Table of spherical codes

Maintained by Henry Cohn

This data is archived at https://hdl.handle.net/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 numerically optimized codes, with cases that are known to be optimal marked with *. Each entry links to coordinates for the code. 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). The entries labeled “needs more optimization” have not fully converged to a local optimum, while most of the others probably have. 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 some polynomials too large to fit below, and upload additions or improvements here.

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. $13 x^{5} - x^{4} + 6 x^{3} + 2 x^{2} - 3 x - 1$
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 preprint.
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 preprint.
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	0.939730074191	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	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 preprint.
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	0.943652307933	James Buddenhagen and D. A. Kottwitz, 1997.
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	0.946396812867	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	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	0.952386964146	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	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	0.952998760356	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	144	0.953228658095	Henry Cohn, 2024.
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	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	147	0.954232032048	Henry Cohn, 2024.
3	148	0.954536844663	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	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	0.955934494320	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	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	0.956672380100	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	0.958127432716	Henry Cohn, 2024.
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	0.959759379334	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	169	0.960021874369	Henry Cohn, 2024.
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	0.960456779730	Henry Cohn, 2024.
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	0.960986468709	Henry Cohn, 2024.
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	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	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 listed in plain text data
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	0.962987455061	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	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	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	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	0.964893730831	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	0.965468021791	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	197	0.965672149432	Henry Cohn, 2024.
3	198	0.965829345943	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	199	0.965916228235	Henry Cohn, 2024.
3	200	0.965942282148	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	201	0.966307019072	Henry Cohn, 2024.
3	202	0.966421093222	Henry Cohn, 2024.
3	203	0.966622724376	Henry Cohn, 2024.
3	204	0.966712897537	Henry Cohn, 2024.
3	205	0.966826988724	Henry Cohn, 2024.
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	0.967822897133	Henry Cohn, 2024.
3	212	0.967927157323	Henry Cohn, 2024.
3	213	0.968163116144	Henry Cohn, 2024.
3	214	0.968277562077	Henry Cohn, 2024.
3	215	0.968453681522	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	0.968776618511	Henry Cohn, 2024.
3	218	0.968883813017	Henry Cohn, 2024.
3	219	0.969051824494	Henry Cohn, 2024.
3	220	0.969138855054	Henry Cohn, 2024.
3	221	0.969215831482	Henry Cohn, 2024.
3	222	0.969434787486	Henry Cohn, 2024.
3	223	0.969554841105	Henry Cohn, 2024.
3	224	0.969694397387	Henry Cohn, 2024.
3	225	0.969832491610	Henry Cohn, 2024.
3	226	0.969910140314	Henry Cohn, 2024.
3	227	0.970130625173	Henry Cohn, 2024.
3	228	0.970249147842	Henry Cohn, 2024.
3	229	0.970372197571	Henry Cohn, 2024.
3	230	0.970483487210	Henry Cohn, 2024.
3	231	0.970608829668	Henry Cohn, 2024.
3	232	0.970693980480	Henry Cohn, 2024.
3	233	0.970852351181	Henry Cohn, 2024.
3	234	0.970907365376	Henry Cohn, 2024.
3	235	0.971109097862	Henry Cohn, 2024.
3	236	0.971194820788	Henry Cohn, 2024.
3	237	0.971302463819	Henry Cohn, 2024.
3	238	0.971452957279	Henry Cohn, 2024.
3	239	0.971571256039	Henry Cohn, 2024.
3	240	0.971657594484	Henry Cohn, 2024.
3	241	0.971802213953	Henry Cohn, 2024.
3	242	0.971893680990	Henry Cohn, 2024.
3	243	0.971985441053	Henry Cohn, 2024.
3	244	0.972112317307	Henry Cohn, 2024.
3	245	0.972207255147	Henry Cohn, 2024.
3	246	0.972337795891	Henry Cohn, 2024.
3	247	0.972484516196	Henry Cohn, 2024.
3	248	0.972579059838	Henry Cohn, 2024.
3	249	0.972727698402	Henry Cohn, 2024.
3	250	0.972810481679	Henry Cohn, 2024.
3	251	0.972879991602	Henry Cohn, 2024.
3	252	0.973005270899	Henry Cohn, 2024.
3	253	0.973112111221	Henry Cohn, 2024.
3	254	0.973167964183	Henry Cohn, 2024.
3	255	0.973336938776	Henry Cohn, 2024.
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	0.973920872604	Henry Cohn, 2024.
3	262	0.974027125019	Henry Cohn, 2024.
3	263	0.974151459437	Henry Cohn, 2024.
3	264	0.974246953956	Henry Cohn, 2024.
3	265	0.974330655728	Henry Cohn, 2024.
3	266	0.974398321697	Henry Cohn, 2024.
3	267	0.974465987487	Henry Cohn, 2024.
3	268	0.974543890479	Henry Cohn, 2024.
3	269	0.974603593006	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 listed in plain text data
3	271	0.974808781633	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	0.975320045419	Henry Cohn, 2024.
3	277	0.975403482592	Henry Cohn, 2024.
3	278	0.975464347280	Henry Cohn, 2024.
3	279	0.975521244171	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	0.975926949121	Henry Cohn, 2024.
3	284	0.976026277163	Henry Cohn, 2024.
3	285	0.976130656685	Henry Cohn, 2024.
3	286	0.976199213799	Henry Cohn, 2024.
3	287	0.976292535597	Henry Cohn, 2024.
3	288	0.976364794706	Henry Cohn, 2024.
3	289	0.976439859800	Henry Cohn, 2024.
3	290	0.976500970455	Henry Cohn, 2024.
3	291	0.976554952830	Henry Cohn, 2024.
3	292	0.976605729892	Henry Cohn, 2024.
3	293	0.976711107353	Henry Cohn, 2024.
3	294	0.976800057925	Henry Cohn, 2024.
3	295	0.976890767575	Henry Cohn, 2024.
3	296	0.976945912178	Henry Cohn, 2024.
3	297	0.977073329897	Henry Cohn, 2024.
3	298	0.977140172393	Henry Cohn, 2024.
3	300	0.977219217071	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	301	0.977392313269	Henry Cohn, 2024.
3	302	0.977458631037	Henry Cohn, 2024.
3	303	0.977523371220	Henry Cohn, 2024.
3	304	0.977583884150	Henry Cohn, 2024.
3	305	0.977632490985	Henry Cohn, 2024.
3	306	0.977704320344	Henry Cohn, 2024.
3	307	0.977814535951	Henry Cohn, 2024.
3	308	0.977892051737	Henry Cohn, 2024.
3	309	0.977961312021	Henry Cohn, 2024.
3	310	0.978013425289	Henry Cohn, 2024.
3	311	0.978090634293	Henry Cohn, 2024.
3	312	0.978122129978	Henry Cohn, 2024.
3	313	0.978231993615	Henry Cohn, 2024.
3	314	0.978279969095	Henry Cohn, 2024.
3	315	0.978359778770	Henry Cohn, 2024.
3	316	0.978410838412	Henry Cohn, 2024.
3	317	0.978487475788	Henry Cohn, 2024.
3	318	0.978544517230	Henry Cohn, 2024.
3	319	0.978603060123	Henry Cohn, 2024.
3	320	0.978663267013	Henry Cohn, 2024.
3	321	0.978701802246	Henry Cohn, 2024.
3	322	0.978826091828	Henry Cohn, 2024.
3	323	0.978911588007	Henry Cohn, 2024.
3	324	0.978995941163	Henry Cohn, 2024.
3	325	0.979043753404	Henry Cohn, 2024.
3	326	0.979098859474	Henry Cohn, 2024.
3	327	0.979175343310	Henry Cohn, 2024.
3	328	0.979227007488	Henry Cohn, 2024.
3	329	0.979277635210	Henry Cohn, 2024.
3	330	0.979324914072	Henry Cohn, 2024.
3	331	0.979373177433	Henry Cohn, 2024.
3	332	0.979423824372	Henry Cohn, 2024.
3	333	0.979491741719	Henry Cohn, 2024.
3	334	0.979582034494	Henry Cohn, 2024.
3	335	0.979642932989	Henry Cohn, 2024.
3	336	0.979690569343	Henry Cohn, 2024.
3	337	0.979787177717	Henry Cohn, 2024.
3	338	0.979838818714	Henry Cohn, 2024.
3	339	0.979904919491	Henry Cohn, 2024.
3	340	0.979949293421	Henry Cohn, 2024.
3	341	0.979999498180	Henry Cohn, 2024.
3	342	0.980044047715	Henry Cohn, 2024.
3	343	0.980089833535	Henry Cohn, 2024.
3	344	0.980135977822	Henry Cohn, 2024.
3	345	0.980198171376	Henry Cohn, 2024.
3	346	0.980275208083	Henry Cohn, 2024.
3	347	0.980349152228	Henry Cohn, 2024.
3	348	0.980406993197	Henry Cohn, 2024.
3	349	0.980468717236	Henry Cohn, 2024.
3	350	0.980516247811	Henry Cohn, 2024.
3	351	0.980576030074	Henry Cohn, 2024.
3	352	0.980619398779	Henry Cohn, 2024.
3	353	0.980684301408	Henry Cohn, 2024.
3	354	0.980732527244	Henry Cohn, 2024.
3	355	0.980776958770	Henry Cohn, 2024.
3	356	0.980824249739	Henry Cohn, 2024.
3	357	0.980871795042	Henry Cohn, 2024.
3	358	0.980901085519	Henry Cohn, 2024.
3	359	0.980938721612	Henry Cohn, 2024.
3	360	0.980946761337	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	361	0.981100649639	Henry Cohn, 2024.
3	362	0.981170817619	Henry Cohn, 2024.
3	363	0.981225268927	Henry Cohn, 2024.
3	364	0.981276718466	Henry Cohn, 2024.
3	365	0.981317422057	Henry Cohn, 2024.
3	366	0.981371676585	Henry Cohn, 2024.
3	367	0.981414713593	Henry Cohn, 2024.
3	368	0.981467030026	Henry Cohn, 2024.
3	369	0.981501369093	Henry Cohn, 2024.
3	370	0.981559453185	Henry Cohn, 2024.
3	371	0.981613640563	Henry Cohn, 2024.
3	372	0.981659202089	Henry Cohn, 2024.
3	373	0.981715627838	Henry Cohn, 2024.
3	374	0.981743695439	Henry Cohn, 2024.
3	375	0.981792889903	Henry Cohn, 2024.
3	376	0.981848936637	Henry Cohn, 2024.
3	377	0.981891941481	Henry Cohn, 2024.
3	378	0.981926575478	Henry Cohn, 2024.
3	379	0.981965339639	Henry Cohn, 2024.
3	380	0.981969354778	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	381	0.982112878900	Henry Cohn, 2024.
3	382	0.982155902082	Henry Cohn, 2024.
3	383	0.982191165481	Henry Cohn, 2024.
3	384	0.982232298422	Henry Cohn, 2024.
3	385	0.982281435205	Henry Cohn, 2024.
3	386	0.982313990090	Henry Cohn, 2024.
3	387	0.982346497569	Henry Cohn, 2024.
3	388	0.982373183314	Henry Cohn, 2024.
3	389	0.982452801700	Henry Cohn, 2024.
3	390	0.982505534054	Henry Cohn, 2024.
3	391	0.982555955538	Henry Cohn, 2024.
3	392	0.982591195901	Henry Cohn, 2024.
3	393	0.982649357699	Henry Cohn, 2024.
3	394	0.982692375827	Henry Cohn, 2024.
3	395	0.982725465540	Henry Cohn, 2024.
3	396	0.982767271242	Henry Cohn, 2024.
3	397	0.982799147942	Henry Cohn, 2024.
3	398	0.982821049056	Henry Cohn, 2024.
3	399	0.982857394033	Henry Cohn, 2024.
3	400	0.982915172693	Henry Cohn, 2024.
3	401	0.982950664531	Henry Cohn, 2024.
3	402	0.982983355551	Henry Cohn, 2024.
3	403	0.983049964328	Henry Cohn, 2024.
3	404	0.983111162319	Henry Cohn, 2024.
3	405	0.983168565133	Henry Cohn, 2024.
3	406	0.983206265163	Henry Cohn, 2024.
3	407	0.983247933087	Henry Cohn, 2024.
3	408	0.983288123210	Henry Cohn, 2024.
3	409	0.983324857501	Henry Cohn, 2024.
3	410	0.983356947085	Henry Cohn, 2024.
3	411	0.983397760620	Henry Cohn, 2024.
3	412	0.983428600189	Henry Cohn, 2024.
3	413	0.983461427167	Henry Cohn, 2024.
3	414	0.983495155996	Henry Cohn, 2024.
3	415	0.983545319874	Henry Cohn, 2024.
3	416	0.983572356049	Henry Cohn, 2024.
3	417	0.983606629508	Henry Cohn, 2024.
3	418	0.983668285529	Henry Cohn, 2024.
3	419	0.983709311243	Henry Cohn, 2024.
3	420	0.983735772266	Henry Cohn, 2024.
3	421	0.983801876824	Henry Cohn, 2024.
3	422	0.983837084033	Henry Cohn, 2024.
3	423	0.983879327689	Henry Cohn, 2024.
3	424	0.983915009758	Henry Cohn, 2024.
3	425	0.983947724258	Henry Cohn, 2024.
3	426	0.983967656850	Henry Cohn, 2024.
3	427	0.984017759902	Henry Cohn, 2024.
3	428	0.984060532882	Henry Cohn, 2024.
3	429	0.984101619025	Henry Cohn, 2024.
3	430	0.984134891966	Henry Cohn, 2024.
3	431	0.984165514392	Henry Cohn, 2024.
3	432	0.984201636678	Henry Cohn, 2024.
3	433	0.984246511178	Henry Cohn, 2024.
3	434	0.984282456245	Henry Cohn, 2024.
3	435	0.984322511171	Henry Cohn, 2024.
3	436	0.984359381088	Henry Cohn, 2024.
3	437	0.984376596212	Henry Cohn, 2024.
3	438	0.984419779873	Henry Cohn, 2024.
3	439	0.984459277522	Henry Cohn, 2024.
3	440	0.984472421765	Henry Cohn, 2024.
3	441	0.984527980944	Henry Cohn, 2024.
3	442	0.984559589051	Henry Cohn, 2024.
3	443	0.984592266668	Henry Cohn, 2024.
3	444	0.984628415926	Henry Cohn, 2024.
3	445	0.984667372267	Henry Cohn, 2024.
3	446	0.984702068844	Henry Cohn, 2024.
3	447	0.984730509217	Henry Cohn, 2024.
3	448	0.984778913431	Henry Cohn, 2024.
3	449	0.984813716313	Henry Cohn, 2024.
3	450	0.984846922702	Henry Cohn, 2024.
3	451	0.984872959880	Henry Cohn, 2024.
3	452	0.984911000119	Henry Cohn, 2024.
3	453	0.984942286924	Henry Cohn, 2024.
3	454	0.984966631269	Henry Cohn, 2024.
3	455	0.984994478749	Henry Cohn, 2024.
3	456	0.985031017295	Henry Cohn, 2024.
3	457	0.985064695326	Henry Cohn, 2024.
3	458	0.985097884587	Henry Cohn, 2024.
3	459	0.985126768610	Henry Cohn, 2024.
3	460	0.985155490468	Henry Cohn, 2024.
3	461	0.985198380759	Henry Cohn, 2024.
3	462	0.985225068424	Henry Cohn, 2024.
3	463	0.985261648362	Henry Cohn, 2024.
3	464	0.985297019486	Henry Cohn, 2024.
3	465	0.985321750708	Henry Cohn, 2024.
3	466	0.985359897849	Henry Cohn, 2024.
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	0.985509915679	Henry Cohn, 2024.
3	472	0.985527599242	Henry Cohn, 2024.
3	473	0.985558412596	Henry Cohn, 2024.
3	474	0.985607101360	Henry Cohn, 2024.
3	475	0.985630320536	Henry Cohn, 2024.
3	476	0.985665218249	Henry Cohn, 2024.
3	477	0.985693505781	Henry Cohn, 2024.
3	478	0.985721554115	Henry Cohn, 2024.
3	479	0.985721775338	Henry Cohn, 2024.
3	480	0.985721861452	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	481	0.985812248918	Henry Cohn, 2024.
3	482	0.985842699690	Henry Cohn, 2024.
3	483	0.985872483761	Henry Cohn, 2024.
3	484	0.985900122939	Henry Cohn, 2024.
3	485	0.985924698901	Henry Cohn, 2024.
3	486	0.985950768752	Henry Cohn, 2024.
3	487	0.985985004243	Henry Cohn, 2024.
3	488	0.986009149228	Henry Cohn, 2024.
3	489	0.986026483781	Henry Cohn, 2024.
3	490	0.986063292599	Henry Cohn, 2024.
3	491	0.986099610800	Henry Cohn, 2024.
3	492	0.986121929372	Henry Cohn, 2024.
3	493	0.986156796272	Henry Cohn, 2024.
3	494	0.986186402493	Henry Cohn, 2024.
3	495	0.986213487487	Henry Cohn, 2024.
3	496	0.986246272307	Henry Cohn, 2024.
3	497	0.986267131233	Henry Cohn, 2024.
3	498	0.986298103712	Henry Cohn, 2024.
3	499	0.986323180888	Henry Cohn, 2024.
3	500	0.986349227234	Henry Cohn, 2024.
3	501	0.986372404028	Henry Cohn, 2024.
3	502	0.986403542281	Henry Cohn, 2024.
3	503	0.986428428291	Henry Cohn, 2024.
3	504	0.986455469484	Henry Cohn, 2024.
3	505	0.986479196655	Henry Cohn, 2024.
3	506	0.986508558172	Henry Cohn, 2024.
3	507	0.986527855040	Henry Cohn, 2024.
3	508	0.986562688022	Henry Cohn, 2024.
3	510	0.986562996172	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	511	0.986645870423	Henry Cohn, 2024.
3	512	0.986668364004	Henry Cohn, 2024.
3	513	0.986700077118	Henry Cohn, 2024.
3	514	0.986720532797	Henry Cohn, 2024.
3	515	0.986749064827	Henry Cohn, 2024.
