadim Borisov, 2026.
30	160	0.113643172188	Vadim Borisov, 2026.
30	161	0.115735620408	Vadim Borisov, 2026.
30	162	0.116547088491	Azmi C. Özgen, 2026.
30	163	0.118593281567	Vadim Borisov, 2026.
30	164	0.120027982420	Vadim Borisov, 2026.
30	165	0.120471231204	Vadim Borisov, 2026.
30	166	0.121700656810	Vadim Borisov, 2026.
30	167	0.121972576757	Vadim Borisov, 2026.
30	168	0.122720964717	Christopher Smolen, 2026.
30	169	0.123546310656	Vadim Borisov, 2026.
30	170	0.124610263655	Vadim Borisov, 2026.
30	171	0.126536094804	Vadim Borisov, 2026.
30	172	0.126561564997	Christopher Smolen, 2026.
30	173	0.127331321664	Vadim Borisov, 2026.
30	174	0.127763046919	Vadim Borisov, 2026.
30	175	0.128052133623	Vadim Borisov, 2026.
30	176	0.128149023336	Christopher Smolen, 2026.
30	189	0.128238684469	Henry Cohn, 2026. $92 x^{2} - 4 x - 1$
30	202	0.128238684469	Azmi C. Özgen, 2026. $92 x^{2} - 4 x - 1$
30	203	0.131299528409	Vadim Borisov, 2026.
30	204	0.131300871322	Christopher Smolen, 2026.
30	205	0.131426317278	Christopher Smolen, 2026.
30	206	0.133993008325	Vadim Borisov, 2026.
30	207	0.134198096435	Azmi C. Özgen, 2026.
30	208	0.136351388951	Christopher Smolen, 2026.
30	209	0.138569306708	Vadim Borisov, 2026.
30	210	0.140431023568	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	211	0.142094077267	Vadim Borisov, 2026.
30	212	0.142211576462	Vadim Borisov, 2026.
30	213	0.142211578818	Christopher Smolen, 2026.
30	214	0.142333699629	Vadim Borisov, 2026.
30	215	0.142388459838	Vadim Borisov, 2026.
30	216	0.142777229635	Azmi C. Özgen, 2026.
30	217	0.142848844891	Vadim Borisov, 2026.
30	226	0.142857142858	Henry Cohn and Ilmari Vahteristo, 2026. $7 x - 1$
30	227	0.145530979454	Azmi C. Özgen, 2026.
30	228	0.145741383518	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	229	0.146090171377	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	230	0.146299201668	Christopher Smolen, 2026.
30	231	0.146311681174	Christopher Smolen, 2026.
30	232	0.146625686751	Christopher Smolen, 2026.
30	233	0.146666740737	Christopher Smolen, 2026.
30	234	0.146807637214	Christopher Smolen, 2026.
30	235	0.146992566173	Vadim Borisov, 2026.
30	241	0.147102976680	Henry Cohn, 2026. $87 x^{2} - 6 x - 1$
30	242	0.147543300425	Vadim Borisov, 2026.
30	243	0.147543671797	Christopher Smolen, 2026.
30	244	0.147648015357	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	245	0.147707354665	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	246	0.147817513517	Christopher Smolen, 2026.
30	247	0.147888456126	Christopher Smolen, 2026.
30	248	0.147933551460	Christopher Smolen, 2026.
30	249	0.147966728122	Christopher Smolen, 2026.
30	250	0.147988354405	Christopher Smolen, 2026.
30	251	0.148047668045	Christopher Smolen, 2026.
30	252	0.148267705291	Vadim Borisov, 2026.
30	253	0.148372165903	Christopher Smolen, 2026.
30	254	0.148737883412	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	255	0.149505156406	Vadim Borisov, 2026.
30	256	0.149777485157	Vadim Borisov, 2026.
30	257	0.150343048695	Christopher Smolen, 2026.
30	258	0.150741430916	Azmi C. Özgen, 2026.
30	259	0.151503333879	Azmi C. Özgen, 2026.
30	260	0.152133181137	Azmi C. Özgen, 2026.
30	261	0.152974305265	Azmi C. Özgen, 2026.
30	262	0.153584918103	Azmi C. Özgen, 2026.
30	263	0.153997081641	Azmi C. Özgen, 2026.
30	264	0.154035894285	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	265	0.155262019236	Azmi C. Özgen, 2026.
30	266	0.155928017594	Azmi C. Özgen, 2026.
30	267	0.156610570129	Azmi C. Özgen, 2026.
30	268	0.157233002085	Azmi C. Özgen, 2026.
30	269	0.157984513263	Azmi C. Özgen, 2026.
30	270	0.158694924241	Azmi C. Özgen, 2026.
30	271	0.159306155030	Azmi C. Özgen, 2026.
30	272	0.159418871089	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	273	0.159595018968	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	274	0.161194265611	Azmi C. Özgen, 2026.
30	275	0.161742057202	Vadim Borisov, 2026.
30	276	0.161775738972	Vadim Borisov, 2026.
30	277	0.161795471810	Vadim Borisov, 2026.
30	278	0.161859176963	Vadim Borisov, 2026.
30	279	0.161861715752	Vadim Borisov, 2026.
30	280	0.161888295238	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	281	0.161929883852	Vadim Borisov, 2026.
30	282	0.161952726819	Christopher Smolen, 2026.
30	284	0.162074485894	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	285	0.162103539793	Christopher Smolen, 2026.
30	286	0.162491243782	Christopher Smolen, 2026.
30	287	0.162747618799	Christopher Smolen, 2026.
30	288	0.162853742551	Christopher Smolen, 2026.
30	289	0.162970515602	Christopher Smolen, 2026.
30	290	0.163058825281	Christopher Smolen, 2026.
30	291	0.163149661866	Christopher Smolen, 2026.
30	292	0.163238356803	Christopher Smolen, 2026.
30	293	0.163279434148	Christopher Smolen, 2026.
30	294	0.163348812238	Christopher Smolen, 2026.
30	295	0.163417653478	Vadim Borisov, 2026.
30	296	0.163467558438	Christopher Smolen, 2026.
30	297	0.163549479444	Azmi C. Özgen, 2026.
30	298	0.163661934051	Christopher Smolen, 2026.
30	299	0.163783689527	Azmi C. Özgen, 2026.
30	300	0.163872033902	Christopher Smolen, 2026.
30	301	0.163991535686	Azmi C. Özgen, 2026.
30	302	0.164082912931	Azmi C. Özgen, 2026.
30	303	0.164340808678	Azmi C. Özgen, 2026.
30	304	0.164423746557	Azmi C. Özgen, 2026.
30	305	0.164515933905	Vadim Borisov, 2026.
30	306	0.164619451308	Azmi C. Özgen, 2026.
30	307	0.164656024692	Azmi C. Özgen, 2026.
30	308	0.164832110112	Vadim Borisov, 2026.
30	309	0.164877607617	Azmi C. Özgen, 2026.
30	310	0.164915444626	Vadim Borisov, 2026.
30	311	0.165060061403	Azmi C. Özgen, 2026.
30	312	0.165114543858	Azmi C. Özgen, 2026.
30	313	0.165159494048	Azmi C. Özgen, 2026.
30	314	0.165237841548	Azmi C. Özgen, 2026.
30	315	0.165303919731	Vadim Borisov, 2026.
30	316	0.165369497284	Azmi C. Özgen, 2026.
30	317	0.165453201596	Azmi C. Özgen, 2026.
30	318	0.165546328236	Vadim Borisov, 2026.
30	319	0.165665191730	Vadim Borisov, 2026.
30	320	0.165694191837	Azmi C. Özgen, 2026.
30	321	0.165735512171	Vadim Borisov, 2026.
30	322	0.165916298713	Vadim Borisov, 2026.
30	323	0.166008400795	Vadim Borisov, 2026.
30	324	0.166067905227	Vadim Borisov, 2026.
30	325	0.166243558320	Vadim Borisov, 2026.
30	326	0.166298072737	Vadim Borisov, 2026.
30	327	0.166459043475	Vadim Borisov, 2026.
30	328	0.166477921249	Vadim Borisov, 2026.
30	329	0.166503507383	Vadim Borisov, 2026.
30	330	0.166521281415	Vadim Borisov, 2026.
30	331	0.166567361024	Vadim Borisov, 2026.
30	351	0.166666666667	Henry Cohn, 2026. $6 x - 1$
30	352	0.166948892783	Christopher Smolen, 2026.
30	353	0.167011711427	Vadim Borisov, 2026.
30	354	0.167011852413	Vadim Borisov, 2026.
30	355	0.167012030377	Vadim Borisov, 2026.
30	356	0.167012244538	Vadim Borisov, 2026.
30	357	0.167012433454	Vadim Borisov, 2026.
30	358	0.167012770109	Vadim Borisov, 2026.
30	359	0.167013041300	Vadim Borisov, 2026.
30	360	0.167013256972	Vadim Borisov, 2026.
30	361	0.167030237448	Vadim Borisov, 2026.
30	362	0.167130798404	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	363	0.167228546733	Vadim Borisov, 2026.
30	364	0.167847026529	Vadim Borisov, 2026.
30	365	0.169309511617	Azmi C. Özgen, 2026.
30	366	0.171188234700	Vadim Borisov, 2026.
30	367	0.172587693502	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	368	0.173564743390	Vadim Borisov, 2026.
30	369	0.174795813920	Azmi C. Özgen, 2026.
30	370	0.175818318853	Vadim Borisov, 2026.
30	371	0.176058742822	Azmi C. Özgen, 2026.
30	372	0.177300003880	Azmi C. Özgen, 2026.
30	373	0.177369313167	Azmi C. Özgen, 2026.
30	374	0.178645342514	Vadim Borisov, 2026.
30	375	0.179016179845	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	376	0.179308589633	Vadim Borisov, 2026.
30	377	0.180176745201	Azmi C. Özgen, 2026.
30	378	0.180883951064	Azmi C. Özgen, 2026.
30	379	0.181475381413	Azmi C. Özgen, 2026.
30	380	0.182037913689	Vadim Borisov, 2026.
30	381	0.182580177739	Azmi C. Özgen, 2026.
30	382	0.182937748546	Azmi C. Özgen, 2026.
30	383	0.183373197581	Vadim Borisov, 2026.
30	384	0.183781005832	Vadim Borisov, 2026.
30	385	0.184455834531	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	386	0.184851102686	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	387	0.187283141800	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	388	0.187357801967	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	389	0.187395285524	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	390	0.187441395762	Christopher Smolen, 2026.
30	391	0.188324550244	Vadim Borisov, 2026.
30	392	0.188324567061	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	393	0.189034975205	Vadim Borisov, 2026.
30	394	0.189078190534	Azmi C. Özgen, 2026.
30	395	0.189485993244	Azmi C. Özgen, 2026.
30	396	0.189727055569	Azmi C. Özgen, 2026.
30	397	0.189994626590	Azmi C. Özgen, 2026.
30	398	0.190404165342	Azmi C. Özgen, 2026.