3	516	0.986773903019	Henry Cohn, 2024.
3	517	0.986799492641	Henry Cohn, 2024.
3	518	0.986819754209	Henry Cohn, 2024.
3	519	0.986848175284	Henry Cohn, 2024.
3	520	0.986876145782	Henry Cohn, 2024.
3	522	0.986932183100	Henry Cohn, 2024.
3	524	0.987070068574	Henry Cohn, 2024, needs more optimization.
3	525	0.987134555001	Henry Cohn, 2024, needs more optimization.
3	526	0.987173333337	Henry Cohn, 2024, needs more optimization.
3	528	0.987179372570	Henry Cohn, 2024, needs more optimization.
3	531	0.987221194219	Henry Cohn, 2024, needs more optimization.
3	532	0.987298353235	Henry Cohn, 2024, needs more optimization.
3	533	0.987313971342	Henry Cohn, 2024, needs more optimization.
3	534	0.987344414714	Henry Cohn, 2024, needs more optimization.
3	540	0.987358115550	Henry Cohn, 2024.
3	541	0.987500444050	Henry Cohn, 2024, needs more optimization.
3	543	0.987517357041	Henry Cohn, 2024, needs more optimization.
3	545	0.987575488899	Henry Cohn, 2024, needs more optimization.
3	547	0.987620718087	Henry Cohn, 2024, needs more optimization.
3	552	0.987622742921	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	553	0.987760372780	Henry Cohn, 2024, needs more optimization.
3	555	0.987772384641	Henry Cohn, 2024, needs more optimization.
3	560	0.987804896421	Henry Cohn, 2024.
3	562	0.987960065671	Henry Cohn, 2024, needs more optimization.
3	563	0.987974286996	Henry Cohn, 2024, needs more optimization.
3	564	0.988015767659	Henry Cohn, 2024, needs more optimization.
3	565	0.988022531360	Henry Cohn, 2024, needs more optimization.
3	572	0.988045168272	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	574	0.988189414335	Henry Cohn, 2024, needs more optimization.
3	576	0.988225553531	Henry Cohn, 2024, needs more optimization.
3	582	0.988260666630	Henry Cohn, 2024.
3	583	0.988409118768	Henry Cohn, 2024, needs more optimization.
3	584	0.988429937671	Henry Cohn, 2024, needs more optimization.
3	585	0.988430094715	Henry Cohn, 2024, needs more optimization.
3	586	0.988460833755	Henry Cohn, 2024, needs more optimization.
3	587	0.988461736730	Henry Cohn, 2024, needs more optimization.
3	588	0.988496246867	Henry Cohn, 2024, needs more optimization.
3	590	0.988502706481	Henry Cohn, 2024, needs more optimization.
3	591	0.988536666720	Henry Cohn, 2024, needs more optimization.
3	592	0.988537123812	Henry Cohn, 2024, needs more optimization.
3	593	0.988586903063	Henry Cohn, 2024, needs more optimization.
3	600	0.988601034993	Henry Cohn, 2024.
3	601	0.988724831099	Henry Cohn, 2024, needs more optimization.
3	602	0.988729843364	Henry Cohn, 2024, needs more optimization.
3	604	0.988789952686	Henry Cohn, 2024, needs more optimization.
3	605	0.988803910640	Henry Cohn, 2024, needs more optimization.
3	612	0.988822833992	Henry Cohn, 2024.
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	0.989091928803	Henry Cohn, 2024, needs more optimization.
3	623	0.989124070209	Henry Cohn, 2024, needs more optimization.
3	624	0.989139505877	Henry Cohn, 2024, needs more optimization.
3	625	0.989147182469	Henry Cohn, 2024, needs more optimization.
3	626	0.989193144685	Henry Cohn, 2024, needs more optimization.
3	627	0.989212946169	Henry Cohn, 2024, needs more optimization.
3	628	0.989216861683	Henry Cohn, 2024, needs more optimization.
3	629	0.989244098490	Henry Cohn, 2024, needs more optimization.
3	630	0.989248749281	Henry Cohn, 2024, needs more optimization.
3	631	0.989260937073	Henry Cohn, 2024, needs more optimization.
3	632	0.989276684332	Henry Cohn, 2024, needs more optimization.
3	633	0.989303273064	Henry Cohn, 2024, needs more optimization.
3	640	0.989309635125	Henry Cohn, 2024.
3	642	0.989332573182	Henry Cohn, 2024.
3	643	0.989452385674	Henry Cohn, 2024, needs more optimization.
3	645	0.989467981312	Henry Cohn, 2024, needs more optimization.
3	646	0.989518876408	Henry Cohn, 2024, needs more optimization.
3	647	0.989530974133	Henry Cohn, 2024, needs more optimization.
3	648	0.989544149040	Henry Cohn, 2024, needs more optimization.
3	649	0.989564049855	Henry Cohn, 2024, needs more optimization.
3	650	0.989578342312	Henry Cohn, 2024, needs more optimization.
3	652	0.989585948294	Henry Cohn, 2024, needs more optimization.
3	654	0.989607580092	Henry Cohn, 2024, needs more optimization.
3	660	0.989627376614	Henry Cohn, 2024.
3	661	0.989733927936	Henry Cohn, 2024, needs more optimization.
3	663	0.989752532045	Henry Cohn, 2024, needs more optimization.
3	664	0.989798867397	Henry Cohn, 2024, needs more optimization.
3	665	0.989801315138	Henry Cohn, 2024, needs more optimization.
3	672	0.989805947885	Henry Cohn, 2024.
3	680	0.989925830497	Henry Cohn, 2024.
3	681	0.990042369770	Henry Cohn, 2024, needs more optimization.
3	682	0.990047659785	Henry Cohn, 2024, needs more optimization.
3	692	0.990060116362	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	702	0.990207682442	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	703	0.990341580125	Henry Cohn, 2024, needs more optimization.
3	704	0.990350573317	Henry Cohn, 2024, needs more optimization.
3	706	0.990376246150	Henry Cohn, 2024, needs more optimization.
3	707	0.990401112844	Henry Cohn, 2024, needs more optimization.
3	708	0.990414278256	Henry Cohn, 2024, needs more optimization.
3	711	0.990450177778	Henry Cohn, 2024, needs more optimization.
3	712	0.990461738716	Henry Cohn, 2024, needs more optimization.
3	715	0.990479613717	Henry Cohn, 2024, needs more optimization.
3	720	0.990483363237	Henry Cohn, 2024.
3	721	0.990580797616	Henry Cohn, 2024, needs more optimization.
3	722	0.990610436585	Henry Cohn, 2024, needs more optimization.
3	723	0.990613217077	Henry Cohn, 2024, needs more optimization.
3	732	0.990623187196	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	740	0.990730815439	Henry Cohn, 2024.
3	750	0.990847475915	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	752	0.990872395915	Henry Cohn, 2024.
3	753	0.990991032801	Henry Cohn, 2024, needs more optimization.
3	755	0.991022913227	Henry Cohn, 2024, needs more optimization.
3	756	0.991035192932	Henry Cohn, 2024, needs more optimization.
3	758	0.991038437820	Henry Cohn, 2024, needs more optimization.
3	761	0.991063426688	Henry Cohn, 2024, needs more optimization.
3	770	0.991085755280	Henry Cohn, 2024.
3	780	0.991203514614	Henry Cohn, 2024.
3	782	0.991222201087	Henry Cohn, 2024.
3	783	0.991328528269	Henry Cohn, 2024, needs more optimization.
3	792	0.991331558735	Henry Cohn, 2024.
3	800	0.991421236921	Henry Cohn, 2024.
3	802	0.991539847367	Henry Cohn, 2024, needs more optimization.
3	812	0.991551443868	Henry Cohn, 2024.
3	813	0.991634158400	Henry Cohn, 2024, needs more optimization.
3	814	0.991670665099	Henry Cohn, 2024, needs more optimization.
3	816	0.991675784634	Henry Cohn, 2024, needs more optimization.
3	817	0.991713645183	Henry Cohn, 2024, needs more optimization.
3	819	0.991714320469	Henry Cohn, 2024, needs more optimization.
3	830	0.991724915725	Henry Cohn, 2024.
3	840	0.991804916272	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	852	0.991904249523	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	860	0.992000324488	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	872	0.992098850920	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	873	0.992201290404	Henry Cohn, 2024, needs more optimization.
3	882	0.992208997020	Henry Cohn, 2024.
3	883	0.992314839844	Henry Cohn, 2024, needs more optimization.
3	886	0.992322756743	Henry Cohn, 2024, needs more optimization.
3	888	0.992346368978	Henry Cohn, 2024, needs more optimization.
3	889	0.992354404308	Henry Cohn, 2024, needs more optimization.
3	890	0.992359580205	Henry Cohn, 2024, needs more optimization.
3	900	0.992360793848	Henry Cohn, 2024.
3	912	0.992458117635	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	920	0.992529804942	Henry Cohn, 2024.
3	930	0.992603658000	Henry Cohn, 2024.
3	931	0.992696378869	Henry Cohn, 2024, needs more optimization.
3	942	0.992697727936	Henry Cohn, 2024.
3	950	0.992759278250	Henry Cohn, 2024.
3	960	0.992830967656	Henry Cohn, 2024.
3	962	0.992849707370	Henry Cohn, 2024.
3	972	0.992923191999	Henry Cohn, 2024.
3	980	0.992974636259	Henry Cohn, 2024.
3	992	0.993062786669	Henry Cohn, 2024.
3	1002	0.993129515697	Henry Cohn, 2024.
3	1010	0.993176753480	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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	1022	0.993261497684	R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3	1024	0.993275446250	Henry Cohn, 2024.
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	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. $8 x^{3} - 12 x^{2} - 2 x + 1$
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. $4 x - 1$
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 listed in plain text data
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 listed in plain text data
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	0.590765903981	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	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	0.610129491380	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	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	0.655275291940	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.685400923882	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 listed in plain text data
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	0.719201447268	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	57	0.722369011238	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.726684776289	Henry Cohn, 2023.
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	0.733882912083	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	63	0.738725457117	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.745999226475	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	67	0.748969904957	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	68	0.751044492573	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
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	0.753734083742	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	71	0.756376011349	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
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	0.759550197779	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 listed in plain text data
4	77	0.765202573468	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.773060404434	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	80	0.775691898187	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	81	0.777799422383	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	82	0.779757103986	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	83	0.781072136090	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.783715099666	Henry Cohn, 2023.
4	86	0.784955041928	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	87	0.785515524692	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	88	0.785927666189	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	0.791393158982	Henry Cohn, 2023.
4	92	0.792211352845	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	93	0.793047017525	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	94	0.793553795279	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	95	0.796982807650	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	96	0.797981478600	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	97	0.799480375605	Henry Cohn, 2023.
4	98	0.800765983579	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.803178973721	Henry Cohn, 2023.
4	101	0.803902192346	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	102	0.804700846950	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	103	0.805093353044	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	104	0.806317125369	Henry Cohn, 2023.
4	105	0.807105117165	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	106	0.807631911086	Henry Cohn, 2023.
4	107	0.808031896636	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	108	0.808494083227	Henry Cohn, 2023.
4	109	0.808699173872	Henry Cohn, 2023.
4	110	0.808930756191	Henry Cohn, 2023.
4	111	0.809003099109	Henry Cohn, 2023.
4	112	0.809016934794	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	113	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	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	0.824643413995	Henry Cohn, 2023.
4	122	0.826376579266	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	123	0.827332082575	Henry Cohn, 2023.
4	124	0.829082801027	Henry Cohn, 2023.
4	125	0.830275233675	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	126	0.831282604091	Henry Cohn, 2023.
4	127	0.832258618537	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	128	0.833185396681	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	129	0.833853231839	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	130	0.834775630298	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4	131	0.835693409968	Henry Cohn, 2023, needs more optimization.
4	132	0.835950897310	Henry Cohn, 2023, needs more optimization.
4	133	0.837065462160	Henry Cohn, 2023, needs more optimization.
4	134	0.837644001569	Henry Cohn, 2024, needs more optimization.
4	135	0.838195660112	Henry Cohn, 2024, needs more optimization.
4	136	0.838543322434	Henry Cohn, 2023, needs more optimization.
4	137	0.838888930101	Henry Cohn, 2023, needs more optimization.
4	138	0.839095955165	Henry Cohn, 2023, needs more optimization.
4	139	0.839507791715	Henry Cohn, 2023, needs more optimization.
4	140	0.839810972618	Henry Cohn, 2024, needs more optimization.
4	141	0.840152856169	Henry Cohn, 2023, needs more optimization.
4	142	0.840929169817	Henry Cohn, 2023, needs more optimization.
4	143	0.842653745823	Henry Cohn, 2023, needs more optimization.
4	144	0.843254481871	Henry Cohn, 2023, needs more optimization.
4	145	0.845008678584	Henry Cohn, 2023, needs more optimization.
4	146	0.846045194932	Henry Cohn, 2023, needs more optimization.
4	147	0.847009948771	Henry Cohn, 2023, needs more optimization.
4	148	0.847504724481	Henry Cohn, 2024, needs more optimization.
4	149	0.847742312753	Henry Cohn, 2024, needs more optimization.
4	150	0.848022802396	Henry Cohn, 2024, needs more optimization.
4	151	0.848408795562	Henry Cohn, 2024, needs more optimization.
4	152	0.848746833989	Henry Cohn, 2023, needs more optimization.
4	153	0.849142430834	Henry Cohn, 2023, needs more optimization.
4	154	0.849448181317	Henry Cohn, 2023, needs more optimization.
4	155	0.850536831859	Henry Cohn, 2023, needs more optimization.
4	156	0.852462662344	Henry Cohn, 2023, needs more optimization.
4	157	0.853204487103	Henry Cohn, 2023, needs more optimization.
4	158	0.853647178109	Henry Cohn, 2023, needs more optimization.
4	159	0.853860652797	Henry Cohn, 2024, needs more optimization.
4	160	0.854022548424	Henry Cohn, 2023, needs more optimization.
4	161	0.855045927047	Henry Cohn, 2023, needs more optimization.
4	162	0.856194348159	Henry Cohn, 2023, needs more optimization.
4	163	0.856549957906	Henry Cohn, 2023, needs more optimization.
4	164	0.856772040869	Henry Cohn, 2024, needs more optimization.
4	165	0.856908324465	Henry Cohn, 2023, needs more optimization.
4	166	0.857226413990	Henry Cohn, 2023, needs more optimization.
4	167	0.857623980333	Henry Cohn, 2023, needs more optimization.
4	168	0.859328603191	Henry Cohn, 2024, needs more optimization.
4	169	0.860547738259	Henry Cohn, 2023, needs more optimization.
4	170	0.861420806496	Henry Cohn, 2024, needs more optimization.
4	171	0.861964544982	Henry Cohn, 2023, needs more optimization.
4	172	0.862494620321	Henry Cohn, 2023, needs more optimization.
4	173	0.862801682442	Henry Cohn, 2024, needs more optimization.
4	174	0.863316707621	Henry Cohn, 2023, needs more optimization.
4	175	0.863375428751	Henry Cohn, 2023, needs more optimization.
4	176	0.863644343086	Henry Cohn, 2024, needs more optimization.
4	177	0.863815065836	Henry Cohn, 2023, needs more optimization.
4	178	0.863942889203	Henry Cohn, 2023, needs more optimization.
4	179	0.864723294244	Henry Cohn, 2023, needs more optimization.
4	180	0.865816755621	Henry Cohn, 2024, needs more optimization.
4	181	0.866621416405	Henry Cohn, 2024, needs more optimization.
4	182	0.867179481119	Henry Cohn, 2024, needs more optimization.
4	183	0.867376094909	Henry Cohn, 2023, needs more optimization.
4	184	0.867796264121	Henry Cohn, 2023, needs more optimization.
4	185	0.868236586383	Henry Cohn, 2023, needs more optimization.
4	186	0.868600747516	Henry Cohn, 2024, needs more optimization.
4	187	0.868985093744	Henry Cohn, 2023, needs more optimization.
4	188	0.869250376158	Henry Cohn, 2023, needs more optimization.
4	189	0.869501337551	Henry Cohn, 2024, needs more optimization.
4	190	0.870058300815	Henry Cohn, 2023, needs more optimization.
4	191	0.871106291214	Henry Cohn, 2023, needs more optimization.
4	192	0.871418138221	Henry Cohn, 2024, needs more optimization.
4	193	0.871562084144	Henry Cohn, 2024, needs more optimization.
4	194	0.871796404633	Henry Cohn, 2024, needs more optimization.
4	195	0.872110243106	Henry Cohn, 2023, needs more optimization.
4	196	0.872635690426	Henry Cohn, 2024, needs more optimization.
4	197	0.873494455343	Henry Cohn, 2024, needs more optimization.
4	198	0.874188781732	Henry Cohn, 2024, needs more optimization.
4	199	0.875079674042	Henry Cohn, 2024, needs more optimization.
4	200	0.875770718696	Henry Cohn, 2024, needs more optimization.
4	201	0.876332304627	Henry Cohn, 2024, needs more optimization.
4	202	0.876704999875	Henry Cohn, 2024, needs more optimization.
4	203	0.876959848971	Henry Cohn, 2024, needs more optimization.
4	204	0.877408934054	Henry Cohn, 2024, needs more optimization.
4	205	0.877549928518	Henry Cohn, 2024, needs more optimization.
4	207	0.878050769268	Henry Cohn, 2024, needs more optimization.
4	208	0.878261915269	Henry Cohn, 2024, needs more optimization.
4	209	0.878664873842	Henry Cohn, 2024, needs more optimization.
4	210	0.879224182109	Henry Cohn, 2024, needs more optimization.
4	211	0.879780492920	Henry Cohn, 2024, needs more optimization.
4	213	0.879969041117	Henry Cohn, 2024, needs more optimization.
4	214	0.879981578515	Henry Cohn, 2024, needs more optimization.
4	215	0.880281642326	Henry Cohn, 2024, needs more optimization.
4	216	0.880915819237	Henry Cohn, 2024, needs more optimization.
4	217	0.881542976248	Henry Cohn, 2024, needs more optimization.
4	218	0.882220591860	Henry Cohn, 2024, needs more optimization.