30	399	0.190416837359	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	400	0.190427750070	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	401	0.190977162138	Azmi C. Özgen, 2026.
30	402	0.191387905427	Azmi C. Özgen, 2026.
30	403	0.191600569844	Azmi C. Özgen, 2026.
30	404	0.191758035108	Azmi C. Özgen, 2026.
30	405	0.192100579097	Vadim Borisov, 2026.
30	406	0.192361605248	Azmi C. Özgen, 2026.
30	407	0.192609744013	Vadim Borisov, 2026.
30	408	0.192810497698	Azmi C. Özgen, 2026.
30	409	0.192972252122	Azmi C. Özgen, 2026.
30	410	0.193137656647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	411	0.193323718223	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	412	0.193405203984	Christopher Smolen, 2026.
30	460	0.194630872484	Henry Cohn, 2026. $149 x - 29$
30	461	0.194698998158	Vadim Borisov, 2026.
30	462	0.194804963216	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	463	0.194841518438	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
30	464	0.194854079550	Vadim Borisov, 2026.
30	465	0.194855073396	Vadim Borisov, 2026.
30	466	0.195268903643	Azmi C. Özgen, 2026.
30	467	0.195935251064	Azmi C. Özgen, 2026.
30	468	0.197897686351	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	469	0.198264635626	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	470	0.198429752944	Azmi C. Özgen, 2026.
30	471	0.198509136408	Azmi C. Özgen, 2026.
30	472	0.198565677539	Azmi C. Özgen, 2026.
30	473	0.198613681666	Azmi C. Özgen, 2026.
30	474	0.198657327998	Azmi C. Özgen, 2026.
30	475	0.198746164309	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	476	0.198784474067	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	477	0.198847575435	Azmi C. Özgen, 2026.
30	478	0.198867570288	Azmi C. Özgen, 2026.
30	479	0.198924624195	Azmi C. Özgen, 2026.
30	480	0.198971041749	Vadim Borisov, 2026.
30	481	0.198980353261	Vadim Borisov, 2026.
30	482	0.198989226388	Azmi C. Özgen, 2026.
30	483	0.198999965530	Azmi C. Özgen, 2026.
30	484	0.199036621773	Azmi C. Özgen, 2026.
30	485	0.199078631418	Azmi C. Özgen, 2026.
30	486	0.199120449408	Azmi C. Özgen, 2026.
30	487	0.199137921301	Vadim Borisov, 2026.
30	488	0.199143170577	Vadim Borisov, 2026.
30	489	0.199146961752	Vadim Borisov, 2026.
30	490	0.199149568900	Azmi C. Özgen, 2026.
30	491	0.199180231930	Azmi C. Özgen, 2026.
30	492	0.199233773032	Azmi C. Özgen, 2026.
30	493	0.199249798923	Azmi C. Özgen, 2026.
30	494	0.199258528804	Azmi C. Özgen, 2026.
30	495	0.199316057917	Azmi C. Özgen, 2026.
30	496	0.199329315714	Azmi C. Özgen, 2026.
30	497	0.199364830232	Azmi C. Özgen, 2026.
30	498	0.199373204080	Azmi C. Özgen, 2026.
30	499	0.199387181228	Azmi C. Özgen, 2026.
30	500	0.199400954550	Azmi C. Özgen, 2026.
30	501	0.199442846241	Azmi C. Özgen, 2026.
30	502	0.199454094282	Vadim Borisov, 2026.
30	503	0.199457070956	Azmi C. Özgen, 2026.
30	504	0.199484465867	Vadim Borisov, 2026.
30	505	0.199487694288	Azmi C. Özgen, 2026.
30	506	0.199510499217	Azmi C. Özgen, 2026.
30	507	0.199525979224	Azmi C. Özgen, 2026.
30	508	0.199536306292	Azmi C. Özgen, 2026.
30	509	0.199573271182	Azmi C. Özgen, 2026.
30	510	0.199576792969	Azmi C. Özgen, 2026.
30	511	0.199602454373	Vadim Borisov, 2026.
30	512	0.199607846401	Vadim Borisov, 2026.
30	513	0.199607856079	Azmi C. Özgen, 2026.
30	514	0.199622412356	Azmi C. Özgen, 2026.
30	515	0.199634881374	Vadim Borisov, 2026.
30	516	0.199655982465	Azmi C. Özgen, 2026.
30	517	0.199670483652	Azmi C. Özgen, 2026.
30	518	0.199687853518	Vadim Borisov, 2026.
30	519	0.199688379373	Azmi C. Özgen, 2026.
30	520	0.199706533242	Vadim Borisov, 2026.
30	521	0.199721231171	Vadim Borisov, 2026.
30	522	0.199721618058	Azmi C. Özgen, 2026.
30	523	0.199730969737	Vadim Borisov, 2026.
30	524	0.199763830942	Vadim Borisov, 2026.
30	525	0.199771673005	Vadim Borisov, 2026.
30	526	0.199782074081	Azmi C. Özgen, 2026.
30	527	0.199782447031	Vadim Borisov, 2026.
30	528	0.199795036493	Vadim Borisov, 2026.
30	529	0.199796260398	Azmi C. Özgen, 2026.
30	530	0.199813620784	Vadim Borisov, 2026.
30	531	0.199815227348	Vadim Borisov, 2026.
30	532	0.199815252644	Vadim Borisov, 2026.
30	533	0.199828891089	Vadim Borisov, 2026.
30	534	0.199829678066	Vadim Borisov, 2026.
30	535	0.199847775482	Vadim Borisov, 2026.
30	536	0.199850088543	Vadim Borisov, 2026.
30	537	0.199859537807	Vadim Borisov, 2026.
30	538	0.199860221577	Vadim Borisov, 2026.
30	539	0.199866776732	Vadim Borisov, 2026.
30	540	0.199879335846	Vadim Borisov, 2026.
30	541	0.199880259106	Christopher Smolen, 2026.
30	656	0.2	Henry Cohn, 2026. $5 x - 1$
30	657	0.203357314598	Henry Cohn, 2026.
30	658	0.205762572239	Vadim Borisov, 2026.
30	659	0.206632966146	Vadim Borisov, 2026.
30	660	0.206640693086	Azmi C. Özgen, 2026.
30	661	0.211832115206	Azmi C. Özgen, 2026.
30	662	0.212317609694	Azmi C. Özgen, 2026.
30	663	0.214697170865	Azmi C. Özgen, 2026.
30	664	0.215499437259	Azmi C. Özgen, 2026.
30	665	0.216472802884	Azmi C. Özgen, 2026.
30	666	0.217790140493	Azmi C. Özgen, 2026.
30	667	0.219045427210	Azmi C. Özgen, 2026.
30	668	0.219906882494	Vadim Borisov, 2026.
30	669	0.219983709482	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	670	0.220116036052	Vadim Borisov, 2026.
30	671	0.220464076237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	672	0.220480751507	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	673	0.220687553426	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	674	0.220806848711	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	675	0.220982416359	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	676	0.221265025392	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	677	0.221409180356	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	678	0.221432971388	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	679	0.221439930271	Vadim Borisov, 2026.
30	680	0.221445411868	Vadim Borisov, 2026.
30	681	0.221446158624	Christopher Smolen, 2026.
30	682	0.223916709722	Vadim Borisov, 2026.
30	683	0.224167986949	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	684	0.224334509308	Vadim Borisov, 2026.
30	685	0.224423478300	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	686	0.224597900259	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	689	0.224831775724	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	691	0.224928293781	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	692	0.225023223985	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	693	0.225046000276	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	694	0.225994081446	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	695	0.226873672994	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	696	0.227401173305	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	697	0.228645291312	Vadim Borisov, 2026.
30	698	0.228792031226	Vadim Borisov, 2026.
30	699	0.228851820490	Vadim Borisov, 2026.
30	700	0.228946339082	Vadim Borisov, 2026.
30	701	0.229162523872	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	702	0.229195167508	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	703	0.229295029562	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	704	0.229443904314	Vadim Borisov, 2026.
30	705	0.229532022202	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	706	0.229601059292	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	707	0.229752020225	Vadim Borisov, 2026.
30	708	0.229759535996	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	709	0.229789842991	Vadim Borisov, 2026.
30	710	0.229789942263	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	711	0.232266944778	Azmi C. Özgen, 2026.
30	712	0.232310870524	Vadim Borisov, 2026.
30	713	0.232429794496	Azmi C. Özgen, 2026.
30	714	0.232565766748	Azmi C. Özgen, 2026.
30	715	0.232618717966	Azmi C. Özgen, 2026.
30	716	0.232702139166	Azmi C. Özgen, 2026.
30	717	0.232842354458	Vadim Borisov, 2026.
30	718	0.232917431912	Azmi C. Özgen, 2026.
30	719	0.232970667586	Azmi C. Özgen, 2026.
30	720	0.232990866465	Azmi C. Özgen, 2026.
30	721	0.233132527238	Vadim Borisov, 2026.
30	722	0.233181765815	Azmi C. Özgen, 2026.
30	723	0.233212405401	Azmi C. Özgen, 2026.
30	724	0.233276581007	Azmi C. Özgen, 2026.
30	725	0.233329871493	Azmi C. Özgen, 2026.
30	726	0.233359278096	Azmi C. Özgen, 2026.
30	727	0.233363512023	Azmi C. Özgen, 2026.
30	728	0.233438527402	Azmi C. Özgen, 2026.
30	729	0.233454570914	Azmi C. Özgen, 2026.
30	730	0.233507140448	Azmi C. Özgen, 2026.
30	731	0.233554649804	Vadim Borisov, 2026.
30	732	0.233557413360	Azmi C. Özgen, 2026.
30	733	0.233611837338	Azmi C. Özgen, 2026.
30	734	0.233622862539	Vadim Borisov, 2026.
30	735	0.233634861627	Vadim Borisov, 2026.
30	736	0.233635127338	Vadim Borisov, 2026.
30	737	0.233668614649	Vadim Borisov, 2026.
30	738	0.233676106992	Vadim Borisov, 2026.
30	739	0.233684698898	Vadim Borisov, 2026.
30	740	0.233695852726	Azmi C. Özgen, 2026.
30	741	0.233706887788	Vadim Borisov, 2026.
30	742	0.233710724387	Henry Cohn, 2026.
30	743	0.233710724474	Henry Cohn, 2026.
30	744	0.233761258474	Vadim Borisov, 2026.
30	745	0.233825319771	Vadim Borisov, 2026.
30	746	0.233892857467	Vadim Borisov, 2026.
30	747	0.233977923676	Vadim Borisov, 2026.
30	748	0.234077028567	Azmi C. Özgen, 2026.
30	749	0.234348000388	Vadim Borisov, 2026.
30	750	0.234521494205	Vadim Borisov, 2026.
30	751	0.238899335093	Vadim Borisov, 2026.
30	752	0.238921181572	Vadim Borisov, 2026.
30	753	0.238921468844	Azmi C. Özgen, 2026.
30	754	0.238999783464	Azmi C. Özgen, 2026.
30	755	0.239218796347	Vadim Borisov, 2026.
30	756	0.239256720157	Vadim Borisov, 2026.
30	757	0.239277620542	Vadim Borisov, 2026.
30	758	0.239280285672	Azmi C. Özgen, 2026.
30	759	0.239427721792	Vadim Borisov, 2026.
30	760	0.239427761529	Vadim Borisov, 2026.
30	761	0.239428148874	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	762	0.239552209428	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	763	0.239760573514	Azmi C. Özgen, 2026.
30	764	0.240026201650	Azmi C. Özgen, 2026.
30	765	0.240060994197	Vadim Borisov, 2026.
30	766	0.240168956167	Azmi C. Özgen, 2026.
30	767	0.240216096486	Azmi C. Özgen, 2026.
30	768	0.240349867945	Azmi C. Özgen, 2026.
30	769	0.240415325448	Azmi C. Özgen, 2026.
30	770	0.240610807679	Vadim Borisov, 2026.
30	771	0.240613773273	Vadim Borisov, 2026.
30	772	0.240687023111	Azmi C. Özgen, 2026.
30	773	0.240832624249	Vadim Borisov, 2026.
30	774	0.240846656065	Vadim Borisov, 2026.
30	775	0.240846759746	Henry Cohn, 2026.
30	776	0.241275995560	Vadim Borisov, 2026.
30	777	0.241277128618	Vadim Borisov, 2026.
30	778	0.241278142606	Christopher Smolen, 2026.
30	779	0.241589318868	Vadim Borisov, 2026.
30	780	0.241660973658	Vadim Borisov, 2026.
30	781	0.241692522398	Vadim Borisov, 2026.
30	783	0.241693446580	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	784	0.241821988098	Vadim Borisov, 2026.
30	786	0.241935823239	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	787	0.242196613546	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	788	0.242370086689	Vadim Borisov, 2026.
30	789	0.242411090712	Vadim Borisov, 2026.
30	790	0.242429380582	Vadim Borisov, 2026.
30	791	0.242539068892	Vadim Borisov, 2026.
30	792	0.242541851071	Azmi C. Özgen, 2026.
30	793	0.242650055831	Azmi C. Özgen, 2026.
30	794	0.242751706801	Vadim Borisov, 2026.
30	795	0.242844676324	Azmi C. Özgen, 2026.
30	796	0.242975723138	Azmi C. Özgen, 2026.
30	797	0.243006851990	Vadim Borisov, 2026.
30	798	0.243275214185	Vadim Borisov, 2026.
30	799	0.243338013110	Vadim Borisov, 2026.
30	800	0.243442790811	Azmi C. Özgen, 2026.
30	801	0.243567110155	Azmi C. Özgen, 2026.
30	802	0.243628110788	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	803	0.243635290826	Azmi C. Özgen, 2026.
30	804	0.243755532635	Azmi C. Özgen, 2026.
30	805	0.244012065055	Vadim Borisov, 2026.
30	806	0.244120102292	Vadim Borisov, 2026.
30	807	0.244137411822	Vadim Borisov, 2026.
30	808	0.244221429635	Azmi C. Özgen, 2026.
30	809	0.244251684270	Azmi C. Özgen, 2026.
30	810	0.244281582122	Azmi C. Özgen, 2026.
30	811	0.244355268871	Vadim Borisov, 2026.
30	812	0.244483778063	Vadim Borisov, 2026.
30	813	0.244634360737	Vadim Borisov, 2026.
30	814	0.244664110279	Vadim Borisov, 2026.
30	815	0.244672981977	Vadim Borisov, 2026.
30	816	0.244751155286	Vadim Borisov, 2026.
30	817	0.244785636906	Vadim Borisov, 2026.
30	818	0.244795824011	Vadim Borisov, 2026.
30	819	0.244886937524	Azmi C. Özgen, 2026.
30	820	0.245034926739	Azmi C. Özgen, 2026.
30	821	0.245046155897	Vadim Borisov, 2026.
30	822	0.245167632557	Azmi C. Özgen, 2026.
30	823	0.245302759045	Vadim Borisov, 2026.
30	824	0.245346637854	Vadim Borisov, 2026.
30	825	0.245445630245	Vadim Borisov, 2026.
30	826	0.245542761886	Vadim Borisov, 2026.
30	827	0.245583791784	Vadim Borisov, 2026.
30	828	0.245586283567	Azmi C. Özgen, 2026.
30	829	0.245638969241	Vadim Borisov, 2026.
30	830	0.245643105008	Azmi C. Özgen, 2026.
30	831	0.245769247029	Azmi C. Özgen, 2026.
30	832	0.245911726611	Vadim Borisov, 2026.
30	833	0.245912669609	Azmi C. Özgen, 2026.
30	834	0.245925895582	Vadim Borisov, 2026.
30	835	0.246058699698	Vadim Borisov, 2026.
30	836	0.246156182823	Vadim Borisov, 2026.
30	837	0.246193166415	Vadim Borisov, 2026.
30	838	0.246226446274	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	839	0.246252205109	Vadim Borisov, 2026.
30	840	0.246267476145	Vadim Borisov, 2026.
30	841	0.246296814160	Vadim Borisov, 2026.
30	842	0.246372726758	Azmi C. Özgen, 2026.
30	843	0.246497863251	Azmi C. Özgen, 2026.
30	844	0.246567014415	Azmi C. Özgen, 2026.
30	845	0.246667308022	Azmi C. Özgen, 2026.
30	846	0.246705534421	Azmi C. Özgen, 2026.
30	847	0.246799776956	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	848	0.246923910270	Azmi C. Özgen, 2026.
30	849	0.246947028825	Azmi C. Özgen, 2026.
30	850	0.246977646001	Vadim Borisov, 2026.
30	851	0.246981455841	Azmi C. Özgen, 2026.
30	852	0.246992420827	Vadim Borisov, 2026.
30	855	0.247085977745	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	856	0.247125017237	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	857	0.247156866587	Vadim Borisov, 2026.
30	858	0.247225075560	Azmi C. Özgen, 2026.
30	859	0.247254938226	Azmi C. Özgen, 2026.
30	860	0.247291862656	Azmi C. Özgen, 2026.
30	861	0.247303424058	Vadim Borisov, 2026.
30	862	0.247358591014	Vadim Borisov, 2026.
30	863	0.247389504701	Vadim Borisov, 2026.
30	864	0.247473927336	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	865	0.247560569780	Vadim Borisov, 2026.
30	866	0.247568055274	Vadim Borisov, 2026.
30	867	0.247624401330	Azmi C. Özgen, 2026.
30	868	0.247657150760	Vadim Borisov, 2026.
30	869	0.247733603923	Vadim Borisov, 2026.
30	870	0.247792913645	Azmi C. Özgen, 2026.
30	871	0.247797906401	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	872	0.247817056241	Vadim Borisov, 2026.
30	873	0.247839261463	Vadim Borisov, 2026.
30	874	0.247846941210	Vadim Borisov, 2026.
30	875	0.247849416123	Vadim Borisov, 2026.
30	876	0.247915498507	Azmi C. Özgen, 2026.
30	877	0.247946992451	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	878	0.247960065073	Vadim Borisov, 2026.
30	879	0.247965619626	Azmi C. Özgen, 2026.
30	880	0.247994719978	Vadim Borisov, 2026.
30	881	0.248094034484	Vadim Borisov, 2026.
30	882	0.248117207478	Azmi C. Özgen, 2026.
30	883	0.248160029335	Vadim Borisov, 2026.
30	884	0.248186162829	Vadim Borisov, 2026.
30	885	0.248188630517	Vadim Borisov, 2026.
30	886	0.248248986065	Vadim Borisov, 2026.
30	887	0.248258592181	Azmi C. Özgen, 2026.
30	888	0.248302162091	Vadim Borisov, 2026.
30	889	0.248334786308	Vadim Borisov, 2026.
30	890	0.248337392707	Vadim Borisov, 2026.
30	891	0.248353644769	Azmi C. Özgen, 2026.
30	892	0.248392161068	Vadim Borisov, 2026.
30	893	0.248422043235	Azmi C. Özgen, 2026.
30	894	0.248435761946	Vadim Borisov, 2026.
30	895	0.248444035325	Vadim Borisov, 2026.
30	896	0.248444127269	Vadim Borisov, 2026.
30	897	0.248446175009	Vadim Borisov, 2026.
30	898	0.248501242009	Azmi C. Özgen, 2026.
30	899	0.248512875314	Azmi C. Özgen, 2026.
30	900	0.248546981986	Vadim Borisov, 2026.
30	901	0.248550087073	Vadim Borisov, 2026.
30	904	0.248588196042	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	905	0.248609661829	Vadim Borisov, 2026.
30	906	0.248618495405	Vadim Borisov, 2026.
30	907	0.248619164778	Vadim Borisov, 2026.
30	908	0.248627662338	Vadim Borisov, 2026.
30	909	0.248680918169	Azmi C. Özgen, 2026.
30	910	0.248734479510	Vadim Borisov, 2026.
30	912	0.248737083690	Vadim Borisov, 2026.
30	913	0.248742882666	Vadim Borisov, 2026.
30	914	0.248766101768	Azmi C. Özgen, 2026.
30	915	0.248778040892	Vadim Borisov, 2026.
30	916	0.248781886213	Pavlos Moros, 2026.
30	917	0.248822091021	Pavlos Moros, 2026.
30	918	0.248830307463	Pavlos Moros, 2026.
30	919	0.248839453479	Pavlos Moros, 2026.
30	920	0.248850678834	Pavlos Moros, 2026.
30	921	0.248859603583	Pavlos Moros, 2026.
30	922	0.248870588671	Pavlos Moros, 2026.
30	923	0.248882952356	Vadim Borisov, 2026.
30	924	0.248897594577	Pavlos Moros, 2026.
30	925	0.248904985431	Vadim Borisov, 2026.
30	926	0.248909743656	Vadim Borisov, 2026.
30	927	0.248912833187	Vadim Borisov, 2026.
30	928	0.248912938393	Vadim Borisov, 2026.
30	929	0.248916114779	Pavlos Moros, 2026.
30	930	0.248930405422	Vadim Borisov, 2026.
30	931	0.248930573849	Pavlos Moros, 2026.
30	932	0.248941309994	Vadim Borisov, 2026.
30	933	0.248944037555	Pavlos Moros, 2026.
30	934	0.248956333231	Pavlos Moros, 2026.
30	935	0.248968223702	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	936	0.248980896007	Vadim Borisov, 2026.
30	937	0.248983559165	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	938	0.248996115780	Vadim Borisov, 2026.
30	939	0.249007151338	Vadim Borisov, 2026.
30	940	0.249020759372	Pavlos Moros, 2026.
30	941	0.249035921505	Vadim Borisov, 2026.
30	942	0.249039214656	Vadim Borisov, 2026.
30	943	0.249052853749	Vadim Borisov, 2026.
30	944	0.249074689161	Vadim Borisov, 2026.