4	220	0.882612817810	Henry Cohn, 2024, needs more optimization.
4	221	0.883119622754	Henry Cohn, 2024, needs more optimization.
4	222	0.883568877273	Henry Cohn, 2024, needs more optimization.
4	223	0.884321620229	Henry Cohn, 2024, needs more optimization.
4	224	0.884691957592	Henry Cohn, 2024, needs more optimization.
4	225	0.885247282559	Henry Cohn, 2024, needs more optimization.
4	226	0.885385924386	Henry Cohn, 2024, needs more optimization.
4	227	0.885568149832	Henry Cohn, 2024, needs more optimization.
4	228	0.885921077647	Henry Cohn, 2024, needs more optimization.
4	230	0.886378896283	Henry Cohn, 2024, needs more optimization.
4	231	0.886863514657	Henry Cohn, 2024, needs more optimization.
4	233	0.887442267680	Henry Cohn, 2024, needs more optimization.
4	234	0.887616154966	Henry Cohn, 2024, needs more optimization.
4	235	0.887935933360	Henry Cohn, 2024, needs more optimization.
4	236	0.888136774545	Henry Cohn, 2024, needs more optimization.
4	237	0.888466234092	Henry Cohn, 2024, needs more optimization.
4	238	0.888956646525	Henry Cohn, 2024, needs more optimization.
4	239	0.889406829129	Henry Cohn, 2024, needs more optimization.
4	240	0.889614550496	Henry Cohn, 2024, needs more optimization.
4	241	0.889895138110	Henry Cohn, 2024, needs more optimization.
4	242	0.890285478529	Henry Cohn, 2024, needs more optimization.
4	243	0.890336503447	Henry Cohn, 2024, needs more optimization.
4	244	0.890776113766	Henry Cohn, 2024, needs more optimization.
4	245	0.891059661460	Henry Cohn, 2024, needs more optimization.
4	246	0.891251467891	Henry Cohn, 2024, needs more optimization.
4	247	0.891800101825	Henry Cohn, 2024, needs more optimization.
4	248	0.892325124030	Henry Cohn, 2024, needs more optimization.
4	249	0.892362999922	Henry Cohn, 2024, needs more optimization.
4	250	0.892837586835	Henry Cohn, 2024, needs more optimization.
4	251	0.893110278794	Henry Cohn, 2024, needs more optimization.
4	252	0.893392539857	Henry Cohn, 2024, needs more optimization.
4	253	0.893785136271	Henry Cohn, 2024, needs more optimization.
4	254	0.893946035806	Henry Cohn, 2024, needs more optimization.
4	255	0.894031439216	Henry Cohn, 2024, needs more optimization.
4	256	0.894642036631	Henry Cohn, 2024, needs more optimization.
4	258	0.896031971126	Henry Cohn, 2024, needs more optimization.
4	259	0.896648201463	Henry Cohn, 2024, needs more optimization.
4	261	0.897528201386	Henry Cohn, 2024, needs more optimization.
4	263	0.897598076583	Henry Cohn, 2024, needs more optimization.
4	266	0.898754022621	Henry Cohn, 2024, needs more optimization.
4	267	0.899370660160	Henry Cohn, 2024, needs more optimization.
4	269	0.899457610338	Henry Cohn, 2024, needs more optimization.
4	270	0.899634344178	Henry Cohn, 2024, needs more optimization.
4	272	0.900078208079	Henry Cohn, 2024, needs more optimization.
4	273	0.900463263979	Henry Cohn, 2024, needs more optimization.
4	274	0.901019373459	Henry Cohn, 2024, needs more optimization.
4	276	0.901025494283	Henry Cohn, 2024, needs more optimization.
4	277	0.901388468226	Henry Cohn, 2024, needs more optimization.
4	278	0.902031580440	Henry Cohn, 2024, needs more optimization.
4	279	0.902156166798	Henry Cohn, 2024, needs more optimization.
4	280	0.902250973471	Henry Cohn, 2024, needs more optimization.
4	282	0.902286939269	Henry Cohn, 2024, needs more optimization.
4	285	0.903101045501	Henry Cohn, 2024, needs more optimization.
4	286	0.903620324742	Henry Cohn, 2024, needs more optimization.
4	288	0.904135083536	Henry Cohn, 2024, needs more optimization.
4	291	0.904392951497	Henry Cohn, 2024, needs more optimization.
4	292	0.905202290997	Henry Cohn, 2024, needs more optimization.
4	293	0.905354900373	Henry Cohn, 2024, needs more optimization.
4	294	0.905536005427	Henry Cohn, 2024, needs more optimization.
4	296	0.905770696895	Henry Cohn, 2024, needs more optimization.
4	298	0.906097210743	Henry Cohn, 2024, needs more optimization.
4	299	0.906625091281	Henry Cohn, 2024, needs more optimization.
4	300	0.906890051793	Henry Cohn, 2024, needs more optimization.
4	301	0.906904540387	Henry Cohn, 2024, needs more optimization.
4	306	0.907336286614	Henry Cohn, 2024, needs more optimization.
4	307	0.908014784148	Henry Cohn, 2024, needs more optimization.
4	308	0.908200268315	Henry Cohn, 2024, needs more optimization.
4	309	0.908760825389	Henry Cohn, 2024, needs more optimization.
4	310	0.908777658754	Henry Cohn, 2024, needs more optimization.
4	311	0.909010904461	Henry Cohn, 2024, needs more optimization.
4	312	0.909286399495	Henry Cohn, 2024, needs more optimization.
4	313	0.909308193471	Henry Cohn, 2024, needs more optimization.
4	315	0.909400096030	Henry Cohn, 2024, needs more optimization.
4	316	0.909591590227	Henry Cohn, 2024, needs more optimization.
4	317	0.910205412186	Henry Cohn, 2024, needs more optimization.
4	318	0.910265577259	Henry Cohn, 2024, needs more optimization.
4	319	0.910522175388	Henry Cohn, 2024, needs more optimization.
4	320	0.910558493950	Henry Cohn, 2024, needs more optimization.
4	321	0.910568185365	Henry Cohn, 2024, needs more optimization.
4	322	0.911008768843	Henry Cohn, 2024, needs more optimization.
4	323	0.911180305994	Henry Cohn, 2024, needs more optimization.
4	324	0.911353633046	Henry Cohn, 2024, needs more optimization.
4	325	0.911698777803	Henry Cohn, 2024, needs more optimization.
4	327	0.911720244978	Henry Cohn, 2024, needs more optimization.
4	328	0.912117496103	Henry Cohn, 2024, needs more optimization.
4	329	0.912282348502	Henry Cohn, 2024, needs more optimization.
4	330	0.912630063376	Henry Cohn, 2024, needs more optimization.
4	331	0.912732578812	Henry Cohn, 2024, needs more optimization.
4	332	0.912959490978	Henry Cohn, 2024, needs more optimization.
4	333	0.913024530220	Henry Cohn, 2024, needs more optimization.
4	334	0.913059192245	Henry Cohn, 2024, needs more optimization.
4	335	0.913442192634	Henry Cohn, 2024, needs more optimization.
4	336	0.913494328455	Henry Cohn, 2024, needs more optimization.
4	342	0.913523258748	Henry Cohn, 2024, needs more optimization.
4	343	0.914471393379	Henry Cohn, 2024, needs more optimization.
4	344	0.914531092841	Henry Cohn, 2024, needs more optimization.
4	345	0.915073179915	Henry Cohn, 2024, needs more optimization.
4	346	0.915176292935	Henry Cohn, 2024, needs more optimization.
4	347	0.915334458859	Henry Cohn, 2024, needs more optimization.
4	348	0.915599741975	Henry Cohn, 2024, needs more optimization.
4	353	0.915865414787	Henry Cohn, 2024, needs more optimization.
4	354	0.916426923601	Henry Cohn, 2024, needs more optimization.
4	355	0.916515692544	Henry Cohn, 2024, needs more optimization.
4	356	0.916957950190	Henry Cohn, 2024, needs more optimization.
4	358	0.917020771421	Henry Cohn, 2024, needs more optimization.
4	360	0.917256233542	Henry Cohn, 2024, needs more optimization.
4	361	0.917623808120	Henry Cohn, 2024, needs more optimization.
4	363	0.917733587088	Henry Cohn, 2024, needs more optimization.
4	365	0.918000164673	Henry Cohn, 2024, needs more optimization.
4	367	0.918189168888	Henry Cohn, 2024, needs more optimization.
4	369	0.918597177409	Henry Cohn, 2024, needs more optimization.
4	370	0.918814735563	Henry Cohn, 2024, needs more optimization.
4	371	0.919061519127	Henry Cohn, 2024, needs more optimization.
4	372	0.919162449026	Henry Cohn, 2024, needs more optimization.
4	373	0.919321280701	Henry Cohn, 2024, needs more optimization.
4	374	0.919345045026	Henry Cohn, 2024, needs more optimization.
4	375	0.919696980017	Henry Cohn, 2024, needs more optimization.
4	376	0.919891120458	Henry Cohn, 2024, needs more optimization.
4	377	0.919929828299	Henry Cohn, 2024, needs more optimization.
4	378	0.920365392326	Henry Cohn, 2024, needs more optimization.
4	379	0.920375778648	Henry Cohn, 2024, needs more optimization.
4	380	0.920460222008	Henry Cohn, 2024, needs more optimization.
4	381	0.920477880901	Henry Cohn, 2024, needs more optimization.
4	384	0.920515492657	Henry Cohn, 2024, needs more optimization.
4	385	0.921077631099	Henry Cohn, 2024, needs more optimization.
4	387	0.921222859095	Henry Cohn, 2024, needs more optimization.
4	388	0.921550392734	Henry Cohn, 2024, needs more optimization.
4	390	0.921631016949	Henry Cohn, 2024, needs more optimization.
4	391	0.921828300771	Henry Cohn, 2024, needs more optimization.
4	392	0.922010224988	Henry Cohn, 2024, needs more optimization.
4	393	0.922080240451	Henry Cohn, 2024, needs more optimization.
4	395	0.922338646692	Henry Cohn, 2024, needs more optimization.
4	396	0.922522591033	Henry Cohn, 2024, needs more optimization.
4	397	0.922524302218	Henry Cohn, 2024, needs more optimization.
4	398	0.922793367710	Henry Cohn, 2024, needs more optimization.
4	400	0.922843424735	Henry Cohn, 2024, needs more optimization.
4	402	0.923120163378	Henry Cohn, 2024, needs more optimization.
4	403	0.923277366092	Henry Cohn, 2024, needs more optimization.
4	406	0.923725163017	Henry Cohn, 2024, needs more optimization.
4	407	0.923958639290	Henry Cohn, 2024, needs more optimization.
4	408	0.924028851556	Henry Cohn, 2024, needs more optimization.
4	409	0.924128617452	Henry Cohn, 2024, needs more optimization.
4	410	0.924268226075	Henry Cohn, 2024, needs more optimization.
4	412	0.924334111010	Henry Cohn, 2024, needs more optimization.
4	414	0.924685293588	Henry Cohn, 2024, needs more optimization.
4	416	0.924787098694	Henry Cohn, 2024, needs more optimization.
4	417	0.925143169014	Henry Cohn, 2024, needs more optimization.
4	418	0.925215357608	Henry Cohn, 2024, needs more optimization.
4	419	0.925386026549	Henry Cohn, 2024, needs more optimization.
4	420	0.925398894946	Henry Cohn, 2024, needs more optimization.
4	421	0.925720158568	Henry Cohn, 2024, needs more optimization.
4	422	0.925781611302	Henry Cohn, 2024, needs more optimization.
4	423	0.925833708453	Henry Cohn, 2024, needs more optimization.
4	424	0.925943620262	Henry Cohn, 2024, needs more optimization.
4	425	0.926068704461	Henry Cohn, 2024, needs more optimization.
4	426	0.926089923301	Henry Cohn, 2024, needs more optimization.
4	427	0.926437672306	Henry Cohn, 2024, needs more optimization.
4	429	0.926535128316	Henry Cohn, 2024, needs more optimization.
4	431	0.926689698203	Henry Cohn, 2024, needs more optimization.
4	432	0.926730918922	Henry Cohn, 2024, needs more optimization.
4	435	0.926903229834	Henry Cohn, 2024, needs more optimization.
4	436	0.927191361642	Henry Cohn, 2024, needs more optimization.
4	437	0.927474684699	Henry Cohn, 2024, needs more optimization.
4	439	0.927500149239	Henry Cohn, 2024, needs more optimization.
4	440	0.927680635319	Henry Cohn, 2024, needs more optimization.
4	441	0.927972971942	Henry Cohn, 2024, needs more optimization.
4	442	0.927993769906	Henry Cohn, 2024, needs more optimization.
4	444	0.927994407780	Henry Cohn, 2024, needs more optimization.
4	445	0.928190771378	Henry Cohn, 2024, needs more optimization.
4	448	0.928441233171	Henry Cohn, 2024, needs more optimization.
4	449	0.928793413524	Henry Cohn, 2024, needs more optimization.
4	450	0.928857664093	Henry Cohn, 2024, needs more optimization.
4	451	0.928914998111	Henry Cohn, 2024, needs more optimization.
4	453	0.929135185883	Henry Cohn, 2024, needs more optimization.
4	454	0.929153871986	Henry Cohn, 2024, needs more optimization.
4	455	0.929195232623	Henry Cohn, 2024, needs more optimization.
4	457	0.929452803216	Henry Cohn, 2024, needs more optimization.
4	458	0.929675496475	Henry Cohn, 2024, needs more optimization.
4	459	0.929728188346	Henry Cohn, 2024, needs more optimization.
4	460	0.929745874111	Henry Cohn, 2024, needs more optimization.
4	462	0.929945638899	Henry Cohn, 2024, needs more optimization.
4	463	0.930183172652	Henry Cohn, 2024, needs more optimization.
4	465	0.930337598899	Henry Cohn, 2024, needs more optimization.
4	467	0.930584125024	Henry Cohn, 2024, needs more optimization.
4	468	0.930584544269	Henry Cohn, 2024, needs more optimization.
4	469	0.930710596651	Henry Cohn, 2024, needs more optimization.
4	471	0.930817587249	Henry Cohn, 2024, needs more optimization.
4	473	0.930977638621	Henry Cohn, 2024, needs more optimization.
4	474	0.931237308971	Henry Cohn, 2024, needs more optimization.
4	476	0.931355307171	Henry Cohn, 2024, needs more optimization.
4	477	0.931486514475	Henry Cohn, 2024, needs more optimization.
4	478	0.931548548453	Henry Cohn, 2024, needs more optimization.
4	479	0.931731898838	Henry Cohn, 2024, needs more optimization.
4	481	0.931856524115	Henry Cohn, 2024, needs more optimization.
4	483	0.931948157734	Henry Cohn, 2024, needs more optimization.
4	484	0.932130185974	Henry Cohn, 2024, needs more optimization.
4	485	0.932210994062	Henry Cohn, 2024, needs more optimization.
4	487	0.932274161903	Henry Cohn, 2024, needs more optimization.
4	489	0.932596306901	Henry Cohn, 2024, needs more optimization.
4	490	0.932721997765	Henry Cohn, 2024, needs more optimization.
4	491	0.932795362387	Henry Cohn, 2024, needs more optimization.
4	492	0.933071539779	Henry Cohn, 2024, needs more optimization.
4	493	0.933073025685	Henry Cohn, 2024, needs more optimization.
4	494	0.933190654360	Henry Cohn, 2024, needs more optimization.
4	495	0.933365575500	Henry Cohn, 2024, needs more optimization.
4	497	0.933379181035	Henry Cohn, 2024, needs more optimization.
4	498	0.933462214055	Henry Cohn, 2024, needs more optimization.
4	499	0.933586139530	Henry Cohn, 2024, needs more optimization.
4	501	0.933613519113	Henry Cohn, 2024, needs more optimization.
4	502	0.933762931747	Henry Cohn, 2024, needs more optimization.
4	503	0.933834273938	Henry Cohn, 2024, needs more optimization.
4	504	0.933917979097	Henry Cohn, 2024, needs more optimization.
4	506	0.934162428034	Henry Cohn, 2024, needs more optimization.
4	508	0.934259784750	Henry Cohn, 2024, needs more optimization.
4	509	0.934458205803	Henry Cohn, 2024, needs more optimization.
4	512	0.934503377224	Henry Cohn, 2024, needs more optimization.
4	513	0.934763790621	Henry Cohn, 2024, needs more optimization.
4	514	0.934862891592	Henry Cohn, 2024, needs more optimization.
4	515	0.934964728304	Henry Cohn, 2024, needs more optimization.
4	517	0.935001334617	Henry Cohn, 2024, needs more optimization.
4	518	0.935009372457	Henry Cohn, 2024, needs more optimization.
4	519	0.935120262505	Henry Cohn, 2024, needs more optimization.
4	521	0.935423559411	Henry Cohn, 2024, needs more optimization.
4	522	0.935464829472	Henry Cohn, 2024, needs more optimization.
4	523	0.935597705796	Henry Cohn, 2024, needs more optimization.
4	524	0.935611528967	Henry Cohn, 2024, needs more optimization.
4	527	0.935839603809	Henry Cohn, 2024, needs more optimization.
4	528	0.936033507005	Henry Cohn, 2024, needs more optimization.
4	529	0.936050904829	Henry Cohn, 2024, needs more optimization.
4	530	0.936126012920	Henry Cohn, 2024, needs more optimization.
4	531	0.936200360571	Henry Cohn, 2024, needs more optimization.
4	532	0.936238746929	Henry Cohn, 2024, needs more optimization.
4	533	0.936295103921	Henry Cohn, 2024, needs more optimization.
4	534	0.936541248278	Henry Cohn, 2024, needs more optimization.
4	535	0.936592863633	Henry Cohn, 2024, needs more optimization.
4	536	0.936692841871	Henry Cohn, 2024, needs more optimization.
4	537	0.936731570500	Henry Cohn, 2024, needs more optimization.
4	538	0.936746449910	Henry Cohn, 2024, needs more optimization.
4	539	0.936908028170	Henry Cohn, 2024, needs more optimization.
4	541	0.937012832796	Henry Cohn, 2024, needs more optimization.