30	945	0.249082488815	Vadim Borisov, 2026.
30	946	0.249100508393	Vadim Borisov, 2026.
30	947	0.249100710237	Vadim Borisov, 2026.
30	948	0.249100852743	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	949	0.249113091924	Vadim Borisov, 2026.
30	950	0.249114011104	Vadim Borisov, 2026.
30	951	0.249129543556	Vadim Borisov, 2026.
30	952	0.249155242629	Vadim Borisov, 2026.
30	953	0.249155432527	Vadim Borisov, 2026.
30	954	0.249170595092	Azmi C. Özgen, 2026.
30	955	0.249212049029	Vadim Borisov, 2026.
30	956	0.249215411441	Vadim Borisov, 2026.
30	957	0.249222650785	Azmi C. Özgen, 2026.
30	958	0.249246478759	Azmi C. Özgen, 2026.
30	959	0.249280639846	Azmi C. Özgen, 2026.
30	960	0.249291207147	Vadim Borisov, 2026.
30	961	0.249291994665	Vadim Borisov, 2026.
30	962	0.249294344294	Vadim Borisov, 2026.
30	963	0.249294694140	Vadim Borisov, 2026.
30	964	0.249295220840	Vadim Borisov, 2026.
30	965	0.249298162079	Vadim Borisov, 2026.
30	966	0.249299849211	Vadim Borisov, 2026.
30	967	0.249307859615	Vadim Borisov, 2026.
30	968	0.249311551783	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	969	0.249327260688	Vadim Borisov, 2026.
30	970	0.249333220395	Vadim Borisov, 2026.
30	971	0.249333741509	Azmi C. Özgen, 2026.
30	972	0.249361251815	Vadim Borisov, 2026.
30	973	0.249368498592	Vadim Borisov, 2026.
30	974	0.249381610920	Vadim Borisov, 2026.
30	975	0.249384346218	Azmi C. Özgen, 2026.
30	976	0.249409147509	Vadim Borisov, 2026.
30	977	0.249423799705	Vadim Borisov, 2026.
30	978	0.249426515729	Vadim Borisov, 2026.
30	979	0.249427818437	Vadim Borisov, 2026.
30	980	0.249433211031	Vadim Borisov, 2026.
30	981	0.249450773342	Vadim Borisov, 2026.
30	982	0.249454840033	Vadim Borisov, 2026.
30	983	0.249454954243	Azmi C. Özgen, 2026.
30	984	0.249474809396	Vadim Borisov, 2026.
30	985	0.249494987497	Vadim Borisov, 2026.
30	987	0.249500349306	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	989	0.249500351107	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	990	0.249510092665	Vadim Borisov, 2026.
30	991	0.249510388584	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	992	0.249515503277	Azmi C. Özgen, 2026.
30	993	0.249537787096	Vadim Borisov, 2026.
30	994	0.249543255369	Vadim Borisov, 2026.
30	995	0.249545452735	Vadim Borisov, 2026.
30	996	0.249554160194	Vadim Borisov, 2026.
30	997	0.249558599293	Vadim Borisov, 2026.
30	998	0.249560715047	Vadim Borisov, 2026.
30	999	0.249562123198	Vadim Borisov, 2026.
30	1000	0.249562599427	Vadim Borisov, 2026.
30	1001	0.249562760862	Vadim Borisov, 2026.
30	1002	0.249563032784	Vadim Borisov, 2026.
30	1003	0.249712464634	Vadim Borisov, 2026.
30	1004	0.249713785746	Vadim Borisov, 2026.
30	1005	0.249713878556	Vadim Borisov, 2026.
30	1006	0.249723494195	Vadim Borisov, 2026.
30	1007	0.249731930085	Vadim Borisov, 2026.
30	1008	0.249734907331	Vadim Borisov, 2026.
30	1009	0.249738992992	Vadim Borisov, 2026.
30	1010	0.249739868781	Vadim Borisov, 2026.
30	1011	0.249741512240	Vadim Borisov, 2026.
30	1012	0.249742978758	Vadim Borisov, 2026.
30	1013	0.249743143597	Azmi C. Özgen, 2026.
30	1014	0.249755925788	Vadim Borisov, 2026.
30	1015	0.249764622500	Vadim Borisov, 2026.
30	1016	0.249764639627	Vadim Borisov, 2026.
30	1017	0.249805201969	Vadim Borisov, 2026.
30	1018	0.249805242058	Vadim Borisov, 2026.
30	1019	0.249807376036	Vadim Borisov, 2026.
30	1020	0.249808528931	Vadim Borisov, 2026.
30	1021	0.249808638212	Vadim Borisov, 2026.
30	1022	0.249810499618	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
30	1023	0.249810559742	Vadim Borisov, 2026.
30	1024	0.249811498294	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	63	0.026092422671	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $26071 x^{3} - 961 x^{2} - 31 x + 1$
31	64	0.030322662292	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	65	0.037040514725	Christopher Smolen, 2026.
31	66	0.037249051133	Henry Cohn, 2026.
31	67	0.038109704996	Henry Cohn, 2026.
31	68	0.041075532616	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	69	0.043092400031	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	70	0.043156377747	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	71	0.044029001585	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	72	0.044564016321	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	73	0.046872508016	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	74	0.047441297082	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	75	0.050052417828	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	76	0.050583924084	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	77	0.051425063888	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	78	0.055152987826	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	79	0.056809635566	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	80	0.058210793301	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	81	0.059519854799	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	82	0.060853400475	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	83	0.061582731661	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	84	0.062187218111	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	85	0.063438707260	Azmi C. Özgen, 2026.
31	86	0.064362068208	Henry Cohn, 2026.
31	87	0.065597463702	Azmi C. Özgen, 2026.
31	88	0.067035098470	Azmi C. Özgen, 2026.
31	89	0.068505789160	Arhan Canli, 2026.
31	90	0.069720204889	Arhan Canli, 2026.
31	91	0.070915695915	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	92	0.071760316922	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	93	0.072795558071	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	94	0.073167668548	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	95	0.074047778646	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	96	0.074288475351	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	97	0.074605482179	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	98	0.076256749092	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	99	0.076842236854	Christopher Smolen, 2026.
31	100	0.076902253773	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	101	0.076929383285	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	102	0.077131921308	Christopher Smolen, 2026.
31	103	0.077229468685	Christopher Smolen, 2026.
31	104	0.077329823942	Christopher Smolen, 2026.
31	105	0.077802575827	Christopher Smolen, 2026.
31	106	0.078186704237	Christopher Smolen, 2026.
31	107	0.078393751519	Christopher Smolen, 2026.
31	108	0.079505765564	Azmi C. Özgen, 2026.
31	109	0.079671093945	Christopher Smolen, 2026.
31	110	0.080208248533	Azmi C. Özgen, 2026.
31	111	0.080609062503	Christopher Smolen, 2026.
31	112	0.080705670377	Christopher Smolen, 2026.
31	113	0.081243640518	Azmi C. Özgen, 2026.
31	114	0.081640021319	Vadim Borisov, 2026.
31	115	0.082043429980	Christopher Smolen, 2026.
31	117	0.083333333334	Henry Cohn and Ilmari Vahteristo, 2026. $12 x - 1$
31	120	0.084959387951	Henry Cohn, 2026. $115 x^{2} + 2 x - 1$
31	121	0.087116176625	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	122	0.087169389827	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	123	0.088359393816	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	124	0.088576639166	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	125	0.088958387187	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	126	0.089575387152	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	127	0.089599225623	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	128	0.089804123720	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	129	0.090377510283	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	130	0.090499560248	Christopher Smolen, 2026.
31	131	0.090712237595	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	132	0.091043641431	Christopher Smolen, 2026.
31	133	0.092202013141	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	134	0.093655093227	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	135	0.094003199532	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	136	0.094800816343	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	137	0.094805736174	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	138	0.094828259048	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	139	0.094912385422	Christopher Smolen, 2026.
31	140	0.095203973700	Christopher Smolen, 2026.
31	141	0.095375293779	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	142	0.095516728140	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	143	0.095628313571	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	144	0.096786288000	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	145	0.097077241294	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	146	0.097123845858	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	147	0.097881679938	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	148	0.099069163988	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	149	0.101300319632	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	150	0.103421955646	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	151	0.104379913165	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
31	152	0.107065892498	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	153	0.107454098993	Vadim Borisov, 2026.
31	154	0.108217357496	Vadim Borisov, 2026.
31	155	0.109449362262	Vadim Borisov, 2026.
31	156	0.109606200637	Vadim Borisov, 2026.
31	157	0.109930165873	Vadim Borisov, 2026.
31	158	0.110345909008	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	159	0.110391949789	Christopher Smolen, 2026.
31	160	0.110974351408	Christopher Smolen, 2026.
31	161	0.111463185662	Vadim Borisov, 2026.
31	162	0.111916852110	Vadim Borisov, 2026.
31	163	0.113039185484	Vadim Borisov, 2026.
31	164	0.113819959936	Vadim Borisov, 2026.
31	165	0.114203549874	Vadim Borisov, 2026.
31	166	0.115441092776	Vadim Borisov, 2026.
31	167	0.116345347375	Vadim Borisov, 2026.
31	168	0.117274732821	Vadim Borisov, 2026.
31	169	0.118249836423	Vadim Borisov, 2026.
31	170	0.119251077384	Vadim Borisov, 2026.
31	171	0.119940509010	Vadim Borisov, 2026.
31	172	0.121224936334	Vadim Borisov, 2026.
31	173	0.122320078708	Vadim Borisov, 2026.
31	174	0.123626165220	Vadim Borisov, 2026.
31	175	0.124753326706	Christopher Smolen, 2026.
31	176	0.125599790950	Vadim Borisov, 2026.
31	177	0.126340468045	Vadim Borisov, 2026.
31	178	0.127037783709	Vadim Borisov, 2026.
31	179	0.127657930090	Vadim Borisov, 2026.
31	180	0.127763108434	Vadim Borisov, 2026.
31	181	0.127936589511	Vadim Borisov, 2026.
31	182	0.127977200222	Vadim Borisov, 2026.
31	183	0.128086927667	Vadim Borisov, 2026.
31	184	0.128135016942	Vadim Borisov, 2026.
31	185	0.128235500723	Vadim Borisov, 2026.
31	186	0.128235799841	Vadim Borisov, 2026.
31	187	0.128235849610	Vadim Borisov, 2026.
31	188	0.128235978034	Vadim Borisov, 2026.
31	189	0.128236032347	Vadim Borisov, 2026.
31	190	0.128236103710	Henry Cohn, 2026.
31	191	0.128238148236	Vadim Borisov, 2026.
31	192	0.128238242450	Christopher Smolen, 2026.
31	193	0.128238399855	Christopher Smolen, 2026.
31	194	0.128238462151	Christopher Smolen, 2026.
31	195	0.128238519499	Vadim Borisov, 2026.
31	196	0.128238553222	Christopher Smolen, 2026.
31	197	0.128238644859	Vadim Borisov, 2026.