4	543	0.937157082228	Henry Cohn, 2024, needs more optimization.
4	544	0.937189452957	Henry Cohn, 2024, needs more optimization.
4	545	0.937222136014	Henry Cohn, 2024, needs more optimization.
4	547	0.937434903044	Henry Cohn, 2024, needs more optimization.
4	548	0.937584188766	Henry Cohn, 2024, needs more optimization.
4	550	0.937651721882	Henry Cohn, 2024, needs more optimization.
4	552	0.937697963129	Henry Cohn, 2024, needs more optimization.
4	556	0.937865276365	Henry Cohn, 2024, needs more optimization.
4	557	0.938279720196	Henry Cohn, 2024, needs more optimization.
4	559	0.938323528078	Henry Cohn, 2024, needs more optimization.
4	560	0.938412256910	Henry Cohn, 2024, needs more optimization.
4	561	0.938492545286	Henry Cohn, 2024, needs more optimization.
4	562	0.938603381696	Henry Cohn, 2024, needs more optimization.
4	563	0.938684730378	Henry Cohn, 2024, needs more optimization.
4	564	0.938780881729	Henry Cohn, 2024, needs more optimization.
4	565	0.938805921651	Henry Cohn, 2024, needs more optimization.
4	566	0.938978338214	Henry Cohn, 2024, needs more optimization.
4	567	0.938995858884	Henry Cohn, 2024, needs more optimization.
4	568	0.939010375899	Henry Cohn, 2024, needs more optimization.
4	569	0.939079760251	Henry Cohn, 2024, needs more optimization.
4	571	0.939138200216	Henry Cohn, 2024, needs more optimization.
4	572	0.939340790062	Henry Cohn, 2024, needs more optimization.
4	573	0.939389556028	Henry Cohn, 2024, needs more optimization.
4	574	0.939454593889	Henry Cohn, 2024, needs more optimization.
4	576	0.939520115001	Henry Cohn, 2024, needs more optimization.
4	577	0.939656060183	Henry Cohn, 2024, needs more optimization.
4	579	0.939713952351	Henry Cohn, 2024, needs more optimization.
4	581	0.939839776713	Henry Cohn, 2024, needs more optimization.
4	582	0.939946428177	Henry Cohn, 2024, needs more optimization.
4	583	0.939947850421	Henry Cohn, 2024, needs more optimization.
4	584	0.940159293002	Henry Cohn, 2024, needs more optimization.
4	585	0.940247897197	Henry Cohn, 2024, needs more optimization.
4	586	0.940254989285	Henry Cohn, 2024, needs more optimization.
4	587	0.940317292817	Henry Cohn, 2024, needs more optimization.
4	589	0.940347798729	Henry Cohn, 2024, needs more optimization.
4	591	0.940576047539	Henry Cohn, 2024, needs more optimization.
4	592	0.940683828473	Henry Cohn, 2024, needs more optimization.
4	593	0.940743955439	Henry Cohn, 2024, needs more optimization.
4	595	0.940762613878	Henry Cohn, 2024, needs more optimization.
4	596	0.940972510374	Henry Cohn, 2024, needs more optimization.
4	600	0.941004765661	Henry Cohn, 2024, needs more optimization.
4	601	0.941160530937	Henry Cohn, 2024, needs more optimization.
4	602	0.941341296768	Henry Cohn, 2024, needs more optimization.
4	604	0.941425016281	Henry Cohn, 2024, needs more optimization.
4	605	0.941542975117	Henry Cohn, 2024, needs more optimization.
4	606	0.941692370139	Henry Cohn, 2024, needs more optimization.
4	607	0.941701088451	Henry Cohn, 2024, needs more optimization.
4	608	0.941751632562	Henry Cohn, 2024, needs more optimization.
4	610	0.941856112416	Henry Cohn, 2024, needs more optimization.
4	612	0.941879298244	Henry Cohn, 2024, needs more optimization.
4	613	0.942020567161	Henry Cohn, 2024, needs more optimization.
4	614	0.942020998008	Henry Cohn, 2024, needs more optimization.
4	616	0.942182230086	Henry Cohn, 2024, needs more optimization.
4	618	0.942259650617	Henry Cohn, 2024, needs more optimization.
4	619	0.942390469832	Henry Cohn, 2024, needs more optimization.
4	620	0.942496233552	Henry Cohn, 2024, needs more optimization.
4	621	0.942552614970	Henry Cohn, 2024, needs more optimization.
4	623	0.942675507343	Henry Cohn, 2024, needs more optimization.
4	624	0.942771304037	Henry Cohn, 2024, needs more optimization.
4	625	0.942788381239	Henry Cohn, 2024, needs more optimization.
4	627	0.942870798244	Henry Cohn, 2024, needs more optimization.
4	628	0.942989059396	Henry Cohn, 2024, needs more optimization.
4	629	0.943022934062	Henry Cohn, 2024, needs more optimization.
4	630	0.943023074275	Henry Cohn, 2024, needs more optimization.
4	632	0.943117258171	Henry Cohn, 2024, needs more optimization.
4	633	0.943269155431	Henry Cohn, 2024, needs more optimization.
4	634	0.943347014993	Henry Cohn, 2024, needs more optimization.
4	637	0.943353013497	Henry Cohn, 2024, needs more optimization.
4	639	0.943601633167	Henry Cohn, 2024, needs more optimization.
4	640	0.943631054456	Henry Cohn, 2024, needs more optimization.
4	642	0.943819551657	Henry Cohn, 2024, needs more optimization.
4	644	0.943876018348	Henry Cohn, 2024, needs more optimization.
4	645	0.944015124088	Henry Cohn, 2024, needs more optimization.
4	649	0.944124089788	Henry Cohn, 2024, needs more optimization.
4	650	0.944261879687	Henry Cohn, 2024, needs more optimization.
4	651	0.944352062876	Henry Cohn, 2024, needs more optimization.
4	652	0.944372902932	Henry Cohn, 2024, needs more optimization.
4	653	0.944425282372	Henry Cohn, 2024, needs more optimization.
4	656	0.944456640520	Henry Cohn, 2024, needs more optimization.
4	657	0.944603803521	Henry Cohn, 2024, needs more optimization.
4	658	0.944698131479	Henry Cohn, 2024, needs more optimization.
4	659	0.944779041579	Henry Cohn, 2024, needs more optimization.
4	660	0.944867383735	Henry Cohn, 2024, needs more optimization.
4	661	0.944897628731	Henry Cohn, 2024, needs more optimization.
4	662	0.944983480546	Henry Cohn, 2024, needs more optimization.
4	663	0.945008498175	Henry Cohn, 2024, needs more optimization.
4	664	0.945040638735	Henry Cohn, 2024, needs more optimization.
4	665	0.945062359818	Henry Cohn, 2024, needs more optimization.
4	667	0.945215255966	Henry Cohn, 2024, needs more optimization.
4	669	0.945305557154	Henry Cohn, 2024, needs more optimization.
4	672	0.945349042312	Henry Cohn, 2024, needs more optimization.
4	674	0.945589670775	Henry Cohn, 2024, needs more optimization.
4	675	0.945698202546	Henry Cohn, 2024, needs more optimization.
4	677	0.945727813302	Henry Cohn, 2024, needs more optimization.
4	679	0.945766126812	Henry Cohn, 2024, needs more optimization.
4	680	0.945906107433	Henry Cohn, 2024, needs more optimization.
4	681	0.945930566955	Henry Cohn, 2024, needs more optimization.
4	682	0.946043583772	Henry Cohn, 2024, needs more optimization.
4	683	0.946088239936	Henry Cohn, 2024, needs more optimization.
4	685	0.946168155356	Henry Cohn, 2024, needs more optimization.
4	687	0.946239030546	Henry Cohn, 2024, needs more optimization.
4	689	0.946297396159	Henry Cohn, 2024, needs more optimization.
4	690	0.946347682760	Henry Cohn, 2024, needs more optimization.
4	691	0.946505904804	Henry Cohn, 2024, needs more optimization.
4	692	0.946570218624	Henry Cohn, 2024, needs more optimization.
4	694	0.946572146831	Henry Cohn, 2024, needs more optimization.
4	696	0.946633974711	Henry Cohn, 2024, needs more optimization.
4	697	0.946748809585	Henry Cohn, 2024, needs more optimization.
4	698	0.946827862264	Henry Cohn, 2024, needs more optimization.
4	699	0.946873111175	Henry Cohn, 2024, needs more optimization.
4	702	0.946967097739	Henry Cohn, 2024, needs more optimization.
4	704	0.947075199199	Henry Cohn, 2024, needs more optimization.
4	705	0.947125687941	Henry Cohn, 2024, needs more optimization.
4	706	0.947179880161	Henry Cohn, 2024, needs more optimization.
4	707	0.947297954769	Henry Cohn, 2024, needs more optimization.
4	708	0.947401519820	Henry Cohn, 2024, needs more optimization.
4	709	0.947448054159	Henry Cohn, 2024, needs more optimization.
4	711	0.947495886619	Henry Cohn, 2024, needs more optimization.
4	712	0.947564199733	Henry Cohn, 2024, needs more optimization.
4	714	0.947595704217	Henry Cohn, 2024, needs more optimization.
4	715	0.947745908779	Henry Cohn, 2024, needs more optimization.
4	718	0.947762265614	Henry Cohn, 2024, needs more optimization.
4	719	0.947881803894	Henry Cohn, 2024, needs more optimization.
4	720	0.947947001150	Henry Cohn, 2024, needs more optimization.
4	721	0.947983450951	Henry Cohn, 2024, needs more optimization.
4	722	0.948076585581	Henry Cohn, 2024, needs more optimization.
4	724	0.948146194564	Henry Cohn, 2024, needs more optimization.
4	725	0.948223637667	Henry Cohn, 2024, needs more optimization.
4	727	0.948237011664	Henry Cohn, 2024, needs more optimization.
4	729	0.948314255602	Henry Cohn, 2024, needs more optimization.
4	731	0.948402018338	Henry Cohn, 2024, needs more optimization.
4	732	0.948463656747	Henry Cohn, 2024, needs more optimization.
4	733	0.948576833762	Henry Cohn, 2024, needs more optimization.
4	735	0.948647746403	Henry Cohn, 2024, needs more optimization.
4	740	0.948764602285	Henry Cohn, 2024, needs more optimization.
4	742	0.948889210791	Henry Cohn, 2024, needs more optimization.
4	744	0.949013987012	Henry Cohn, 2024, needs more optimization.
4	745	0.949097780271	Henry Cohn, 2024, needs more optimization.
4	746	0.949157951373	Henry Cohn, 2024, needs more optimization.
4	747	0.949175359195	Henry Cohn, 2024, needs more optimization.
4	748	0.949211879808	Henry Cohn, 2024, needs more optimization.
4	749	0.949301151765	Henry Cohn, 2024, needs more optimization.
4	750	0.949352042783	Henry Cohn, 2024, needs more optimization.
4	753	0.949374590018	Henry Cohn, 2024, needs more optimization.
4	754	0.949493342573	Henry Cohn, 2024, needs more optimization.
4	755	0.949536053758	Henry Cohn, 2024, needs more optimization.
4	756	0.949570024969	Henry Cohn, 2024, needs more optimization.
4	758	0.949679993740	Henry Cohn, 2024, needs more optimization.
4	760	0.949698281428	Henry Cohn, 2024, needs more optimization.
4	761	0.949830530944	Henry Cohn, 2024, needs more optimization.
4	762	0.949870867868	Henry Cohn, 2024, needs more optimization.
4	763	0.949896782665	Henry Cohn, 2024, needs more optimization.
4	765	0.949947066532	Henry Cohn, 2024, needs more optimization.
4	768	0.950027503574	Henry Cohn, 2024, needs more optimization.
4	769	0.950117935696	Henry Cohn, 2024, needs more optimization.
4	774	0.950142456068	Henry Cohn, 2024, needs more optimization.
4	775	0.950419343346	Henry Cohn, 2024, needs more optimization.
4	777	0.950455824780	Henry Cohn, 2024, needs more optimization.
4	779	0.950556681098	Henry Cohn, 2024, needs more optimization.
4	781	0.950627715798	Henry Cohn, 2024, needs more optimization.
4	782	0.950749835344	Henry Cohn, 2024, needs more optimization.
4	783	0.950754099569	Henry Cohn, 2024, needs more optimization.
4	785	0.950781459010	Henry Cohn, 2024, needs more optimization.
4	786	0.950857470732	Henry Cohn, 2024, needs more optimization.
4	787	0.950918625095	Henry Cohn, 2024, needs more optimization.
4	789	0.950951512914	Henry Cohn, 2024, needs more optimization.
4	790	0.950968600006	Henry Cohn, 2024, needs more optimization.
4	792	0.951127827762	Henry Cohn, 2024, needs more optimization.
4	798	0.951213307390	Henry Cohn, 2024, needs more optimization.
4	800	0.951426373948	Henry Cohn, 2024, needs more optimization.
4	803	0.951508977666	Henry Cohn, 2024, needs more optimization.
4	805	0.951637923919	Henry Cohn, 2024, needs more optimization.
4	806	0.951647217143	Henry Cohn, 2024, needs more optimization.
4	807	0.951734713688	Henry Cohn, 2024, needs more optimization.
4	809	0.951807105735	Henry Cohn, 2024, needs more optimization.
4	811	0.951870089357	Henry Cohn, 2024, needs more optimization.
4	813	0.951915892684	Henry Cohn, 2024, needs more optimization.
4	815	0.951959591272	Henry Cohn, 2024, needs more optimization.
4	816	0.951998989762	Henry Cohn, 2024, needs more optimization.
4	817	0.952089094389	Henry Cohn, 2024, needs more optimization.
4	819	0.952173127751	Henry Cohn, 2024, needs more optimization.
4	820	0.952244889921	Henry Cohn, 2024, needs more optimization.
4	821	0.952297584872	Henry Cohn, 2024, needs more optimization.
4	826	0.952297838543	Henry Cohn, 2024, needs more optimization.
4	827	0.952527854961	Henry Cohn, 2024, needs more optimization.
4	828	0.952565944696	Henry Cohn, 2024, needs more optimization.
4	831	0.952607763800	Henry Cohn, 2024, needs more optimization.
4	832	0.952664755133	Henry Cohn, 2024, needs more optimization.
4	833	0.952795305017	Henry Cohn, 2024, needs more optimization.
4	836	0.952806034530	Henry Cohn, 2024, needs more optimization.
4	837	0.952856303570	Henry Cohn, 2024, needs more optimization.
4	838	0.952880720569	Henry Cohn, 2024, needs more optimization.
4	840	0.953009752220	Henry Cohn, 2024, needs more optimization.
4	842	0.953019036637	Henry Cohn, 2024, needs more optimization.
4	843	0.953081881684	Henry Cohn, 2024, needs more optimization.
4	845	0.953166271372	Henry Cohn, 2024, needs more optimization.
4	846	0.953237238764	Henry Cohn, 2024, needs more optimization.
4	847	0.953269901570	Henry Cohn, 2024, needs more optimization.
4	849	0.953329218667	Henry Cohn, 2024, needs more optimization.
4	850	0.953336803449	Henry Cohn, 2024, needs more optimization.
4	853	0.953394325543	Henry Cohn, 2024, needs more optimization.
4	854	0.953493297216	Henry Cohn, 2024, needs more optimization.
4	858	0.953551717885	Henry Cohn, 2024, needs more optimization.
4	859	0.953687851096	Henry Cohn, 2024, needs more optimization.
4	860	0.953762562894	Henry Cohn, 2024, needs more optimization.
4	862	0.953785986297	Henry Cohn, 2024, needs more optimization.
4	864	0.953811425363	Henry Cohn, 2024, needs more optimization.
4	866	0.953907044918	Henry Cohn, 2024, needs more optimization.
4	868	0.953978598906	Henry Cohn, 2024, needs more optimization.
4	869	0.954069160565	Henry Cohn, 2024, needs more optimization.
4	873	0.954089575585	Henry Cohn, 2024, needs more optimization.
4	874	0.954174938911	Henry Cohn, 2024, needs more optimization.
4	875	0.954299277061	Henry Cohn, 2024, needs more optimization.
4	876	0.954302083495	Henry Cohn, 2024, needs more optimization.
4	879	0.954306999135	Henry Cohn, 2024, needs more optimization.
4	880	0.954433156342	Henry Cohn, 2024, needs more optimization.
4	881	0.954481885478	Henry Cohn, 2024, needs more optimization.
4	882	0.954507916806	Henry Cohn, 2024, needs more optimization.
4	883	0.954545874882	Henry Cohn, 2024, needs more optimization.
4	884	0.954591245325	Henry Cohn, 2024, needs more optimization.
4	885	0.954627764742	Henry Cohn, 2024, needs more optimization.
4	886	0.954657519991	Henry Cohn, 2024, needs more optimization.
4	887	0.954725933600	Henry Cohn, 2024, needs more optimization.
4	888	0.954729812279	Henry Cohn, 2024, needs more optimization.
4	889	0.954730044896	Henry Cohn, 2024, needs more optimization.
4	890	0.954765733812	Henry Cohn, 2024, needs more optimization.
4	891	0.954779850741	Henry Cohn, 2024, needs more optimization.
4	893	0.954827776041	Henry Cohn, 2024, needs more optimization.
4	896	0.954923249127	Henry Cohn, 2024, needs more optimization.
4	897	0.954989516017	Henry Cohn, 2024, needs more optimization.
4	898	0.955049945073	Henry Cohn, 2024, needs more optimization.
4	900	0.955052861715	Henry Cohn, 2024, needs more optimization.
4	901	0.955150564281	Henry Cohn, 2024, needs more optimization.
4	902	0.955183632150	Henry Cohn, 2024, needs more optimization.
4	904	0.955215889833	Henry Cohn, 2024, needs more optimization.
4	905	0.955286672897	Henry Cohn, 2024, needs more optimization.
4	907	0.955348240380	Henry Cohn, 2024, needs more optimization.
4	908	0.955365101478	Henry Cohn, 2024, needs more optimization.
4	909	0.955371085695	Henry Cohn, 2024, needs more optimization.
4	910	0.955414451205	Henry Cohn, 2024, needs more optimization.