31	198	0.128238658963	Vadim Borisov, 2026.
31	199	0.128238662805	Vadim Borisov, 2026.
31	200	0.128238676090	Christopher Smolen, 2026.
31	206	0.128238684469	Henry Cohn, 2026. $92 x^{2} - 4 x - 1$
31	207	0.128398285812	Christopher Smolen, 2026.
31	208	0.130789421108	Azmi C. Özgen, 2026.
31	209	0.131581671021	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	210	0.132066699633	Vadim Borisov, 2026.
31	211	0.132067369410	Christopher Smolen, 2026.
31	212	0.133196820563	Azmi C. Özgen, 2026.
31	213	0.134765245809	Azmi C. Özgen, 2026.
31	214	0.136133395356	Vadim Borisov, 2026.
31	215	0.136958450055	Vadim Borisov, 2026.
31	216	0.137880808612	Azmi C. Özgen, 2026.
31	217	0.139001764613	Azmi C. Özgen, 2026.
31	218	0.140297936455	Azmi C. Özgen, 2026.
31	219	0.141522186371	Vadim Borisov, 2026.
31	220	0.141705746827	Vadim Borisov, 2026.
31	221	0.141732572303	Christopher Smolen, 2026.
31	222	0.141928880782	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	223	0.142062172028	Vadim Borisov, 2026.
31	224	0.142067736484	Christopher Smolen, 2026.
31	225	0.142326553210	Vadim Borisov, 2026.
31	226	0.142579848046	Azmi C. Özgen, 2026.
31	242	0.142857142858	Henry Cohn and Ilmari Vahteristo, 2026. $7 x - 1$
31	243	0.146164306778	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	244	0.146429467748	Vadim Borisov, 2026.
31	245	0.146480698485	Vadim Borisov, 2026.
31	246	0.146643283253	Christopher Smolen, 2026.
31	247	0.146770268365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	248	0.146823236663	Christopher Smolen, 2026.
31	249	0.147061754239	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	250	0.147143538345	Christopher Smolen, 2026.
31	251	0.147192717506	Christopher Smolen, 2026.
31	252	0.147269464389	Christopher Smolen, 2026.
31	253	0.147443776321	Christopher Smolen, 2026.
31	254	0.147525775907	Christopher Smolen, 2026.
31	255	0.147597020911	Christopher Smolen, 2026.
31	256	0.147725951933	Christopher Smolen, 2026.
31	257	0.147905734270	Christopher Smolen, 2026.
31	258	0.148252993651	Vadim Borisov, 2026.
31	259	0.148593550089	Vadim Borisov, 2026.
31	260	0.148595215405	Christopher Smolen, 2026.
31	261	0.148606931201	Christopher Smolen, 2026.
31	262	0.149039322307	Christopher Smolen, 2026.
31	263	0.149255807666	Azmi C. Özgen, 2026.
31	264	0.149658831018	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	265	0.150066233148	Christopher Smolen, 2026.
31	266	0.150501486248	Azmi C. Özgen, 2026.
31	267	0.150575139074	Azmi C. Özgen, 2026.
31	268	0.150895101401	Azmi C. Özgen, 2026.
31	269	0.151399010216	Azmi C. Özgen, 2026.
31	270	0.151940976019	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	271	0.152091246782	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	272	0.152970874049	Christopher Smolen, 2026.
31	273	0.154262758798	Azmi C. Özgen, 2026.
31	274	0.154445131501	Azmi C. Özgen, 2026.
31	275	0.154517563964	Azmi C. Özgen, 2026.
31	276	0.155392959539	Azmi C. Özgen, 2026.
31	277	0.155575219844	Christopher Smolen, 2026.
31	278	0.156409495275	Azmi C. Özgen, 2026.
31	279	0.156740150569	Azmi C. Özgen, 2026.
31	280	0.157472765679	Azmi C. Özgen, 2026.
31	281	0.158198174694	Azmi C. Özgen, 2026.
31	282	0.158771517819	Azmi C. Özgen, 2026.
31	283	0.159108593720	Azmi C. Özgen, 2026.
31	284	0.159472795335	Azmi C. Özgen, 2026.
31	285	0.160030914908	Azmi C. Özgen, 2026.
31	286	0.160424015135	Azmi C. Özgen, 2026.
31	287	0.160984997814	Azmi C. Özgen, 2026.
31	288	0.161565599685	Vadim Borisov, 2026.
31	289	0.161646232773	Vadim Borisov, 2026.
31	290	0.161685775114	Vadim Borisov, 2026.
31	291	0.161701213533	Vadim Borisov, 2026.
31	292	0.161727526336	Vadim Borisov, 2026.
31	293	0.161775682759	Vadim Borisov, 2026.
31	294	0.161790984952	Vadim Borisov, 2026.
31	295	0.161809171741	Pavlos Moros, 2026.
31	296	0.161848724516	Vadim Borisov, 2026.
31	297	0.161889557173	Vadim Borisov, 2026.
31	298	0.161939727700	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	299	0.161995497704	Christopher Smolen, 2026.
31	300	0.162103498027	Christopher Smolen, 2026.
31	301	0.162136073328	Azmi C. Özgen, 2026.
31	302	0.162279414139	Azmi C. Özgen, 2026.
31	303	0.162438525509	Azmi C. Özgen, 2026.
31	304	0.162481500044	Azmi C. Özgen, 2026.
31	305	0.162717677309	Azmi C. Özgen, 2026.
31	306	0.162870458920	Vadim Borisov, 2026.
31	307	0.162905701959	Azmi C. Özgen, 2026.
31	308	0.162924332929	Christopher Smolen, 2026.
31	309	0.163175839794	Azmi C. Özgen, 2026.
31	310	0.163324510055	Azmi C. Özgen, 2026.
31	311	0.163415986176	Vadim Borisov, 2026.
31	312	0.163510806725	Christopher Smolen, 2026.
31	313	0.163579990841	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	314	0.163798896796	Azmi C. Özgen, 2026.
31	315	0.163842837591	Azmi C. Özgen, 2026.
31	316	0.163884414425	Azmi C. Özgen, 2026.
31	317	0.164008157512	Azmi C. Özgen, 2026.
31	318	0.164042271277	Vadim Borisov, 2026.
31	319	0.164151976424	Vadim Borisov, 2026.
31	320	0.164264046796	Azmi C. Özgen, 2026.
31	321	0.164341315006	Vadim Borisov, 2026.
31	322	0.164425951070	Vadim Borisov, 2026.
31	323	0.164464116590	Azmi C. Özgen, 2026.
31	324	0.164626887434	Azmi C. Özgen, 2026.
31	325	0.164653294854	Azmi C. Özgen, 2026.
31	326	0.164703508305	Azmi C. Özgen, 2026.
31	327	0.164792941265	Vadim Borisov, 2026.
31	328	0.164926727862	Azmi C. Özgen, 2026.
31	329	0.165038954682	Azmi C. Özgen, 2026.
31	330	0.165127844140	Azmi C. Özgen, 2026.
31	331	0.165180903465	Azmi C. Özgen, 2026.
31	332	0.165206280797	Azmi C. Özgen, 2026.
31	333	0.165302565004	Azmi C. Özgen, 2026.
31	334	0.165428241181	Azmi C. Özgen, 2026.
31	335	0.165523573092	Azmi C. Özgen, 2026.
31	336	0.165558394453	Azmi C. Özgen, 2026.
31	337	0.165745359338	Vadim Borisov, 2026.
31	338	0.165847809073	Azmi C. Özgen, 2026.
31	339	0.165993069003	Azmi C. Özgen, 2026.
31	340	0.166121011088	Vadim Borisov, 2026.
31	341	0.166172588412	Vadim Borisov, 2026.
31	342	0.166366059196	Azmi C. Özgen, 2026.
31	343	0.166487413461	Vadim Borisov, 2026.
31	344	0.166529670065	Vadim Borisov, 2026.
31	351	0.166666666667	Kevin Li, 2026. $6 x - 1$
31	361	0.166666666667	Henry Cohn, 2026. $6 x - 1$
31	362	0.166695834939	Vadim Borisov, 2026.
31	365	0.166735343017	Vadim Borisov, 2026.
31	366	0.166735419208	Vadim Borisov, 2026.
31	367	0.166735719203	Christopher Smolen, 2026.
31	368	0.166825436147	Vadim Borisov, 2026.
31	369	0.166825654180	Azmi C. Özgen, 2026.
31	370	0.166931949608	Christopher Smolen, 2026.
31	371	0.167128620738	Vadim Borisov, 2026.
31	372	0.167600182340	Vadim Borisov, 2026.
31	373	0.167965093827	Azmi C. Özgen, 2026.
31	374	0.168174009639	Azmi C. Özgen, 2026.
31	375	0.169809461944	Azmi C. Özgen, 2026.
31	376	0.170772126077	Azmi C. Özgen, 2026.
31	377	0.171014957747	Vadim Borisov, 2026.
31	378	0.171780310139	Vadim Borisov, 2026.
31	379	0.172388391583	Azmi C. Özgen, 2026.
31	380	0.172918077957	Vadim Borisov, 2026.
31	381	0.172947453430	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	382	0.174228556949	Azmi C. Özgen, 2026.
31	383	0.174630984776	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	384	0.175151261636	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	385	0.175483506329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	386	0.176200555649	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	387	0.176529349974	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	388	0.176940184739	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	389	0.177160443004	Christopher Smolen, 2026.
31	390	0.178693806895	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	391	0.179458219904	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	392	0.179991436806	Vadim Borisov, 2026.
31	393	0.181271172632	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	394	0.181670306047	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	395	0.181818203055	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	396	0.182251246793	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	397	0.182638331866	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	398	0.182891709125	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	400	0.183521095679	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	401	0.184313426085	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	402	0.184731104610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	404	0.185134313829	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	405	0.185603586025	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	406	0.186165601920	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	408	0.186382071866	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	409	0.186959917443	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	410	0.187172234173	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	412	0.187238257470	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	413	0.187680861329	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	414	0.188083662702	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	416	0.188182995106	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	417	0.188602902031	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	418	0.188880866790	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	419	0.189186877841	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	420	0.189222655394	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	421	0.189480916056	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	422	0.189774375231	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	424	0.190045898340	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	425	0.190248572466	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	427	0.190635341365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	428	0.190806406862	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	429	0.191033613221	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	432	0.191143422857	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	433	0.191231647971	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	436	0.191821171357	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	437	0.193304008389	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	438	0.193304015389	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	439	0.193475236143	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	473	0.194630872484	Henry Cohn, 2026. $149 x - 29$
31	474	0.194790626576	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	479	0.196885786347	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	480	0.197463903354	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	481	0.197528117416	Azmi C. Özgen, 2026.
31	484	0.197640238476	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	485	0.197874083867	Vadim Borisov, 2026.
31	486	0.197874109510	Vadim Borisov, 2026.
31	487	0.197874119814	Vadim Borisov, 2026.
31	488	0.197874119955	Vadim Borisov, 2026.