4	911	0.955449796686	Henry Cohn, 2024, needs more optimization.
4	912	0.955463734593	Henry Cohn, 2024, needs more optimization.
4	914	0.955532504369	Henry Cohn, 2024, needs more optimization.
4	915	0.955628499737	Henry Cohn, 2024, needs more optimization.
4	918	0.955658313675	Henry Cohn, 2024, needs more optimization.
4	919	0.955727763243	Henry Cohn, 2024, needs more optimization.
4	920	0.955764433928	Henry Cohn, 2024, needs more optimization.
4	921	0.955837536375	Henry Cohn, 2024, needs more optimization.
4	922	0.955842353628	Henry Cohn, 2024, needs more optimization.
4	923	0.955850144285	Henry Cohn, 2024, needs more optimization.
4	924	0.955881499734	Henry Cohn, 2024, needs more optimization.
4	926	0.955896280562	Henry Cohn, 2024, needs more optimization.
4	927	0.955995435638	Henry Cohn, 2024, needs more optimization.
4	928	0.956028848513	Henry Cohn, 2024, needs more optimization.
4	929	0.956054401569	Henry Cohn, 2024, needs more optimization.
4	930	0.956074827191	Henry Cohn, 2024, needs more optimization.
4	931	0.956108274375	Henry Cohn, 2024, needs more optimization.
4	933	0.956137991454	Henry Cohn, 2024, needs more optimization.
4	934	0.956195225508	Henry Cohn, 2024, needs more optimization.
4	936	0.956244121903	Henry Cohn, 2024, needs more optimization.
4	937	0.956298249830	Henry Cohn, 2024, needs more optimization.
4	939	0.956362877162	Henry Cohn, 2024, needs more optimization.
4	940	0.956386720816	Henry Cohn, 2024, needs more optimization.
4	941	0.956420093644	Henry Cohn, 2024, needs more optimization.
4	942	0.956470218742	Henry Cohn, 2024, needs more optimization.
4	943	0.956499740104	Henry Cohn, 2024, needs more optimization.
4	944	0.956513607178	Henry Cohn, 2024, needs more optimization.
4	945	0.956544683564	Henry Cohn, 2024, needs more optimization.
4	947	0.956550215283	Henry Cohn, 2024, needs more optimization.
4	950	0.956609598011	Henry Cohn, 2024, needs more optimization.
4	952	0.956712484074	Henry Cohn, 2024, needs more optimization.
4	953	0.956792045991	Henry Cohn, 2024, needs more optimization.
4	955	0.956824088061	Henry Cohn, 2024, needs more optimization.
4	956	0.956860795759	Henry Cohn, 2024, needs more optimization.
4	957	0.956892010585	Henry Cohn, 2024, needs more optimization.
4	959	0.956946251206	Henry Cohn, 2024, needs more optimization.
4	960	0.956949581643	Henry Cohn, 2024, needs more optimization.
4	961	0.957050214016	Henry Cohn, 2024, needs more optimization.
4	963	0.957083854517	Henry Cohn, 2024, needs more optimization.
4	964	0.957106230310	Henry Cohn, 2024, needs more optimization.
4	965	0.957148465347	Henry Cohn, 2024, needs more optimization.
4	968	0.957208958546	Henry Cohn, 2024, needs more optimization.
4	969	0.957267596429	Henry Cohn, 2024, needs more optimization.
4	971	0.957320528962	Henry Cohn, 2024, needs more optimization.
4	972	0.957336758499	Henry Cohn, 2024, needs more optimization.
4	975	0.957437845084	Henry Cohn, 2024, needs more optimization.
4	977	0.957495119507	Henry Cohn, 2024, needs more optimization.
4	979	0.957553140244	Henry Cohn, 2024, needs more optimization.
4	981	0.957619518519	Henry Cohn, 2024, needs more optimization.
4	985	0.957700785593	Henry Cohn, 2024, needs more optimization.
4	986	0.957736958580	Henry Cohn, 2024, needs more optimization.
4	989	0.957832018405	Henry Cohn, 2024, needs more optimization.
4	992	0.957893243237	Henry Cohn, 2024, needs more optimization.
4	993	0.957969235162	Henry Cohn, 2024, needs more optimization.
4	994	0.957998372107	Henry Cohn, 2024, needs more optimization.
4	995	0.958021383055	Henry Cohn, 2024, needs more optimization.
4	998	0.958058819199	Henry Cohn, 2024, needs more optimization.
4	999	0.958094896802	Henry Cohn, 2024, needs more optimization.
4	1001	0.958101646044	Henry Cohn, 2024, needs more optimization.
4	1003	0.958189273472	Henry Cohn, 2024, needs more optimization.
4	1004	0.958255392006	Henry Cohn, 2024, needs more optimization.
4	1007	0.958318328203	Henry Cohn, 2024, needs more optimization.
4	1008	0.958383245319	Henry Cohn, 2024, needs more optimization.
4	1010	0.958429693501	Henry Cohn, 2024, needs more optimization.
4	1013	0.958459170454	Henry Cohn, 2024, needs more optimization.
4	1014	0.958557938703	Henry Cohn, 2024, needs more optimization.
4	1015	0.958593448969	Henry Cohn, 2024, needs more optimization.
4	1016	0.958633544661	Henry Cohn, 2024, needs more optimization.
4	1017	0.958638496262	Henry Cohn, 2024, needs more optimization.
4	1020	0.958673443818	Henry Cohn, 2024, needs more optimization.
4	1021	0.958685243756	Henry Cohn, 2024, needs more optimization.
4	1024	0.958714533977	Henry Cohn, 2024, needs more optimization.
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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	0.493828518628	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	0.499972875265	Henry Cohn, 2023.
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, preprint, 2023, arXiv:2301.08272. $2 x - 1$
5	41	0.514994652513	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.540671650625	Henry Cohn, 2023.
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	0.560142118522	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	53	0.566884877287	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	54	0.571075966439	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	55	0.574605986788	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.587022815774	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.596253477246	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.609103619699	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.615266925767	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.631407903402	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	77	0.636489609343	Henry Cohn, 2023.
5	78	0.640236710534	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	79	0.643753931686	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	80	0.646962010484	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	81	0.648895058528	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	82	0.651451569925	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	83	0.655404165086	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	84	0.657612544747	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	85	0.659252982679	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	86	0.660931914755	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.664477235588	Henry Cohn, 2023.
5	89	0.666348002159	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 2$
5	91	0.670415125494	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	92	0.672086633602	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	93	0.673832801501	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	94	0.675241775244	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	95	0.676620972599	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	96	0.677473018556	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	97	0.679247181253	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	98	0.680270697922	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	99	0.682139658875	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	100	0.683153328317	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	101	0.685227033891	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	102	0.687443384374	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	103	0.688905344259	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	104	0.689715883701	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	105	0.690732711178	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	106	0.692904385572	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	107	0.693864161444	Henry Cohn, 2023.
5	108	0.695372507746	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	109	0.696434702697	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	110	0.698105091973	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	111	0.699318689076	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	112	0.700444084148	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.703017238158	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	115	0.704067616852	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	116	0.705352999078	Henry Cohn, 2023.
5	117	0.706882139184	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	118	0.708028481260	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	119	0.709352721791	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	120	0.710428888246	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	121	0.711530238360	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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	0.713919145519	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	124	0.715099002544	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	125	0.716605852787	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	126	0.717145190665	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	127	0.718613506119	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	128	0.719656002161	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	129	0.720947869041	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	130	0.721730094738	N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5	131	0.723853049306	Henry Cohn, 2024, needs more optimization.
5	132	0.724870292733	Henry Cohn, 2024, needs more optimization.
5	133	0.726115431768	Henry Cohn, 2024, needs more optimization.
5	134	0.726883347614	Henry Cohn, 2024, needs more optimization.
5	135	0.727908200588	Henry Cohn, 2024, needs more optimization.
5	136	0.728827454181	Henry Cohn, 2024, needs more optimization.
5	137	0.730159471985	Henry Cohn, 2024, needs more optimization.
5	138	0.730266353459	Henry Cohn, 2024, needs more optimization.
5	139	0.731267033689	Henry Cohn, 2024, needs more optimization.
5	140	0.732117175105	Henry Cohn, 2024, needs more optimization.
5	141	0.733715250168	Henry Cohn, 2024, needs more optimization.
5	142	0.733715264397	Henry Cohn, 2024, needs more optimization.
5	143	0.734612488045	Henry Cohn, 2024, needs more optimization.
5	144	0.735438115559	Henry Cohn, 2024, needs more optimization.
5	145	0.736707343716	Henry Cohn, 2023, needs more optimization.
5	146	0.736774681076	Henry Cohn, 2023, needs more optimization.
5	147	0.737461390161	Henry Cohn, 2023, needs more optimization.
5	148	0.737471422467	Henry Cohn, 2023, needs more optimization.
5	149	0.738329535904	Henry Cohn, 2023, needs more optimization.
5	150	0.738349348874	Henry Cohn, 2023, needs more optimization.
5	151	0.739827413128	Henry Cohn, 2023, needs more optimization.
5	152	0.739876199454	Henry Cohn, 2023, needs more optimization.
5	153	0.740886797585	Henry Cohn, 2024, needs more optimization.
5	154	0.742051826605	Henry Cohn, 2024, needs more optimization.
5	157	0.743366608620	Henry Cohn, 2024, needs more optimization.
5	160	0.744260268055	Henry Cohn, 2024, needs more optimization.
5	161	0.748204728701	Henry Cohn, 2024, needs more optimization.
5	162	0.749359603117	Henry Cohn, 2024, needs more optimization.
5	163	0.750237841180	Henry Cohn, 2024, needs more optimization.
5	164	0.750908384766	Henry Cohn, 2024, needs more optimization.
5	165	0.752262899782	Henry Cohn, 2024, needs more optimization.
5	166	0.752579543240	Henry Cohn, 2023, needs more optimization.
5	167	0.754184794494	Henry Cohn, 2023, needs more optimization.
5	168	0.754284937443	Henry Cohn, 2023, needs more optimization.
5	169	0.755554921649	Henry Cohn, 2024, needs more optimization.
5	170	0.755995383248	Henry Cohn, 2023, needs more optimization.
5	171	0.757381694341	Henry Cohn, 2023, needs more optimization.
5	172	0.757394587080	Henry Cohn, 2023, needs more optimization.
5	173	0.759220863348	Henry Cohn, 2024, needs more optimization.
5	174	0.759690425040	Henry Cohn, 2023, needs more optimization.
5	175	0.761136575965	Henry Cohn, 2023, needs more optimization.
5	176	0.761291596002	Henry Cohn, 2023, needs more optimization.
5	177	0.762892588521	Henry Cohn, 2024, needs more optimization.
5	178	0.763382076889	Henry Cohn, 2023, needs more optimization.
5	179	0.764704800226	Henry Cohn, 2024, needs more optimization.
5	180	0.764936880585	Henry Cohn, 2023, needs more optimization.
5	181	0.765794767023	Henry Cohn, 2024, needs more optimization.
5	182	0.766427153803	Henry Cohn, 2023, needs more optimization.
5	185	0.767363496202	Henry Cohn, 2024, needs more optimization.
5	186	0.769346904184	Henry Cohn, 2024, needs more optimization.
5	187	0.769462725018	Henry Cohn, 2024, needs more optimization.
5	188	0.769560654051	Henry Cohn, 2024, needs more optimization.
5	190	0.770238782947	Henry Cohn, 2024, needs more optimization.
5	191	0.771575064156	Henry Cohn, 2024, needs more optimization.
5	193	0.772600271615	Henry Cohn, 2024, needs more optimization.
5	194	0.773695413313	Henry Cohn, 2024, needs more optimization.
5	196	0.773853606274	Henry Cohn, 2024, needs more optimization.
5	197	0.774320422769	Henry Cohn, 2024, needs more optimization.
5	198	0.775195125837	Henry Cohn, 2024, needs more optimization.
5	200	0.775830092166	Henry Cohn, 2024, needs more optimization.
5	201	0.776505734000	Henry Cohn, 2024, needs more optimization.
5	202	0.778049467958	Henry Cohn, 2024, needs more optimization.
5	203	0.778198546739	Henry Cohn, 2024, needs more optimization.
5	204	0.778316345232	Henry Cohn, 2024, needs more optimization.
5	205	0.779140257571	Henry Cohn, 2024, needs more optimization.
5	207	0.780230950029	Henry Cohn, 2024, needs more optimization.
5	208	0.781370933380	Henry Cohn, 2024, needs more optimization.
5	209	0.781423800855	Henry Cohn, 2024, needs more optimization.
5	210	0.782491866581	Henry Cohn, 2024, needs more optimization.
5	211	0.782993982704	Henry Cohn, 2024, needs more optimization.
5	212	0.783052185734	Henry Cohn, 2024, needs more optimization.
5	213	0.783806380081	Henry Cohn, 2024, needs more optimization.
5	215	0.784476666738	Henry Cohn, 2024, needs more optimization.
5	216	0.785746375620	Henry Cohn, 2024, needs more optimization.
5	218	0.786086042985	Henry Cohn, 2024, needs more optimization.
5	219	0.787031878255	Henry Cohn, 2024, needs more optimization.
5	220	0.787324856769	Henry Cohn, 2024, needs more optimization.
5	221	0.787599160203	Henry Cohn, 2024, needs more optimization.
5	222	0.788152190621	Henry Cohn, 2024, needs more optimization.
5	223	0.788530298061	Henry Cohn, 2024, needs more optimization.
5	224	0.788941339819	Henry Cohn, 2024, needs more optimization.
5	225	0.789730905769	Henry Cohn, 2024, needs more optimization.
5	226	0.789861304377	Henry Cohn, 2024, needs more optimization.
5	227	0.790582113513	Henry Cohn, 2024, needs more optimization.
5	228	0.790985469247	Henry Cohn, 2024, needs more optimization.
5	229	0.791078730919	Henry Cohn, 2024, needs more optimization.
5	230	0.791851866093	Henry Cohn, 2024, needs more optimization.
5	231	0.792568674016	Henry Cohn, 2024, needs more optimization.
5	232	0.793035378530	Henry Cohn, 2024, needs more optimization.
5	233	0.793046724488	Henry Cohn, 2024, needs more optimization.
5	234	0.793705982393	Henry Cohn, 2024, needs more optimization.
5	235	0.793722240144	Henry Cohn, 2024, needs more optimization.
5	236	0.794287616417	Henry Cohn, 2024, needs more optimization.
5	237	0.794839310491	Henry Cohn, 2024, needs more optimization.
5	238	0.795046053129	Henry Cohn, 2024, needs more optimization.
5	239	0.795899330658	Henry Cohn, 2024, needs more optimization.
5	240	0.796046678229	Henry Cohn, 2024, needs more optimization.
5	241	0.796348115337	Henry Cohn, 2024, needs more optimization.
5	242	0.796961742331	Henry Cohn, 2024, needs more optimization.
5	243	0.797430341595	Henry Cohn, 2024, needs more optimization.
5	244	0.797794966275	Henry Cohn, 2024, needs more optimization.
5	245	0.798017421367	Henry Cohn, 2024, needs more optimization.
5	246	0.798323201171	Henry Cohn, 2024, needs more optimization.
5	247	0.799019810739	Henry Cohn, 2024, needs more optimization.
5	248	0.799384175796	Henry Cohn, 2024, needs more optimization.
5	249	0.799923913903	Henry Cohn, 2024, needs more optimization.
5	250	0.799940952008	Henry Cohn, 2024, needs more optimization.
5	251	0.800781081129	Henry Cohn, 2024, needs more optimization.
5	252	0.801170160320	Henry Cohn, 2024, needs more optimization.
5	253	0.801514527195	Henry Cohn, 2024, needs more optimization.
5	254	0.802087710003	Henry Cohn, 2024, needs more optimization.
5	255	0.802465141541	Henry Cohn, 2024, needs more optimization.
5	256	0.802732635286	Henry Cohn, 2024, needs more optimization.
5	259	0.804365568744	Henry Cohn, 2024, needs more optimization.
5	261	0.805364089812	Henry Cohn, 2024, needs more optimization.
5	262	0.806196578766	Henry Cohn, 2024, needs more optimization.
5	264	0.806588241089	Henry Cohn, 2024, needs more optimization.
5	265	0.807187315552	Henry Cohn, 2024, needs more optimization.
5	266	0.807775518991	Henry Cohn, 2024, needs more optimization.
5	267	0.807956721814	Henry Cohn, 2024, needs more optimization.
5	268	0.808258420430	Henry Cohn, 2024, needs more optimization.
5	269	0.808642595573	Henry Cohn, 2024, needs more optimization.
5	270	0.808890608595	Henry Cohn, 2024, needs more optimization.
5	272	0.809279650265	Henry Cohn, 2024, needs more optimization.
5	273	0.810261737510	Henry Cohn, 2024, needs more optimization.
5	275	0.810699099617	Henry Cohn, 2024, needs more optimization.
5	276	0.810904628277	Henry Cohn, 2024, needs more optimization.
5	280	0.811088581620	Henry Cohn, 2024, needs more optimization.
5	283	0.812614508146	Henry Cohn, 2024, needs more optimization.
5	284	0.813983997377	Henry Cohn, 2024, needs more optimization.
5	286	0.814078717775	Henry Cohn, 2024, needs more optimization.
5	288	0.814119126700	Henry Cohn, 2024, needs more optimization.
5	291	0.814917952232	Henry Cohn, 2024, needs more optimization.
5	293	0.816028137657	Henry Cohn, 2024, needs more optimization.
5	296	0.816364724088	Henry Cohn, 2024, needs more optimization.
5	297	0.817481814940	Henry Cohn, 2024, needs more optimization.
5	298	0.817840270172	Henry Cohn, 2024, needs more optimization.
5	301	0.818379670150	Henry Cohn, 2024, needs more optimization.
5	302	0.819463983673	Henry Cohn, 2024, needs more optimization.
5	303	0.819658646523	Henry Cohn, 2024, needs more optimization.
5	304	0.820126962577	Henry Cohn, 2024, needs more optimization.
5	305	0.820349173815	Henry Cohn, 2024, needs more optimization.
5	306	0.820472767333	Henry Cohn, 2024, needs more optimization.
5	308	0.820638345789	Henry Cohn, 2024, needs more optimization.
5	309	0.821183950529	Henry Cohn, 2024, needs more optimization.
5	311	0.821586204643	Henry Cohn, 2024, needs more optimization.
5	312	0.822084865801	Henry Cohn, 2024, needs more optimization.
5	313	0.822480648604	Henry Cohn, 2024, needs more optimization.
5	315	0.822724427165	Henry Cohn, 2024, needs more optimization.
5	316	0.823137527884	Henry Cohn, 2024, needs more optimization.
5	317	0.823636887557	Henry Cohn, 2024, needs more optimization.
5	319	0.824128488039	Henry Cohn, 2024, needs more optimization.
5	320	0.824194874505	Henry Cohn, 2024, needs more optimization.
5	321	0.824899150812	Henry Cohn, 2024, needs more optimization.
5	322	0.825301305160	Henry Cohn, 2024, needs more optimization.
5	323	0.825357424042	Henry Cohn, 2024, needs more optimization.
5	325	0.826190770537	Henry Cohn, 2024, needs more optimization.
5	326	0.826227958929	Henry Cohn, 2024, needs more optimization.
5	327	0.826624782521	Henry Cohn, 2024, needs more optimization.
5	328	0.826677144046	Henry Cohn, 2024, needs more optimization.
5	329	0.827055727040	Henry Cohn, 2024, needs more optimization.
5	330	0.827296764854	Henry Cohn, 2024, needs more optimization.
5	331	0.827772318169	Henry Cohn, 2024, needs more optimization.
5	332	0.827811072466	Henry Cohn, 2024, needs more optimization.
5	333	0.828075567302	Henry Cohn, 2024, needs more optimization.
5	334	0.828307204645	Henry Cohn, 2024, needs more optimization.
5	335	0.828618147268	Henry Cohn, 2024, needs more optimization.
5	336	0.828810689470	Henry Cohn, 2024, needs more optimization.
5	337	0.828957776638	Henry Cohn, 2024, needs more optimization.
5	338	0.829186674146	Henry Cohn, 2024, needs more optimization.
5	339	0.829838766006	Henry Cohn, 2024, needs more optimization.
5	341	0.829970527052	Henry Cohn, 2024, needs more optimization.
5	344	0.830356860911	Henry Cohn, 2024, needs more optimization.
5	345	0.831045088218	Henry Cohn, 2024, needs more optimization.
5	346	0.831390275493	Henry Cohn, 2024, needs more optimization.
5	347	0.831601347799	Henry Cohn, 2024, needs more optimization.
5	348	0.831672442113	Henry Cohn, 2024, needs more optimization.
5	349	0.832052653241	Henry Cohn, 2024, needs more optimization.
5	350	0.832425502856	Henry Cohn, 2024, needs more optimization.
5	351	0.832573849774	Henry Cohn, 2024, needs more optimization.
5	352	0.832955547750	Henry Cohn, 2024, needs more optimization.
5	353	0.833014323351	Henry Cohn, 2024, needs more optimization.
5	354	0.833464722235	Henry Cohn, 2024, needs more optimization.
5	356	0.833910528442	Henry Cohn, 2024, needs more optimization.
5	358	0.834071360859	Henry Cohn, 2024, needs more optimization.
5	359	0.834430269447	Henry Cohn, 2024, needs more optimization.
5	360	0.834749623842	Henry Cohn, 2024, needs more optimization.
5	361	0.834786686148	Henry Cohn, 2024, needs more optimization.
5	362	0.835457229262	Henry Cohn, 2024, needs more optimization.
5	364	0.835560062018	Henry Cohn, 2024, needs more optimization.
5	365	0.835705788970	Henry Cohn, 2024, needs more optimization.
5	367	0.836303774293	Henry Cohn, 2024, needs more optimization.
5	368	0.836714323209	Henry Cohn, 2024, needs more optimization.
5	369	0.836782914324	Henry Cohn, 2024, needs more optimization.
5	371	0.837000241908	Henry Cohn, 2024, needs more optimization.
5	372	0.837568827428	Henry Cohn, 2024, needs more optimization.
5	373	0.837984289731	Henry Cohn, 2024, needs more optimization.
5	374	0.838011369229	Henry Cohn, 2024, needs more optimization.
5	376	0.838022067031	Henry Cohn, 2024, needs more optimization.
5	377	0.838408526472	Henry Cohn, 2024, needs more optimization.
5	378	0.838695093407	Henry Cohn, 2024, needs more optimization.
5	379	0.838728975267	Henry Cohn, 2024, needs more optimization.
5	380	0.839034491539	Henry Cohn, 2024, needs more optimization.
5	381	0.839134741746	Henry Cohn, 2024, needs more optimization.
5	382	0.839562405768	Henry Cohn, 2024, needs more optimization.
5	384	0.839566094156	Henry Cohn, 2024, needs more optimization.
5	385	0.840050635133	Henry Cohn, 2024, needs more optimization.
5	386	0.840464741395	Henry Cohn, 2024, needs more optimization.
5	388	0.840602041499	Henry Cohn, 2024, needs more optimization.
5	390	0.840928236435	Henry Cohn, 2024, needs more optimization.
5	391	0.841242182169	Henry Cohn, 2024, needs more optimization.
5	392	0.841390348408	Henry Cohn, 2024, needs more optimization.
5	393	0.841802648465	Henry Cohn, 2024, needs more optimization.
5	394	0.841907172523	Henry Cohn, 2024, needs more optimization.
5	397	0.842312525805	Henry Cohn, 2024, needs more optimization.
5	398	0.842821829194	Henry Cohn, 2024, needs more optimization.
5	400	0.843240089870	Henry Cohn, 2024, needs more optimization.
5	401	0.843303453627	Henry Cohn, 2024, needs more optimization.
5	402	0.843448008706	Henry Cohn, 2024, needs more optimization.
5	403	0.843760372226	Henry Cohn, 2024, needs more optimization.
5	404	0.843982341983	Henry Cohn, 2024, needs more optimization.
5	405	0.844094998240	Henry Cohn, 2024, needs more optimization.
5	406	0.844323377158	Henry Cohn, 2024, needs more optimization.
5	407	0.844626678238	Henry Cohn, 2024, needs more optimization.
5	408	0.844728665046	Henry Cohn, 2024, needs more optimization.
5	409	0.845131657966	Henry Cohn, 2024, needs more optimization.
5	410	0.845162070883	Henry Cohn, 2024, needs more optimization.
5	412	0.845363429802	Henry Cohn, 2024, needs more optimization.
5	413	0.845632012347	Henry Cohn, 2024, needs more optimization.
5	414	0.845999071609	Henry Cohn, 2024, needs more optimization.
5	416	0.846020370040	Henry Cohn, 2024, needs more optimization.
5	418	0.846552824540	Henry Cohn, 2024, needs more optimization.
5	420	0.846821424511	Henry Cohn, 2024, needs more optimization.
5	421	0.847030147027	Henry Cohn, 2024, needs more optimization.
5	422	0.847334138568	Henry Cohn, 2024, needs more optimization.
5	423	0.847587604521	Henry Cohn, 2024, needs more optimization.
5	424	0.847669838081	Henry Cohn, 2024, needs more optimization.
5	425	0.847858641963	Henry Cohn, 2024, needs more optimization.
5	427	0.848207858796	Henry Cohn, 2024, needs more optimization.
5	430	0.848485508273	Henry Cohn, 2024, needs more optimization.
5	433	0.849135870400	Henry Cohn, 2024, needs more optimization.
5	434	0.849363632667	Henry Cohn, 2024, needs more optimization.
5	435	0.849570598863	Henry Cohn, 2024, needs more optimization.
5	436	0.849849099816	Henry Cohn, 2024, needs more optimization.
5	437	0.849957909446	Henry Cohn, 2024, needs more optimization.
5	438	0.850103459975	Henry Cohn, 2024, needs more optimization.
5	439	0.850274420514	Henry Cohn, 2024, needs more optimization.
5	441	0.850486201575	Henry Cohn, 2024, needs more optimization.
5	442	0.850827343879	Henry Cohn, 2024, needs more optimization.
5	443	0.850935072484	Henry Cohn, 2024, needs more optimization.
5	444	0.851209022587	Henry Cohn, 2024, needs more optimization.
5	448	0.851432775789	Henry Cohn, 2024, needs more optimization.
5	449	0.852151140396	Henry Cohn, 2024, needs more optimization.
5	450	0.852162322111	Henry Cohn, 2024, needs more optimization.
5	451	0.852282218652	Henry Cohn, 2024, needs more optimization.
5	452	0.852502182038	Henry Cohn, 2024, needs more optimization.
5	453	0.852717545823	Henry Cohn, 2024, needs more optimization.
5	454	0.852893200243	Henry Cohn, 2024, needs more optimization.
5	455	0.853050002615	Henry Cohn, 2024, needs more optimization.
5	456	0.853095202972	Henry Cohn, 2024, needs more optimization.
5	457	0.853292465907	Henry Cohn, 2024, needs more optimization.
5	458	0.853318679436	Henry Cohn, 2024, needs more optimization.
5	459	0.853448056291	Henry Cohn, 2024, needs more optimization.
5	460	0.853607891027	Henry Cohn, 2024, needs more optimization.
5	461	0.854014934924	Henry Cohn, 2024, needs more optimization.
5	462	0.854139361204	Henry Cohn, 2024, needs more optimization.
5	464	0.854199545036	Henry Cohn, 2024, needs more optimization.
5	465	0.854656043804	Henry Cohn, 2024, needs more optimization.
5	466	0.854685124658	Henry Cohn, 2024, needs more optimization.
5	467	0.854900514284	Henry Cohn, 2024, needs more optimization.
5	468	0.855047111512	Henry Cohn, 2024, needs more optimization.
5	469	0.855154626641	Henry Cohn, 2024, needs more optimization.
5	471	0.855502861326	Henry Cohn, 2024, needs more optimization.
5	473	0.855708510715	Henry Cohn, 2024, needs more optimization.
5	474	0.855914036580	Henry Cohn, 2024, needs more optimization.
5	475	0.856044320281	Henry Cohn, 2024, needs more optimization.
5	476	0.856251176730	Henry Cohn, 2024, needs more optimization.
5	477	0.856311183940	Henry Cohn, 2024, needs more optimization.
5	478	0.856593109572	Henry Cohn, 2024, needs more optimization.
5	479	0.856795015260	Henry Cohn, 2024, needs more optimization.
5	480	0.856848279845	Henry Cohn, 2024, needs more optimization.
5	481	0.857045857514	Henry Cohn, 2024, needs more optimization.
5	484	0.857153369342	Henry Cohn, 2024, needs more optimization.
5	485	0.857420676450	Henry Cohn, 2024, needs more optimization.
5	486	0.857684155167	Henry Cohn, 2024, needs more optimization.
5	487	0.857968881527	Henry Cohn, 2024, needs more optimization.
5	489	0.858087616773	Henry Cohn, 2024, needs more optimization.
5	491	0.858504282110	Henry Cohn, 2024, needs more optimization.
5	492	0.858750770561	Henry Cohn, 2024, needs more optimization.
5	493	0.858795703097	Henry Cohn, 2024, needs more optimization.
5	495	0.859131662939	Henry Cohn, 2024, needs more optimization.
5	496	0.859170534119	Henry Cohn, 2024, needs more optimization.
5	497	0.859408304608	Henry Cohn, 2024, needs more optimization.
5	498	0.859487868753	Henry Cohn, 2024, needs more optimization.
5	499	0.859567838868	Henry Cohn, 2024, needs more optimization.
5	500	0.859706771153	Henry Cohn, 2024, needs more optimization.
5	501	0.859897152580	Henry Cohn, 2024, needs more optimization.
5	502	0.859940964715	Henry Cohn, 2024, needs more optimization.
5	503	0.860146264816	Henry Cohn, 2024, needs more optimization.
5	506	0.860274079827	Henry Cohn, 2024, needs more optimization.
5	507	0.860678561599	Henry Cohn, 2024, needs more optimization.
5	508	0.860834864014	Henry Cohn, 2024, needs more optimization.
5	509	0.860881787214	Henry Cohn, 2024, needs more optimization.
5	510	0.861236555039	Henry Cohn, 2024, needs more optimization.
5	513	0.861244572197	Henry Cohn, 2024, needs more optimization.
5	514	0.861625503796	Henry Cohn, 2024, needs more optimization.
5	515	0.861830077907	Henry Cohn, 2024, needs more optimization.
5	516	0.862046621170	Henry Cohn, 2024, needs more optimization.
5	517	0.862175214074	Henry Cohn, 2024, needs more optimization.
5	518	0.862273900242	Henry Cohn, 2024, needs more optimization.
5	520	0.862325868568	Henry Cohn, 2024, needs more optimization.
5	521	0.862426469177	Henry Cohn, 2024, needs more optimization.
5	523	0.862743700127	Henry Cohn, 2024, needs more optimization.
5	524	0.862946026997	Henry Cohn, 2024, needs more optimization.
5	525	0.863041567481	Henry Cohn, 2024, needs more optimization.
5	526	0.863100633608	Henry Cohn, 2024, needs more optimization.
5	527	0.863259247880	Henry Cohn, 2024, needs more optimization.
5	528	0.863511073342	Henry Cohn, 2024, needs more optimization.
5	530	0.863743087066	Henry Cohn, 2024, needs more optimization.
5	531	0.863845584375	Henry Cohn, 2024, needs more optimization.
5	532	0.864053817183	Henry Cohn, 2024, needs more optimization.
5	533	0.864055692783	Henry Cohn, 2024, needs more optimization.
5	535	0.864307945238	Henry Cohn, 2024, needs more optimization.
5	536	0.864462980256	Henry Cohn, 2024, needs more optimization.
5	537	0.864746499229	Henry Cohn, 2024, needs more optimization.
5	538	0.864763768541	Henry Cohn, 2024, needs more optimization.
5	539	0.864963899451	Henry Cohn, 2024, needs more optimization.
5	541	0.865150496144	Henry Cohn, 2024, needs more optimization.
5	542	0.865205925033	Henry Cohn, 2024, needs more optimization.
5	543	0.865431271794	Henry Cohn, 2024, needs more optimization.
5	544	0.865480762229	Henry Cohn, 2024, needs more optimization.
5	546	0.865658346206	Henry Cohn, 2024, needs more optimization.
5	547	0.865983140110	Henry Cohn, 2024, needs more optimization.
5	548	0.866045826282	Henry Cohn, 2024, needs more optimization.
5	550	0.866116874581	Henry Cohn, 2024, needs more optimization.
5	551	0.866258048697	Henry Cohn, 2024, needs more optimization.
5	552	0.866440792158	Henry Cohn, 2024, needs more optimization.
5	553	0.866716308880	Henry Cohn, 2024, needs more optimization.
5	554	0.866825845809	Henry Cohn, 2024, needs more optimization.
5	555	0.866837487961	Henry Cohn, 2024, needs more optimization.
5	556	0.866974638342	Henry Cohn, 2024, needs more optimization.
5	558	0.867151103958	Henry Cohn, 2024, needs more optimization.
5	559	0.867275706665	Henry Cohn, 2024, needs more optimization.
5	560	0.867581474695	Henry Cohn, 2024, needs more optimization.
5	561	0.867654791888	Henry Cohn, 2024, needs more optimization.
5	562	0.867754993003	Henry Cohn, 2024, needs more optimization.
5	566	0.867930075223	Henry Cohn, 2024, needs more optimization.
5	567	0.868154739433	Henry Cohn, 2024, needs more optimization.
5	568	0.868460903554	Henry Cohn, 2024, needs more optimization.
5	569	0.868640973039	Henry Cohn, 2024, needs more optimization.
5	572	0.868700450314	Henry Cohn, 2024, needs more optimization.
5	573	0.869083028738	Henry Cohn, 2024, needs more optimization.
5	574	0.869165673125	Henry Cohn, 2024, needs more optimization.
5	575	0.869168051733	Henry Cohn, 2024, needs more optimization.
5	576	0.869189760749	Henry Cohn, 2024, needs more optimization.
5	579	0.869376734154	Henry Cohn, 2024, needs more optimization.
5	580	0.869715916888	Henry Cohn, 2024, needs more optimization.
5	581	0.869885323351	Henry Cohn, 2024, needs more optimization.
5	582	0.870002608277	Henry Cohn, 2024, needs more optimization.
5	583	0.870077706418	Henry Cohn, 2024, needs more optimization.
5	584	0.870097004849	Henry Cohn, 2024, needs more optimization.
5	586	0.870351175241	Henry Cohn, 2024, needs more optimization.
5	587	0.870546353949	Henry Cohn, 2024, needs more optimization.
5	588	0.870549506069	Henry Cohn, 2024, needs more optimization.
5	589	0.870682284698	Henry Cohn, 2024, needs more optimization.
5	590	0.870829286630	Henry Cohn, 2024, needs more optimization.
5	591	0.870873097654	Henry Cohn, 2024, needs more optimization.
5	592	0.871137571124	Henry Cohn, 2024, needs more optimization.
5	593	0.871214653695	Henry Cohn, 2024, needs more optimization.
5	594	0.871377567331	Henry Cohn, 2024, needs more optimization.
5	595	0.871469463406	Henry Cohn, 2024, needs more optimization.
5	596	0.871644386395	Henry Cohn, 2024, needs more optimization.
5	598	0.871700372073	Henry Cohn, 2024, needs more optimization.
5	599	0.871913258408	Henry Cohn, 2024, needs more optimization.
5	600	0.871914356253	Henry Cohn, 2024, needs more optimization.
5	603	0.872149965704	Henry Cohn, 2024, needs more optimization.
5	604	0.872395012648	Henry Cohn, 2024, needs more optimization.
5	605	0.872542956026	Henry Cohn, 2024, needs more optimization.
5	606	0.872547887133	Henry Cohn, 2024, needs more optimization.
5	608	0.872799152019	Henry Cohn, 2024, needs more optimization.
5	611	0.873011641373	Henry Cohn, 2024, needs more optimization.
5	613	0.873256545581	Henry Cohn, 2024, needs more optimization.