31	489	0.197874120089	Vadim Borisov, 2026.
31	490	0.197874123167	Vadim Borisov, 2026.
31	491	0.197874123788	Vadim Borisov, 2026.
31	492	0.197874126959	Christopher Smolen, 2026.
31	493	0.198082651935	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	494	0.198104342444	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	495	0.198203587115	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	496	0.198269344930	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	499	0.198324488684	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	500	0.198359838866	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	501	0.198431720360	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	503	0.198641452196	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	504	0.198642114310	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	505	0.198642661049	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	506	0.198642691339	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	507	0.198643680603	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	508	0.198779400290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	509	0.198831819943	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	513	0.198858670497	Vadim Borisov, 2026.
31	514	0.198858698856	Christopher Smolen, 2026.
31	515	0.198957479180	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	516	0.198989321656	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	517	0.199006042974	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	518	0.199032439796	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	519	0.199101123882	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	520	0.199125719158	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	521	0.199168548710	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	522	0.199185771748	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	523	0.199227124977	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	524	0.199243099165	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	526	0.199251149406	Benjamin Meadows, packing-records: candidate improvements to seven record tables for packing, energy and Thomson problems, version 1.3, 2026, doi:10.5281/zenodo.24046261.
31	527	0.199272461108	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	528	0.199282744155	Pavlos Moros, 2026.
31	529	0.199286792962	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	530	0.199310502701	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	531	0.199315512723	Vadim Borisov, 2026.
31	532	0.199318241345	Vadim Borisov, 2026.
31	533	0.199327464813	Azmi C. Özgen, 2026.
31	534	0.199352491128	Vadim Borisov, 2026.
31	535	0.199358216327	Vadim Borisov, 2026.
31	536	0.199380169404	Vadim Borisov, 2026.
31	537	0.199386115996	Azmi C. Özgen, 2026.
31	538	0.199417109356	Azmi C. Özgen, 2026.
31	539	0.199435292788	Azmi C. Özgen, 2026.
31	540	0.199453275231	Vadim Borisov, 2026.
31	541	0.199477851590	Vadim Borisov, 2026.
31	542	0.199483537981	Vadim Borisov, 2026.
31	543	0.199483924957	Vadim Borisov, 2026.
31	544	0.199513132220	Vadim Borisov, 2026.
31	545	0.199527306762	Azmi C. Özgen, 2026.
31	546	0.199540463911	Vadim Borisov, 2026.
31	547	0.199569506918	Vadim Borisov, 2026.
31	548	0.199579209537	Vadim Borisov, 2026.
31	549	0.199592825612	Vadim Borisov, 2026.
31	550	0.199594012454	Vadim Borisov, 2026.
31	551	0.199603773556	Azmi C. Özgen, 2026.
31	552	0.199629240534	Vadim Borisov, 2026.
31	553	0.199638829772	Vadim Borisov, 2026.
31	554	0.199638866783	Vadim Borisov, 2026.
31	555	0.199647691402	Azmi C. Özgen, 2026.
31	556	0.199665253235	Vadim Borisov, 2026.
31	557	0.199670469583	Azmi C. Özgen, 2026.
31	558	0.199687730313	Vadim Borisov, 2026.
31	559	0.199688715474	Vadim Borisov, 2026.
31	560	0.199703980767	Vadim Borisov, 2026.
31	561	0.199711700732	Vadim Borisov, 2026.
31	562	0.199717843709	Vadim Borisov, 2026.
31	563	0.199718377766	Azmi C. Özgen, 2026.
31	564	0.199728637524	Vadim Borisov, 2026.
31	565	0.199728671986	Vadim Borisov, 2026.
31	566	0.199752162090	Vadim Borisov, 2026.
31	567	0.199752572218	Vadim Borisov, 2026.
31	568	0.199759336392	Vadim Borisov, 2026.
31	569	0.199763152109	Vadim Borisov, 2026.
31	570	0.199765605415	Vadim Borisov, 2026.
31	571	0.199765886001	Vadim Borisov, 2026.
31	572	0.199779636937	Vadim Borisov, 2026.
31	573	0.199780522912	Vadim Borisov, 2026.
31	574	0.199804629895	Vadim Borisov, 2026.
31	575	0.199807369454	Vadim Borisov, 2026.
31	576	0.199807401752	Vadim Borisov, 2026.
31	577	0.199821851534	Vadim Borisov, 2026.
31	578	0.199823653366	Vadim Borisov, 2026.
31	579	0.199824422170	Vadim Borisov, 2026.
31	580	0.199824954344	Vadim Borisov, 2026.
31	581	0.199831730813	Vadim Borisov, 2026.
31	582	0.199844106560	Vadim Borisov, 2026.
31	583	0.199844152732	Azmi C. Özgen, 2026.
31	584	0.199856242877	Vadim Borisov, 2026.
31	585	0.199856569903	Vadim Borisov, 2026.
31	688	0.2	Henry Cohn, 2026. $5 x - 1$
31	696	0.2	Azmi C. Özgen, 2026. $5 x - 1$
31	697	0.207548895194	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	698	0.212854172713	Vadim Borisov, 2026.
31	700	0.216255777201	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	701	0.218922711280	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	702	0.219059913304	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	703	0.219144799090	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	704	0.219191466343	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	705	0.219192331062	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	706	0.220050412192	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	707	0.220057492774	Vadim Borisov, 2026.
31	708	0.220059244354	Christopher Smolen, 2026.
31	709	0.220400548732	Henry Cohn, 2026.
31	710	0.221369808805	Azmi C. Özgen, 2026.
31	711	0.221647377862	Azmi C. Özgen, 2026.
31	712	0.221895522686	Azmi C. Özgen, 2026.
31	713	0.222134250241	Azmi C. Özgen, 2026.
31	714	0.222428077578	Azmi C. Özgen, 2026.
31	715	0.222564026432	Vadim Borisov, 2026.
31	716	0.222568949716	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	717	0.222575388164	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
31	718	0.223509600347	Azmi C. Özgen, 2026.
31	719	0.223758327254	Azmi C. Özgen, 2026.
31	720	0.223986389135	Azmi C. Özgen, 2026.
31	721	0.224201432861	Vadim Borisov, 2026.
31	722	0.224541782611	Vadim Borisov, 2026.
31	723	0.224685689536	Vadim Borisov, 2026.
31	724	0.225033104715	Vadim Borisov, 2026.
31	725	0.225177398909	Azmi C. Özgen, 2026.
31	726	0.225438626923	Vadim Borisov, 2026.
31	1024	0.225806451613	Kevin Li, 2026. $31 x - 7$
32	65	0.025347196752	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $28800 x^{3} - 1024 x^{2} - 32 x + 1$
32	66	0.029428688951	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	67	0.036050731887	Henry Cohn, 2026.
32	68	0.036921898559	Henry Cohn, 2026.
32	69	0.037652090605	Henry Cohn, 2026.
32	70	0.040021862884	Vadim Borisov, 2026.
32	71	0.042706545493	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	72	0.042798170341	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	73	0.043467269975	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	74	0.043761897420	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	75	0.046379356397	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	76	0.046402334547	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	77	0.048469763910	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	78	0.049325951233	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	79	0.050766858052	Christopher Smolen, 2026.
32	80	0.053536439382	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	81	0.055107204404	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	82	0.056480445570	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	83	0.057848022736	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	84	0.058871093303	Arhan Canli, 2026.
32	85	0.060305120262	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	86	0.061513234655	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	87	0.061570565029	Christopher Smolen, 2026.
32	88	0.062777635981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	89	0.063491952273	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	90	0.065174391708	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	91	0.066911028790	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	92	0.067975618109	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	93	0.068547238089	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	94	0.069628455890	Christopher Smolen, 2026.
32	95	0.069784494914	Christopher Smolen, 2026.
32	96	0.069869585150	Christopher Smolen, 2026.
32	97	0.070666286606	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	98	0.070821861473	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	99	0.071000311757	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	100	0.071062951170	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	101	0.074910052250	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	102	0.076136903296	Vadim Borisov, 2026.
32	103	0.076657591236	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	104	0.076816334352	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	105	0.076944345885	Vadim Borisov, 2026.
32	106	0.076944364443	Henry Cohn, 2026.
32	107	0.077283621510	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	108	0.077420633437	Henry Cohn, 2026.
32	109	0.077691537391	Christopher Smolen, 2026.
32	110	0.077978411426	Christopher Smolen, 2026.
32	111	0.078854823868	Azmi C. Özgen, 2026.
32	112	0.078983053821	Azmi C. Özgen, 2026.
32	113	0.079889335517	Christopher Smolen, 2026.
32	114	0.080426799269	Vadim Borisov, 2026.
32	115	0.080579299150	Christopher Smolen, 2026.
32	116	0.080687246796	Azmi C. Özgen, 2026.
32	117	0.080794092724	Christopher Smolen, 2026.
32	118	0.081128936404	Azmi C. Özgen, 2026.
32	119	0.082491549310	Azmi C. Özgen, 2026.
32	120	0.083327789093	Christopher Smolen, 2026.
32	121	0.083328671644	Christopher Smolen, 2026.
32	122	0.083641862965	Christopher Smolen, 2026.
32	123	0.084399945401	Christopher Smolen, 2026.
32	124	0.085078021793	Christopher Smolen, 2026.
32	125	0.085761443449	Christopher Smolen, 2026.
32	126	0.086637309650	Vadim Borisov, 2026.
32	127	0.087324784170	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	128	0.087334321254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	129	0.087379317103	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	130	0.087432464289	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	131	0.087494908876	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	132	0.088473191143	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	133	0.089357358433	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	134	0.089446066631	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	135	0.090077107899	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	136	0.090627951671	Christopher Smolen, 2026.
32	137	0.091607048501	Henry Cohn, 2026.
32	138	0.092489592149	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	139	0.092507950060	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	140	0.092897229264	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	141	0.092915396551	Christopher Smolen, 2026.
32	142	0.093367084115	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	143	0.093547288272	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	144	0.093674956853	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	145	0.093867205293	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	146	0.094062256445	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	147	0.094277966689	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	148	0.094571371697	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	149	0.094740615043	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	150	0.096193603075	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	151	0.096698833981	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	152	0.097435930170	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	153	0.099719234877	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	154	0.100548706284	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	155	0.100944452121	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	156	0.101437847245	Ilmari Vahteristo, New spherical codes by tuning an annealing solver, preprint, 2026, arXiv:2610.19988.
32	157	0.104335997468	Vadim Borisov, 2026.
32	158	0.104749756455	Vadim Borisov, 2026.
32	159	0.105409294168	Vadim Borisov, 2026.
32	160	0.105948110059	Vadim Borisov, 2026.
32	161	0.106890067164	Vadim Borisov, 2026.
32	162	0.108159588381	Vadim Borisov, 2026.
32	163	0.108855126647	Christopher Smolen, 2026.
32	164	0.109435789638	Vadim Borisov, 2026.
32	165	0.110037685150	Vadim Borisov, 2026.