5	615	0.873655077187	Henry Cohn, 2024, needs more optimization.
5	616	0.873655815253	Henry Cohn, 2024, needs more optimization.
5	617	0.873694927318	Henry Cohn, 2024, needs more optimization.
5	618	0.873819964436	Henry Cohn, 2024, needs more optimization.
5	619	0.873899892395	Henry Cohn, 2024, needs more optimization.
5	620	0.874014428541	Henry Cohn, 2024, needs more optimization.
5	621	0.874072808850	Henry Cohn, 2024, needs more optimization.
5	622	0.874366316964	Henry Cohn, 2024, needs more optimization.
5	624	0.874396187666	Henry Cohn, 2024, needs more optimization.
5	625	0.874578160131	Henry Cohn, 2024, needs more optimization.
5	628	0.874714925477	Henry Cohn, 2024, needs more optimization.
5	629	0.875001630372	Henry Cohn, 2024, needs more optimization.
5	631	0.875133452902	Henry Cohn, 2024, needs more optimization.
5	632	0.875234293561	Henry Cohn, 2024, needs more optimization.
5	635	0.875373259173	Henry Cohn, 2024, needs more optimization.
5	636	0.875675789672	Henry Cohn, 2024, needs more optimization.
5	638	0.875711170884	Henry Cohn, 2024, needs more optimization.
5	640	0.875852396517	Henry Cohn, 2024, needs more optimization.
5	642	0.876226633771	Henry Cohn, 2024, needs more optimization.
5	644	0.876293400090	Henry Cohn, 2024, needs more optimization.
5	645	0.876614699650	Henry Cohn, 2024, needs more optimization.
5	648	0.876762649138	Henry Cohn, 2024, needs more optimization.
5	649	0.876987819711	Henry Cohn, 2024, needs more optimization.
5	651	0.877028870962	Henry Cohn, 2024, needs more optimization.
5	652	0.877157740745	Henry Cohn, 2024, needs more optimization.
5	653	0.877352497852	Henry Cohn, 2024, needs more optimization.
5	654	0.877494009920	Henry Cohn, 2024, needs more optimization.
5	655	0.877509099472	Henry Cohn, 2024, needs more optimization.
5	656	0.877590475147	Henry Cohn, 2024, needs more optimization.
5	658	0.877619210720	Henry Cohn, 2024, needs more optimization.
5	659	0.877763475717	Henry Cohn, 2024, needs more optimization.
5	660	0.877887494621	Henry Cohn, 2024, needs more optimization.
5	661	0.877984131042	Henry Cohn, 2024, needs more optimization.
5	663	0.878009254707	Henry Cohn, 2024, needs more optimization.
5	664	0.878266437860	Henry Cohn, 2024, needs more optimization.
5	666	0.878380405179	Henry Cohn, 2024, needs more optimization.
5	667	0.878485599017	Henry Cohn, 2024, needs more optimization.
5	668	0.878618794532	Henry Cohn, 2024, needs more optimization.
5	669	0.878697117470	Henry Cohn, 2024, needs more optimization.
5	670	0.878825425526	Henry Cohn, 2024, needs more optimization.
5	671	0.878962663408	Henry Cohn, 2024, needs more optimization.
5	672	0.878989807514	Henry Cohn, 2024, needs more optimization.
5	674	0.879169553714	Henry Cohn, 2024, needs more optimization.
5	675	0.879397322870	Henry Cohn, 2024, needs more optimization.
5	678	0.879452118947	Henry Cohn, 2024, needs more optimization.
5	679	0.879663231041	Henry Cohn, 2024, needs more optimization.
5	681	0.879713860312	Henry Cohn, 2024, needs more optimization.
5	682	0.879911777784	Henry Cohn, 2024, needs more optimization.
5	683	0.879962151626	Henry Cohn, 2024, needs more optimization.
5	684	0.880126685542	Henry Cohn, 2024, needs more optimization.
5	686	0.880185138246	Henry Cohn, 2024, needs more optimization.
5	687	0.880460960820	Henry Cohn, 2024, needs more optimization.
5	688	0.880486385669	Henry Cohn, 2024, needs more optimization.
5	691	0.880569275227	Henry Cohn, 2024, needs more optimization.
5	693	0.880871984413	Henry Cohn, 2024, needs more optimization.
5	694	0.880915878774	Henry Cohn, 2024, needs more optimization.
5	697	0.881151663214	Henry Cohn, 2024, needs more optimization.
5	698	0.881307594158	Henry Cohn, 2024, needs more optimization.
5	701	0.881441027180	Henry Cohn, 2024, needs more optimization.
5	704	0.881682980873	Henry Cohn, 2024, needs more optimization.
5	705	0.882008195150	Henry Cohn, 2024, needs more optimization.
5	706	0.882051706359	Henry Cohn, 2024, needs more optimization.
5	707	0.882130107580	Henry Cohn, 2024, needs more optimization.
5	708	0.882188597988	Henry Cohn, 2024, needs more optimization.
5	709	0.882202800275	Henry Cohn, 2024, needs more optimization.
5	711	0.882430508301	Henry Cohn, 2024, needs more optimization.
5	712	0.882478866731	Henry Cohn, 2024, needs more optimization.
5	713	0.882488454047	Henry Cohn, 2024, needs more optimization.
5	715	0.882698489298	Henry Cohn, 2024, needs more optimization.
5	716	0.882776825715	Henry Cohn, 2024, needs more optimization.
5	718	0.882885029506	Henry Cohn, 2024, needs more optimization.
5	719	0.883096889132	Henry Cohn, 2024, needs more optimization.
5	720	0.883180423876	Henry Cohn, 2024, needs more optimization.
5	721	0.883219842994	Henry Cohn, 2024, needs more optimization.
5	722	0.883226047184	Henry Cohn, 2024, needs more optimization.
5	723	0.883276992636	Henry Cohn, 2024, needs more optimization.
5	725	0.883437265048	Henry Cohn, 2024, needs more optimization.
5	726	0.883629379706	Henry Cohn, 2024, needs more optimization.
5	727	0.883707547779	Henry Cohn, 2024, needs more optimization.
5	728	0.883789970892	Henry Cohn, 2024, needs more optimization.
5	731	0.883849962842	Henry Cohn, 2024, needs more optimization.
5	733	0.884051438759	Henry Cohn, 2024, needs more optimization.
5	734	0.884232429039	Henry Cohn, 2024, needs more optimization.
5	735	0.884315277993	Henry Cohn, 2024, needs more optimization.
5	736	0.884403987239	Henry Cohn, 2024, needs more optimization.
5	738	0.884421975221	Henry Cohn, 2024, needs more optimization.
5	739	0.884537682167	Henry Cohn, 2024, needs more optimization.
5	741	0.884612007344	Henry Cohn, 2024, needs more optimization.
5	742	0.884903908555	Henry Cohn, 2024, needs more optimization.
5	744	0.884931378298	Henry Cohn, 2024, needs more optimization.
5	746	0.885126705969	Henry Cohn, 2024, needs more optimization.
5	747	0.885282632038	Henry Cohn, 2024, needs more optimization.
5	750	0.885337542079	Henry Cohn, 2024, needs more optimization.
5	751	0.885553903822	Henry Cohn, 2024, needs more optimization.
5	752	0.885588240547	Henry Cohn, 2024, needs more optimization.
5	753	0.885669470504	Henry Cohn, 2024, needs more optimization.
5	754	0.885734650099	Henry Cohn, 2024, needs more optimization.
5	756	0.885940460680	Henry Cohn, 2024, needs more optimization.
5	757	0.885952991329	Henry Cohn, 2024, needs more optimization.
5	758	0.886006514193	Henry Cohn, 2024, needs more optimization.
5	759	0.886173648154	Henry Cohn, 2024, needs more optimization.
5	760	0.886228035838	Henry Cohn, 2024, needs more optimization.
5	762	0.886280660119	Henry Cohn, 2024, needs more optimization.
5	763	0.886482522214	Henry Cohn, 2024, needs more optimization.
5	764	0.886497941376	Henry Cohn, 2024, needs more optimization.
5	765	0.886595781673	Henry Cohn, 2024, needs more optimization.
5	768	0.886671289046	Henry Cohn, 2024, needs more optimization.
5	769	0.886950241615	Henry Cohn, 2024, needs more optimization.
5	772	0.887069683254	Henry Cohn, 2024, needs more optimization.
5	773	0.887166302857	Henry Cohn, 2024, needs more optimization.
5	774	0.887261024845	Henry Cohn, 2024, needs more optimization.
5	777	0.887395747281	Henry Cohn, 2024, needs more optimization.
5	778	0.887574308533	Henry Cohn, 2024, needs more optimization.
5	780	0.887602025499	Henry Cohn, 2024, needs more optimization.
5	781	0.887706303584	Henry Cohn, 2024, needs more optimization.
5	783	0.887811222711	Henry Cohn, 2024, needs more optimization.
5	784	0.887992148820	Henry Cohn, 2024, needs more optimization.
5	787	0.888182990228	Henry Cohn, 2024, needs more optimization.
5	789	0.888270403855	Henry Cohn, 2024, needs more optimization.
5	790	0.888388579550	Henry Cohn, 2024, needs more optimization.
5	791	0.888470427741	Henry Cohn, 2024, needs more optimization.
5	792	0.888638348940	Henry Cohn, 2024, needs more optimization.
5	794	0.888713851464	Henry Cohn, 2024, needs more optimization.
5	795	0.888770473237	Henry Cohn, 2024, needs more optimization.
5	796	0.888829768067	Henry Cohn, 2024, needs more optimization.
5	797	0.888876578495	Henry Cohn, 2024, needs more optimization.
5	798	0.888969354507	Henry Cohn, 2024, needs more optimization.
5	800	0.888977985876	Henry Cohn, 2024, needs more optimization.
5	801	0.889252466796	Henry Cohn, 2024, needs more optimization.
5	802	0.889280879522	Henry Cohn, 2024, needs more optimization.
5	803	0.889307923206	Henry Cohn, 2024, needs more optimization.
5	805	0.889471506750	Henry Cohn, 2024, needs more optimization.
5	807	0.889499578559	Henry Cohn, 2024, needs more optimization.
5	808	0.889649407936	Henry Cohn, 2024, needs more optimization.
5	809	0.889731279837	Henry Cohn, 2024, needs more optimization.
5	811	0.889823029790	Henry Cohn, 2024, needs more optimization.
5	812	0.889909164306	Henry Cohn, 2024, needs more optimization.
5	813	0.889979956355	Henry Cohn, 2024, needs more optimization.
5	814	0.890046635657	Henry Cohn, 2024, needs more optimization.
5	817	0.890108868183	Henry Cohn, 2024, needs more optimization.
5	818	0.890266868567	Henry Cohn, 2024, needs more optimization.
5	819	0.890385996844	Henry Cohn, 2024, needs more optimization.
5	820	0.890478958845	Henry Cohn, 2024, needs more optimization.
5	821	0.890657978109	Henry Cohn, 2024, needs more optimization.
5	823	0.890680674688	Henry Cohn, 2024, needs more optimization.
5	824	0.890740727603	Henry Cohn, 2024, needs more optimization.
5	825	0.890847244891	Henry Cohn, 2024, needs more optimization.
5	826	0.890903780680	Henry Cohn, 2024, needs more optimization.
5	829	0.890971959102	Henry Cohn, 2024, needs more optimization.
5	832	0.891126553040	Henry Cohn, 2024, needs more optimization.
5	833	0.891311371756	Henry Cohn, 2024, needs more optimization.
5	834	0.891378704132	Henry Cohn, 2024, needs more optimization.
5	835	0.891551754477	Henry Cohn, 2024, needs more optimization.
5	837	0.891554083247	Henry Cohn, 2024, needs more optimization.
5	838	0.891655942234	Henry Cohn, 2024, needs more optimization.
5	840	0.891794463631	Henry Cohn, 2024, needs more optimization.
5	842	0.891890249568	Henry Cohn, 2024, needs more optimization.
5	845	0.892003657647	Henry Cohn, 2024, needs more optimization.
5	846	0.892125077493	Henry Cohn, 2024, needs more optimization.
5	847	0.892129416853	Henry Cohn, 2024, needs more optimization.
5	851	0.892267206698	Henry Cohn, 2024, needs more optimization.
5	852	0.892425916059	Henry Cohn, 2024, needs more optimization.
5	853	0.892674728337	Henry Cohn, 2024, needs more optimization.
5	854	0.892683379112	Henry Cohn, 2024, needs more optimization.
5	855	0.892710031206	Henry Cohn, 2024, needs more optimization.
5	856	0.892865430148	Henry Cohn, 2024, needs more optimization.
5	857	0.892912051380	Henry Cohn, 2024, needs more optimization.
5	858	0.892925244132	Henry Cohn, 2024, needs more optimization.
5	862	0.893122874927	Henry Cohn, 2024, needs more optimization.
5	863	0.893265322543	Henry Cohn, 2024, needs more optimization.
5	864	0.893350487836	Henry Cohn, 2024, needs more optimization.
5	866	0.893392065409	Henry Cohn, 2024, needs more optimization.
5	867	0.893448779823	Henry Cohn, 2024, needs more optimization.
5	868	0.893488420859	Henry Cohn, 2024, needs more optimization.
5	869	0.893625408722	Henry Cohn, 2024, needs more optimization.
5	870	0.893717181289	Henry Cohn, 2024, needs more optimization.
5	871	0.893760316104	Henry Cohn, 2024, needs more optimization.
5	872	0.893774305089	Henry Cohn, 2024, needs more optimization.
5	873	0.893822219690	Henry Cohn, 2024, needs more optimization.
5	876	0.893890180337	Henry Cohn, 2024, needs more optimization.
5	877	0.894014232502	Henry Cohn, 2024, needs more optimization.
5	880	0.894142258873	Henry Cohn, 2024, needs more optimization.
5	882	0.894285244595	Henry Cohn, 2024, needs more optimization.
5	883	0.894455789858	Henry Cohn, 2024, needs more optimization.
5	884	0.894487326292	Henry Cohn, 2024, needs more optimization.
5	885	0.894564551460	Henry Cohn, 2024, needs more optimization.
5	886	0.894646001125	Henry Cohn, 2024, needs more optimization.
5	888	0.894686608921	Henry Cohn, 2024, needs more optimization.
5	889	0.894821501081	Henry Cohn, 2024, needs more optimization.
5	890	0.894879750200	Henry Cohn, 2024, needs more optimization.
5	892	0.894898856619	Henry Cohn, 2024, needs more optimization.
5	893	0.894961547473	Henry Cohn, 2024, needs more optimization.
5	896	0.895086375676	Henry Cohn, 2024, needs more optimization.
5	897	0.895213205466	Henry Cohn, 2024, needs more optimization.
5	898	0.895347107199	Henry Cohn, 2024, needs more optimization.
5	899	0.895413871078	Henry Cohn, 2024, needs more optimization.
5	900	0.895534212293	Henry Cohn, 2024, needs more optimization.
5	901	0.895550416012	Henry Cohn, 2024, needs more optimization.
5	904	0.895579314721	Henry Cohn, 2024, needs more optimization.
5	907	0.895824459327	Henry Cohn, 2024, needs more optimization.
5	908	0.895979038235	Henry Cohn, 2024, needs more optimization.
5	909	0.896059825873	Henry Cohn, 2024, needs more optimization.
5	911	0.896078996577	Henry Cohn, 2024, needs more optimization.
5	913	0.896177219775	Henry Cohn, 2024, needs more optimization.
5	914	0.896237409331	Henry Cohn, 2024, needs more optimization.
5	916	0.896238597511	Henry Cohn, 2024, needs more optimization.
5	917	0.896384835112	Henry Cohn, 2024, needs more optimization.
5	918	0.896394924234	Henry Cohn, 2024, needs more optimization.
5	920	0.896607363347	Henry Cohn, 2024, needs more optimization.
5	921	0.896608530216	Henry Cohn, 2024, needs more optimization.
5	922	0.896758619537	Henry Cohn, 2024, needs more optimization.
5	923	0.896762832967	Henry Cohn, 2024, needs more optimization.
5	924	0.896827854542	Henry Cohn, 2024, needs more optimization.
5	926	0.896918210136	Henry Cohn, 2024, needs more optimization.
5	927	0.896998267669	Henry Cohn, 2024, needs more optimization.
5	928	0.897002630462	Henry Cohn, 2024, needs more optimization.
5	929	0.897061439607	Henry Cohn, 2024, needs more optimization.
5	930	0.897128660140	Henry Cohn, 2024, needs more optimization.
5	931	0.897160788569	Henry Cohn, 2024, needs more optimization.
5	932	0.897220115218	Henry Cohn, 2024, needs more optimization.
5	934	0.897297497448	Henry Cohn, 2024, needs more optimization.
5	935	0.897392576854	Henry Cohn, 2024, needs more optimization.
5	936	0.897490283052	Henry Cohn, 2024, needs more optimization.
5	937	0.897536023496	Henry Cohn, 2024, needs more optimization.
5	939	0.897571860936	Henry Cohn, 2024, needs more optimization.
5	940	0.897724991667	Henry Cohn, 2024, needs more optimization.
5	941	0.897737257871	Henry Cohn, 2024, needs more optimization.
5	942	0.897800231577	Henry Cohn, 2024, needs more optimization.
5	943	0.897891584509	Henry Cohn, 2024, needs more optimization.
5	945	0.897923343424	Henry Cohn, 2024, needs more optimization.
5	946	0.897955883457	Henry Cohn, 2024, needs more optimization.
5	948	0.898075522532	Henry Cohn, 2024, needs more optimization.
5	951	0.898272343571	Henry Cohn, 2024, needs more optimization.
5	952	0.898289512999	Henry Cohn, 2024, needs more optimization.
5	954	0.898438607429	Henry Cohn, 2024, needs more optimization.
5	957	0.898584436884	Henry Cohn, 2024, needs more optimization.
5	959	0.898656912344	Henry Cohn, 2024, needs more optimization.
5	960	0.898657455112	Henry Cohn, 2024, needs more optimization.
5	962	0.898890715135	Henry Cohn, 2024, needs more optimization.
5	963	0.898892304163	Henry Cohn, 2024, needs more optimization.