32	166	0.110611236025	Vadim Borisov, 2026.
32	167	0.111402228463	Vadim Borisov, 2026.
32	168	0.112036092994	Vadim Borisov, 2026.
32	169	0.112674561694	Azmi C. Özgen, 2026.
32	170	0.113492034744	Vadim Borisov, 2026.
32	171	0.114340165037	Christopher Smolen, 2026.
32	172	0.115391730412	Vadim Borisov, 2026.
32	173	0.116291117442	Vadim Borisov, 2026.
32	174	0.117020215317	Azmi C. Özgen, 2026.
32	175	0.118169589958	Vadim Borisov, 2026.
32	176	0.118961880139	Vadim Borisov, 2026.
32	177	0.119530150365	Vadim Borisov, 2026.
32	178	0.120374651863	Vadim Borisov, 2026.
32	179	0.121260549529	Vadim Borisov, 2026.
32	180	0.121942524329	Vadim Borisov, 2026.
32	181	0.122662840277	Vadim Borisov, 2026.
32	182	0.123457654005	Vadim Borisov, 2026.
32	183	0.124129795287	Christopher Smolen, 2026.
32	184	0.125007025706	Vadim Borisov, 2026.
32	185	0.125742662661	Azmi C. Özgen, 2026.
32	186	0.126189640516	Vadim Borisov, 2026.
32	187	0.126877164768	Vadim Borisov, 2026.
32	188	0.127557408822	Vadim Borisov, 2026.
32	189	0.127845529029	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	190	0.127944078701	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	191	0.127978365852	Christopher Smolen, 2026.
32	192	0.128158876582	Christopher Smolen, 2026.
32	193	0.128166773723	Christopher Smolen, 2026.
32	194	0.128170702732	Christopher Smolen, 2026.
32	195	0.128182699183	Christopher Smolen, 2026.
32	196	0.128190620398	Christopher Smolen, 2026.
32	197	0.128193864598	Christopher Smolen, 2026.
32	198	0.128203067288	Vadim Borisov, 2026.
32	199	0.128204224224	Christopher Smolen, 2026.
32	200	0.128208033576	Christopher Smolen, 2026.
32	201	0.128215853366	Christopher Smolen, 2026.
32	202	0.128223622743	Christopher Smolen, 2026.
32	203	0.128231034545	Vadim Borisov, 2026.
32	204	0.128232395091	Vadim Borisov, 2026.
32	205	0.128233799096	Christopher Smolen, 2026.
32	206	0.128234935217	Christopher Smolen, 2026.
32	207	0.128235855495	Christopher Smolen, 2026.
32	208	0.128236114623	Christopher Smolen, 2026.
32	209	0.128238173720	Christopher Smolen, 2026.
32	210	0.128238844698	Christopher Smolen, 2026.
32	211	0.128575360595	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	212	0.128579797060	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	213	0.128765404947	Azmi C. Özgen, 2026.
32	214	0.130238366852	Vadim Borisov, 2026.
32	215	0.131461198232	Vadim Borisov, 2026.
32	216	0.132046788877	Vadim Borisov, 2026.
32	217	0.132693257614	Vadim Borisov, 2026.
32	218	0.134215458744	Azmi C. Özgen, 2026.
32	219	0.134473333099	Vadim Borisov, 2026.
32	220	0.135921069592	Vadim Borisov, 2026.
32	221	0.136787492355	Vadim Borisov, 2026.
32	222	0.140241375892	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	223	0.140247146697	Vadim Borisov, 2026.
32	224	0.140247183567	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	225	0.140516957266	Vadim Borisov, 2026.
32	226	0.140639852781	Vadim Borisov, 2026.
32	227	0.140788665192	Vadim Borisov, 2026.
32	228	0.140788666214	Christopher Smolen, 2026.
32	229	0.141230606376	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	230	0.141305361095	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	231	0.141346032015	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	232	0.141377637056	Henry Cohn, 2026.
32	233	0.141624857489	Vadim Borisov, 2026.
32	234	0.141757598345	Vadim Borisov, 2026.
32	235	0.142050239011	Azmi C. Özgen, 2026.
32	236	0.142665357295	Azmi C. Özgen, 2026.
32	237	0.142733726808	Azmi C. Özgen, 2026.
32	238	0.142847558039	Christopher Smolen, 2026.
32	248	0.142857142858	Henry Cohn and Ilmari Vahteristo, 2026. $7 x - 1$
32	249	0.142864280985	Christopher Smolen, 2026.
32	250	0.142865155043	Christopher Smolen, 2026.
32	251	0.143805716007	Christopher Smolen, 2026.
32	252	0.144273841223	Christopher Smolen, 2026.
32	253	0.146225488962	Christopher Smolen, 2026.
32	254	0.146347767003	Christopher Smolen, 2026.
32	255	0.146466742015	Christopher Smolen, 2026.
32	256	0.146561719450	Christopher Smolen, 2026.
32	257	0.146567846658	Christopher Smolen, 2026.
32	258	0.146613421904	Christopher Smolen, 2026.
32	259	0.146835466398	Christopher Smolen, 2026.
32	260	0.147129298802	Christopher Smolen, 2026.
32	261	0.147283924248	Azmi C. Özgen, 2026.
32	262	0.147385475507	Vadim Borisov, 2026.
32	263	0.147934866853	Christopher Smolen, 2026.
32	264	0.147991967825	Christopher Smolen, 2026.
32	265	0.148143999721	Azmi C. Özgen, 2026.
32	266	0.148308087868	Christopher Smolen, 2026.
32	267	0.148346484464	Christopher Smolen, 2026.
32	268	0.148579724282	Christopher Smolen, 2026.
32	269	0.148900518776	Azmi C. Özgen, 2026.
32	270	0.149026725588	Christopher Smolen, 2026.
32	271	0.149328172489	Azmi C. Özgen, 2026.
32	272	0.149679402923	Christopher Smolen, 2026.
32	273	0.150387533566	Christopher Smolen, 2026.
32	274	0.150532394414	Azmi C. Özgen, 2026.
32	275	0.150890056738	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	276	0.151041557647	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	277	0.151889124243	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	278	0.151954783285	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	279	0.151991879891	Christopher Smolen, 2026.
32	281	0.153041341466	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	282	0.153237503290	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	283	0.153311293141	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	284	0.153366894633	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	285	0.154699674119	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	286	0.155064736853	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	287	0.155344720462	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	288	0.155523725238	Christopher Smolen, 2026.
32	289	0.156781247486	Azmi C. Özgen, 2026.
32	290	0.157145112209	Azmi C. Özgen, 2026.
32	291	0.157454877612	Azmi C. Özgen, 2026.
32	292	0.158167994438	Azmi C. Özgen, 2026.
32	293	0.158357521157	Azmi C. Özgen, 2026.
32	294	0.158858874266	Azmi C. Özgen, 2026.
32	295	0.159014045173	Vadim Borisov, 2026.
32	296	0.159044060734	Christopher Smolen, 2026.
32	297	0.159858922469	Azmi C. Özgen, 2026.
32	298	0.160449115601	Azmi C. Özgen, 2026.
32	299	0.160870254835	Vadim Borisov, 2026.
32	300	0.160911761468	Vadim Borisov, 2026.
32	301	0.160955785714	Henry Cohn, 2026.
32	302	0.161054811216	Vadim Borisov, 2026.
32	303	0.161202719825	Vadim Borisov, 2026.
32	304	0.161323250221	Vadim Borisov, 2026.
32	305	0.161427721442	Vadim Borisov, 2026.
32	306	0.161434562492	Vadim Borisov, 2026.
32	307	0.161557114787	Vadim Borisov, 2026.
32	308	0.161616767029	Vadim Borisov, 2026.
32	309	0.161679011140	Vadim Borisov, 2026.
32	310	0.161709195251	Christopher Smolen, 2026.
32	311	0.161787678227	Vadim Borisov, 2026.
32	312	0.161844157265	Vadim Borisov, 2026.
32	313	0.161859207904	Henry Cohn, 2026.
32	314	0.161924167481	Azmi C. Özgen, 2026.
32	315	0.161946966456	Henry Cohn, 2026.
32	316	0.162014453229	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	317	0.162040433388	Vadim Borisov, 2026.
32	318	0.162155448129	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	319	0.162226041847	Henry Cohn, 2026.
32	320	0.162266774953	Henry Cohn, 2026.
32	321	0.162303934614	Christopher Smolen, 2026.
32	322	0.162484708614	Henry Cohn, 2026.
32	323	0.162531750160	Henry Cohn, 2026.
32	324	0.162638729161	Henry Cohn, 2026.
32	325	0.162718712210	Henry Cohn, 2026.
32	326	0.162853466613	Henry Cohn, 2026.
32	327	0.162968442322	Henry Cohn, 2026.
32	328	0.163040153006	Henry Cohn, 2026.
32	329	0.163146477629	Henry Cohn, 2026.
32	330	0.163263202902	Henry Cohn, 2026.
32	331	0.163336262679	Henry Cohn, 2026.
32	332	0.163453641015	Henry Cohn, 2026.
32	333	0.163545384242	Henry Cohn, 2026.
32	334	0.163648439108	Henry Cohn, 2026.
32	335	0.163746283122	Henry Cohn, 2026.
32	336	0.163800068754	Henry Cohn, 2026.
32	337	0.163973674200	Henry Cohn, 2026.
32	338	0.164028053430	Henry Cohn, 2026.
32	339	0.164292969052	Henry Cohn, 2026.
32	340	0.164323420156	Henry Cohn, 2026.
32	341	0.164407757835	Henry Cohn, 2026.
32	342	0.164508029623	Vadim Borisov, 2026.
32	343	0.164587956667	Henry Cohn, 2026.
32	344	0.164660266937	Henry Cohn, 2026.
32	345	0.164739178458	Henry Cohn, 2026.
32	346	0.164788312157	Henry Cohn, 2026.
32	347	0.164993995226	Henry Cohn, 2026.
32	348	0.165109143217	Henry Cohn, 2026.
32	349	0.165195803715	Henry Cohn, 2026.
32	350	0.165322855767	Henry Cohn, 2026.
32	351	0.165542843661	Henry Cohn, 2026.
32	352	0.165660498754	Henry Cohn, 2026.
32	353	0.165727059723	Azmi C. Özgen, 2026.
32	354	0.165994045724	Henry Cohn, 2026.
32	355	0.166131251105	Henry Cohn, 2026.
32	356	0.166602466771	Vadim Borisov, 2026.
32	357	0.166605277633	Vadim Borisov, 2026.
32	358	0.166607809983	Henry Cohn, 2026.
32	377	0.166666666666	Henry Cohn, 2026.
32	378	0.166767669510	Azmi C. Özgen, 2026.
32	379	0.166869582379	Vadim Borisov, 2026.
32	380	0.167035018859	Vadim Borisov, 2026.
32	381	0.167482822392	Azmi C. Özgen, 2026.
32	382	0.167672949603	Vadim Borisov, 2026.
32	383	0.168016354776	Azmi C. Özgen, 2026.
32	384	0.168668308774	Azmi C. Özgen, 2026.
32	385	0.169008871614	Vadim Borisov, 2026.
32	386	0.169367698981	Vadim Borisov, 2026.
32	387	0.169529185818	Azmi C. Özgen, 2026.
32	388	0.170063909285	Vadim Borisov, 2026.
32	389	0.170845527120	Vadim Borisov, 2026.
32	390	0.170965382659	Vadim Borisov, 2026.
32	391	0.171552790702	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	392	0.171919092477	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	393	0.172170968373	Vadim Borisov, 2026.
32	394	0.172864884541	Vadim Borisov, 2026.
32	395	0.173437733496	Vadim Borisov, 2026.
32	396	0.174549272067	Vadim Borisov, 2026.
32	397	0.174954410269	Vadim Borisov, 2026.
32	398	0.175340938877	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	399	0.175752955730	Vadim Borisov, 2026.
32	400	0.176344098513	Vadim Borisov, 2026.
32	401	0.176789077954	Vadim Borisov, 2026.
32	402	0.177370055962	Vadim Borisov, 2026.
32	403	0.177745308240	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	404	0.177868944938	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	405	0.178291351891	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	406	0.179005667271	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	407	0.179498267967	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	408	0.179749853431	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	410	0.180183050295	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	411	0.180843780179	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	412	0.180978059648	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	413	0.181174572740	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	414	0.181335143787	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	415	0.181613494402	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	416	0.181693031153	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	417	0.181990901878	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	418	0.182333357611	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	419	0.182826244107	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	420	0.183363752836	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	421	0.183498292812	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	422	0.183856675710	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	423	0.183889289150	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	424	0.184097064971	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	425	0.184377350714	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	428	0.185299952638	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	429	0.185329216625	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	431	0.185831320189	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	432	0.185939539423	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	433	0.186133217135	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	434	0.186287694296	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	435	0.186469390239	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	436	0.186631990772	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	437	0.186818505365	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	438	0.186883757066	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	440	0.187333241860	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	441	0.187610003823	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	442	0.187741090669	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	443	0.187835825092	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	447	0.188533790211	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	448	0.188734071610	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	449	0.188982758611	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	450	0.189247855787	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	451	0.189450378640	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	452	0.189455884919	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	453	0.189621632449	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	454	0.189797788283	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	455	0.190067494847	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	456	0.190228976888	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	457	0.190467016335	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	458	0.190571460629	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	459	0.190727884423	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	460	0.192341896872	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	461	0.192361942228	Vadim Borisov, 2026.
32	462	0.192364208072	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	463	0.192855514965	Azmi C. Özgen, 2026.
32	464	0.192975384403	Azmi C. Özgen, 2026.
32	465	0.193130906561	Vadim Borisov, 2026.
32	466	0.193293338227	Azmi C. Özgen, 2026.
32	467	0.193386527826	Azmi C. Özgen, 2026.
32	468	0.193501491245	Azmi C. Özgen, 2026.
32	469	0.193721422917	Azmi C. Özgen, 2026.
32	470	0.193814528265	Azmi C. Özgen, 2026.
32	471	0.193877612659	Azmi C. Özgen, 2026.
32	472	0.193902734850	Azmi C. Özgen, 2026.
32	473	0.194099092681	Azmi C. Özgen, 2026.
32	474	0.194120485526	Azmi C. Özgen, 2026.
32	475	0.194268027596	Azmi C. Özgen, 2026.
32	476	0.194344222314	Azmi C. Özgen, 2026.
32	477	0.194496137494	Azmi C. Özgen, 2026.
32	478	0.194597733799	Azmi C. Özgen, 2026.
32	479	0.194648129297	Azmi C. Özgen, 2026.
32	528	0.195121951220	Henry Cohn, 2026. $41 x - 8$
32	532	0.198629636729	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	533	0.198661512795	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	534	0.198661800097	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	537	0.198667350388	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	539	0.198692358756	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	541	0.198696242449	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	543	0.198702616922	Vadim Borisov, 2026.
32	544	0.198707385534	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	545	0.198711049022	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	546	0.199250383768	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	547	0.199256633407	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	548	0.199267311737	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	549	0.199272688831	Vadim Borisov, 2026.
32	550	0.199272882471	Vadim Borisov, 2026.
32	551	0.199273527043	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	552	0.199288387864	Vadim Borisov, 2026.
32	553	0.199289134920	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	554	0.199295677711	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	555	0.199304761342	Vadim Borisov, 2026.
32	556	0.199323127360	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	557	0.199334305201	Vadim Borisov, 2026.
32	558	0.199338197783	Vadim Borisov, 2026.
32	559	0.199338229757	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	560	0.199338527961	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	561	0.199347206221	Vadim Borisov, 2026.
32	562	0.199347222672	Vadim Borisov, 2026.
32	563	0.199347228550	Vadim Borisov, 2026.
32	564	0.199347238326	Vadim Borisov, 2026.
32	565	0.199347281231	Vadim Borisov, 2026.
32	568	0.199347286425	Vadim Borisov, 2026.
32	569	0.199347345181	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	570	0.199412962940	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	571	0.199413550139	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	572	0.199413837034	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	573	0.199414008982	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	574	0.199415541081	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	575	0.199435199324	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	576	0.199455937672	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	577	0.199477061689	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	580	0.199505023057	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	583	0.199539498254	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	584	0.199549162009	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	585	0.199561936145	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	587	0.199564154399	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	588	0.199565921645	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	590	0.199579619673	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	591	0.199600793390	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	594	0.199667809342	Vadim Borisov, 2026.
32	595	0.199667920970	Vadim Borisov, 2026.
32	596	0.199671735195	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	597	0.199757546286	Vadim Borisov, 2026.
32	598	0.199800838195	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	599	0.199878822254	Vadim Borisov, 2026.
32	600	0.199881500648	Vadim Borisov, 2026.
32	601	0.199881917242	Vadim Borisov, 2026.
32	602	0.199882055285	Vadim Borisov, 2026.
32	603	0.199893523801	Vadim Borisov, 2026.
32	604	0.199893535958	Vadim Borisov, 2026.
32	605	0.199902651044	Vadim Borisov, 2026.
32	606	0.199905688333	Vadim Borisov, 2026.
32	607	0.199906010970	Vadim Borisov, 2026.
32	608	0.199906101804	Vadim Borisov, 2026.
32	609	0.199906127843	Vadim Borisov, 2026.
32	610	0.199912599434	Vadim Borisov, 2026.
32	611	0.199915459418	Vadim Borisov, 2026.
32	612	0.199920977278	Vadim Borisov, 2026.
32	613	0.199921730924	Vadim Borisov, 2026.
32	614	0.199922506625	Vadim Borisov, 2026.
32	615	0.199922984273	Vadim Borisov, 2026.
32	616	0.199923072148	Vadim Borisov, 2026.
32	617	0.199923081100	Vadim Borisov, 2026.
32	618	0.199929990578	Vadim Borisov, 2026.
32	619	0.199930013805	Vadim Borisov, 2026.
32	620	0.199940584709	Vadim Borisov, 2026.
32	704	0.2	Henry Cohn, 2026. $5 x - 1$
32	705	0.209382766930	Azmi C. Özgen, 2026.
32	706	0.212484277758	Vadim Borisov, 2026.
32	707	0.212613239777	Azmi C. Özgen, 2026.
32	708	0.212863925499	Azmi C. Özgen, 2026.
32	709	0.213058163370	Vadim Borisov, 2026.
32	710	0.213849135795	Vadim Borisov, 2026.
32	711	0.214070172892	Azmi C. Özgen, 2026.
32	712	0.214227013173	Vadim Borisov, 2026.
32	713	0.214425778126	Vadim Borisov, 2026.
32	714	0.214598849023	Vadim Borisov, 2026.
32	715	0.214739983045	Azmi C. Özgen, 2026.
32	716	0.214964717449	Vadim Borisov, 2026.
32	717	0.215179239818	Azmi C. Özgen, 2026.
32	718	0.215298746710	Vadim Borisov, 2026.
32	719	0.215307219104	Vadim Borisov, 2026.
32	720	0.215307704049	Christopher Smolen, 2026.
32	721	0.215928606093	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	722	0.215955912266	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	723	0.215956030715	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	724	0.215957420366	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	725	0.217441692943	Azmi C. Özgen, 2026.
32	726	0.217638213573	Vadim Borisov, 2026.
32	727	0.217852248064	Vadim Borisov, 2026.
32	728	0.217902634719	Azmi C. Özgen, 2026.
32	729	0.218060846456	Azmi C. Özgen, 2026.
32	730	0.218235432892	Vadim Borisov, 2026.
32	731	0.218445430311	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	732	0.218456517594	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	733	0.218470190217	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	734	0.218478249517	Vadim Borisov, 2026.
32	735	0.218478266097	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	736	0.219338714563	Vadim Borisov, 2026.
32	737	0.219338717578	Vadim Borisov, 2026.
32	738	0.219338800976	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	739	0.220352047293	Azmi C. Özgen, 2026.
32	740	0.220484704545	Vadim Borisov, 2026.
32	741	0.220850651108	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	742	0.220914708870	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	743	0.220949818657	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	744	0.220957230299	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	745	0.220965949693	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	746	0.221908201931	Vadim Borisov, 2026.
32	747	0.221990206862	Vadim Borisov, 2026.
32	748	0.222090014092	Vadim Borisov, 2026.
32	749	0.222165913421	Azmi C. Özgen, 2026.
32	750	0.223033731787	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	751	0.223050259609	Vadim Borisov, 2026.
32	752	0.223062688091	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	753	0.223069391410	Vadim Borisov, 2026.
32	754	0.223069438494	Benjamin Meadows, 2026, doi:10.5281/zenodo.23906181.
32	755	0.223757439649	Azmi C. Özgen, 2026.
32	756	0.223879316573	Vadim Borisov, 2026.
32	757	0.224032949176	Vadim Borisov, 2026.
32	758	0.224173022045	Azmi C. Özgen, 2026.
32	759	0.224998890563	Vadim Borisov, 2026.
32	760	0.225114567903	Vadim Borisov, 2026.
32	761	0.225224652051	Azmi C. Özgen, 2026.
32	762	0.225255304837	Vadim Borisov, 2026.
32	763	0.225432312917	Azmi C. Özgen, 2026.
32	764	0.225503663166	Vadim Borisov, 2026.
32	765	0.225589677603	Azmi C. Özgen, 2026.
32	1024	0.225806451613	Code with 1024 points in 31 dimensions. $31 x - 7$
52	325*	0.0625	P. J. Cameron, J. M. Goethals, and J. J. Seidel, Strongly regular graphs having strongly regular subconstituents, J. Algebra 55 (1978), 257–280, doi:10.1016/0021-8693(78)90220-X; V. I. Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Appl. Math. 29 (1992), 1–82, doi:10.1007/BF00053379. $16 x - 1$
64	4224*	0.125	V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874. $8 x - 1$