5	964	0.898906142850	Henry Cohn, 2024, needs more optimization.
5	965	0.899002119483	Henry Cohn, 2024, needs more optimization.
5	966	0.899116480632	Henry Cohn, 2024, needs more optimization.
5	968	0.899160899922	Henry Cohn, 2024, needs more optimization.
5	969	0.899224968330	Henry Cohn, 2024, needs more optimization.
5	970	0.899287580205	Henry Cohn, 2024, needs more optimization.
5	972	0.899355800752	Henry Cohn, 2024, needs more optimization.
5	974	0.899432663991	Henry Cohn, 2024, needs more optimization.
5	976	0.899542355852	Henry Cohn, 2024, needs more optimization.
5	977	0.899663069146	Henry Cohn, 2024, needs more optimization.
5	978	0.899758993949	Henry Cohn, 2024, needs more optimization.
5	979	0.899825790477	Henry Cohn, 2024, needs more optimization.
5	980	0.899833388600	Henry Cohn, 2024, needs more optimization.
5	981	0.899879432042	Henry Cohn, 2024, needs more optimization.
5	983	0.899895404869	Henry Cohn, 2024, needs more optimization.
5	984	0.899930504225	Henry Cohn, 2024, needs more optimization.
5	987	0.900065471715	Henry Cohn, 2024, needs more optimization.
5	988	0.900189901389	Henry Cohn, 2024, needs more optimization.
5	989	0.900365296327	Henry Cohn, 2024, needs more optimization.
5	990	0.900378588779	Henry Cohn, 2024, needs more optimization.
5	991	0.900419394806	Henry Cohn, 2024, needs more optimization.
5	992	0.900450692545	Henry Cohn, 2024, needs more optimization.
5	993	0.900530446359	Henry Cohn, 2024, needs more optimization.
5	995	0.900548348764	Henry Cohn, 2024, needs more optimization.
5	996	0.900643428036	Henry Cohn, 2024, needs more optimization.
5	997	0.900657346509	Henry Cohn, 2024, needs more optimization.
5	998	0.900795311858	Henry Cohn, 2024, needs more optimization.
5	999	0.900816548033	Henry Cohn, 2024, needs more optimization.
5	1001	0.900817500206	Henry Cohn, 2024, needs more optimization.
5	1002	0.900898693755	Henry Cohn, 2024, needs more optimization.
5	1003	0.900933731572	Henry Cohn, 2024, needs more optimization.
5	1004	0.900971917805	Henry Cohn, 2024, needs more optimization.
5	1005	0.901047050635	Henry Cohn, 2024, needs more optimization.
5	1006	0.901094167480	Henry Cohn, 2024, needs more optimization.
5	1007	0.901140387647	Henry Cohn, 2024, needs more optimization.
5	1008	0.901163559146	Henry Cohn, 2024, needs more optimization.
5	1013	0.901329439554	Henry Cohn, 2024, needs more optimization.
5	1014	0.901484467356	Henry Cohn, 2024, needs more optimization.
5	1015	0.901521326498	Henry Cohn, 2024, needs more optimization.
5	1016	0.901641751114	Henry Cohn, 2024, needs more optimization.
5	1018	0.901644032208	Henry Cohn, 2024, needs more optimization.
5	1020	0.901744830386	Henry Cohn, 2024, needs more optimization.
5	1021	0.901748681317	Henry Cohn, 2024, needs more optimization.
5	1024	0.901852772510	Henry Cohn, 2024, needs more optimization.
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 listed in plain text data
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	0.171147649430	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 . Minimal polynomial listed in plain text data
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	0.333202235475	H. Cohn, Small spherical and projective codes, data set, 2022, 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	0.389434959221	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	0.426943929412	Henry Cohn, 2023.
6	46	0.435728619792	J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6	47	0.441277260126	Henry Cohn, 2023. $24 x^{3} + 16 x^{2} - 14 x + 1$
6	48	0.443652559533	Henry Cohn, 2023.
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	0.456559193063	Henry Cohn, 2023.
6	52	0.458253528717	Henry Cohn, 2023.
6	53	0.459152260492	Henry Cohn, 2023.
6	54	0.462714285892	Henry Cohn, 2023. $4104 x^{4} - 216 x^{3} - 3654 x^{2} + 1955 x - 289$
6	55	0.474011768961	Henry Cohn, 2023, needs more optimization.
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	0.479818012263	Henry Cohn, 2023.
6	58	0.482548584905	Henry Cohn, 2024. $20 x^{2} + 9 x - 9$
6	59	0.486119746833	Henry Cohn, 2023.
6	60	0.486877257533	Henry Cohn, 2023.
6	61	0.491751789653	Henry Cohn, 2023.
6	62	0.495376595904	Henry Cohn, 2023.
6	63	0.498122491823	Henry Cohn, 2023.
6	64	0.498526182118	Henry Cohn, 2023.
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	0.517792073302	Bram Cohen, 2023. Minimal polynomial listed in plain text data
6	74	0.524331921924	Bram Cohen, 2023.
6	75	0.527712540702	Henry Cohn, 2024.
6	76	0.530523879593	Henry Cohn, 2023.
6	77	0.533020445638	Henry Cohn, 2023.
6	78	0.533954283180	Henry Cohn, 2023.
6	79	0.534856290459	Henry Cohn, 2023.
6	80	0.536675122656	Henry Cohn, 2024.
6	81	0.539664669993	Henry Cohn, 2023, needs more optimization.
6	82	0.543706976774	Henry Cohn, 2023, needs more optimization.
6	83	0.544070519677	Henry Cohn, 2023.
6	84	0.549146613382	Henry Cohn, 2024, needs more optimization.
6	85	0.549385704407	Henry Cohn, 2024.
6	86	0.550314646242	Henry Cohn, 2023.
6	87	0.551714767476	Henry Cohn, 2023.
6	88	0.554685575117	Henry Cohn, 2023.
6	89	0.556767465683	Henry Cohn, 2023, needs more optimization.
6	90	0.560601279955	Henry Cohn, 2023, needs more optimization.
6	91	0.561694451451	Henry Cohn, 2024, needs more optimization.
6	92	0.562667742915	Henry Cohn, 2023.
6	93	0.563551889988	Henry Cohn, 2023.
6	94	0.565357049060	Henry Cohn, 2024, needs more optimization.
6	95	0.565789396150	Henry Cohn, 2023.
6	96	0.565950871118	Henry Cohn, 2023.
6	97	0.568137237475	Henry Cohn, 2023.
6	98	0.571167178278	Henry Cohn, 2023, needs more optimization.
6	99	0.573881665753	Henry Cohn, 2023.
6	100	0.577516365203	Henry Cohn, 2023, needs more optimization.
6	101	0.578331393550	Henry Cohn, 2023.
6	102	0.580736682189	Henry Cohn, 2023, needs more optimization.
6	103	0.583558629973	Henry Cohn, 2023, needs more optimization.
6	105	0.584988582821	Henry Cohn, 2024, needs more optimization.
6	106	0.586276565408	Henry Cohn, 2023, needs more optimization.
6	107	0.586632181460	Henry Cohn, 2023, needs more optimization.
6	108	0.586632257674	Henry Cohn, 2023, needs more optimization.
6	109	0.586632483770	Henry Cohn, 2023.
6	110	0.587930475567	Henry Cohn, 2024, needs more optimization.
6	111	0.588087142543	Henry Cohn, 2023, needs more optimization.
6	112	0.588090510055	Henry Cohn, 2023.
6	114	0.588109690133	Henry Cohn, 2023.
6	115	0.598750275381	Henry Cohn, 2023, needs more optimization.
6	116	0.598814560693	Henry Cohn, 2023, needs more optimization.
6	117	0.599196560145	Henry Cohn, 2023, needs more optimization.
6	118	0.599246274397	Henry Cohn, 2023, needs more optimization.
6	119	0.599296409159	Henry Cohn, 2023, needs more optimization.
6	120	0.599317371094	Henry Cohn, 2023, needs more optimization.
6	121	0.605179965654	Henry Cohn, 2023, needs more optimization.
6	122	0.607141036746	Henry Cohn, 2023, needs more optimization.
6	123	0.607230476310	Henry Cohn, 2023, needs more optimization.
6	125	0.607974063066	Henry Cohn, 2023, needs more optimization.
6	126	0.610431849246	Henry Cohn, 2023, needs more optimization.
6	127	0.616939502678	Henry Cohn, 2023, needs more optimization.
6	128	0.619567178906	Henry Cohn, 2023, needs more optimization.
6	129	0.621946755831	Henry Cohn, 2024, needs more optimization.
6	130	0.623998718193	Henry Cohn, 2023, needs more optimization.
6	131	0.625866083430	Henry Cohn, 2024, needs more optimization.
6	132	0.626573176423	Henry Cohn, 2023, needs more optimization.
6	133	0.628443332538	Henry Cohn, 2024, needs more optimization.
6	134	0.629040160404	Henry Cohn, 2023, needs more optimization.
6	135	0.631479160568	Henry Cohn, 2024, needs more optimization.
6	136	0.631879495567	Henry Cohn, 2023, needs more optimization.
6	137	0.633414808285	Henry Cohn, 2024, needs more optimization.
6	138	0.634804798566	Henry Cohn, 2023, needs more optimization.
6	139	0.637027746979	Henry Cohn, 2024, needs more optimization.
6	140	0.637606310227	Henry Cohn, 2023, needs more optimization.
6	141	0.639856368996	Henry Cohn, 2023, needs more optimization.
6	142	0.640116851996	Henry Cohn, 2023, needs more optimization.
6	143	0.641951837325	Henry Cohn, 2024, needs more optimization.
6	144	0.642558970194	Henry Cohn, 2023, needs more optimization.
6	145	0.644543244996	Henry Cohn, 2024, needs more optimization.
6	146	0.644984170230	Henry Cohn, 2023, needs more optimization.
6	147	0.646518158093	Henry Cohn, 2023, needs more optimization.
6	148	0.646886119844	Henry Cohn, 2023, needs more optimization.
6	149	0.648936608145	Henry Cohn, 2024, needs more optimization.
6	150	0.649320644907	Henry Cohn, 2023, needs more optimization.
6	151	0.650015852037	Henry Cohn, 2024, needs more optimization.
6	152	0.651648908509	Henry Cohn, 2024, needs more optimization.
6	153	0.652230668565	Henry Cohn, 2024, needs more optimization.
6	154	0.653644937249	Henry Cohn, 2024, needs more optimization.
6	155	0.654150548025	Henry Cohn, 2024, needs more optimization.
6	156	0.654987112079	Henry Cohn, 2024, needs more optimization.
6	157	0.656018757967	Henry Cohn, 2024, needs more optimization.
6	158	0.656525424516	Henry Cohn, 2024, needs more optimization.
6	159	0.657318583056	Henry Cohn, 2024, needs more optimization.
6	160	0.658677261297	Henry Cohn, 2024, needs more optimization.
6	161	0.659167421410	Henry Cohn, 2024, needs more optimization.
6	162	0.659982936670	Henry Cohn, 2024, needs more optimization.
6	163	0.660679813360	Henry Cohn, 2024, needs more optimization.
6	164	0.661116367046	Henry Cohn, 2024, needs more optimization.
6	165	0.662714404839	Henry Cohn, 2024, needs more optimization.
6	166	0.662902091065	Henry Cohn, 2024, needs more optimization.
6	167	0.664124945223	Henry Cohn, 2024, needs more optimization.
6	168	0.664648539965	Henry Cohn, 2024, needs more optimization.
6	169	0.664952949607	Henry Cohn, 2024, needs more optimization.
6	170	0.665738618981	Henry Cohn, 2024, needs more optimization.
6	171	0.666527897763	Henry Cohn, 2024, needs more optimization.
6	172	0.666666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 2$
6	173	0.667820124469	Henry Cohn, 2024, needs more optimization.
6	174	0.669516762391	Henry Cohn, 2024, needs more optimization.
6	175	0.669883297204	Henry Cohn, 2024, needs more optimization.
6	176	0.670666700713	Henry Cohn, 2024, needs more optimization.
6	177	0.671477437402	Henry Cohn, 2024, needs more optimization.
6	179	0.672132034399	Henry Cohn, 2024, needs more optimization.
6	180	0.673683950439	Henry Cohn, 2024, needs more optimization.
6	181	0.674397626095	Henry Cohn, 2024, needs more optimization.
6	182	0.674874096284	Henry Cohn, 2024, needs more optimization.
6	184	0.676229585767	Henry Cohn, 2024, needs more optimization.
6	185	0.677395791507	Henry Cohn, 2024, needs more optimization.
6	186	0.678147760019	Henry Cohn, 2024, needs more optimization.
6	187	0.679016686781	Henry Cohn, 2024, needs more optimization.
6	188	0.679620274326	Henry Cohn, 2024, needs more optimization.
6	189	0.680297973806	Henry Cohn, 2024, needs more optimization.
6	190	0.681127137179	Henry Cohn, 2024, needs more optimization.
6	191	0.681845303970	Henry Cohn, 2024, needs more optimization.
6	192	0.682189498181	Henry Cohn, 2024, needs more optimization.
6	193	0.683028865101	Henry Cohn, 2024, needs more optimization.
6	194	0.684013282888	Henry Cohn, 2024, needs more optimization.
6	195	0.684724502920	Henry Cohn, 2024, needs more optimization.
6	196	0.685116854642	Henry Cohn, 2024, needs more optimization.
6	197	0.685700628986	Henry Cohn, 2024, needs more optimization.
6	198	0.686469220277	Henry Cohn, 2024, needs more optimization.
6	199	0.687044325419	Henry Cohn, 2024, needs more optimization.
6	200	0.687477710320	Henry Cohn, 2024, needs more optimization.
6	201	0.688200251466	Henry Cohn, 2024, needs more optimization.
6	202	0.688417847689	Henry Cohn, 2024, needs more optimization.
6	203	0.689057926979	Henry Cohn, 2024, needs more optimization.
6	208	0.689234171970	Henry Cohn, 2024, needs more optimization.
6	209	0.693112064608	Henry Cohn, 2024, needs more optimization.
6	210	0.693716337621	Henry Cohn, 2024, needs more optimization.
6	211	0.693839447329	Henry Cohn, 2024, needs more optimization.
6	212	0.694555096571	Henry Cohn, 2024, needs more optimization.
6	213	0.695377806302	Henry Cohn, 2024, needs more optimization.
6	214	0.695380445365	Henry Cohn, 2024, needs more optimization.
6	215	0.696065146019	Henry Cohn, 2024, needs more optimization.
6	216	0.696604224724	Henry Cohn, 2024, needs more optimization.
6	217	0.697295185897	Henry Cohn, 2024, needs more optimization.
6	218	0.697836052911	Henry Cohn, 2024, needs more optimization.
6	219	0.697998164422	Henry Cohn, 2024, needs more optimization.
6	220	0.698834720754	Henry Cohn, 2024, needs more optimization.
6	221	0.699270084191	Henry Cohn, 2024, needs more optimization.
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	0.711575934262	Henry Cohn, 2024, needs more optimization.
6	245	0.712023928070	Henry Cohn, 2024, needs more optimization.
6	246	0.712470150490	Henry Cohn, 2024, needs more optimization.
6	247	0.712791957266	Henry Cohn, 2024, needs more optimization.
6	248	0.713435087282	Henry Cohn, 2024, needs more optimization.
6	249	0.713844431254	Henry Cohn, 2024, needs more optimization.
6	250	0.714709048662	Henry Cohn, 2024, needs more optimization.
6	251	0.715178755122	Henry Cohn, 2024, needs more optimization.
6	252	0.715511232601	Henry Cohn, 2024, needs more optimization.
6	253	0.715777453838	Henry Cohn, 2024, needs more optimization.
6	254	0.716537798518	Henry Cohn, 2024, needs more optimization.
6	255	0.716554399508	Henry Cohn, 2024, needs more optimization.
6	256	0.717229018586	Henry Cohn, 2024, needs more optimization.
6	257	0.719017204839	Henry Cohn, 2024, needs more optimization.
6	259	0.719442560946	Henry Cohn, 2024, needs more optimization.
6	260	0.720331919069	Henry Cohn, 2024, needs more optimization.
6	261	0.720944795425	Henry Cohn, 2024, needs more optimization.
6	262	0.721142540456	Henry Cohn, 2024, needs more optimization.
6	263	0.721786058814	Henry Cohn, 2024, needs more optimization.
6	266	0.722569005739	Henry Cohn, 2024, needs more optimization.
6	267	0.723350985590	Henry Cohn, 2024, needs more optimization.
6	268	0.723669549842	Henry Cohn, 2024, needs more optimization.
6	269	0.724195718680	Henry Cohn, 2024, needs more optimization.
6	270	0.724804983081	Henry Cohn, 2024, needs more optimization.
6	272	0.725350538483	Henry Cohn, 2024, needs more optimization.
6	275	0.726527044035	Henry Cohn, 2024, needs more optimization.
6	276	0.726829787549	Henry Cohn, 2024, needs more optimization.
6	278	0.727501321100	Henry Cohn, 2024, needs more optimization.
6	279	0.728145647935	Henry Cohn, 2024, needs more optimization.
6	281	0.728543670785	Henry Cohn, 2024, needs more optimization.
6	282	0.729513984658	Henry Cohn, 2024, needs more optimization.
6	283	0.730014003561	Henry Cohn, 2024, needs more optimization.
6	286	0.730351462534	Henry Cohn, 2024, needs more optimization.
6	287	0.731529829242	Henry Cohn, 2024, needs more optimization.
6	289	0.731875981400	Henry Cohn, 2024, needs more optimization.
6	290	0.732259503230	Henry Cohn, 2024, needs more optimization.
6	291	0.732452285322	Henry Cohn, 2024, needs more optimization.
6	292	0.732765174534	Henry Cohn, 2024, needs more optimization.
6	295	0.732956473776	Henry Cohn, 2024, needs more optimization.
6	296	0.734096404420	Henry Cohn, 2024, needs more optimization.
6	297	0.734429673583	Henry Cohn, 2024, needs more optimization.
6	298	0.734886010843	Henry Cohn, 2024, needs more optimization.
6	299	0.735485977061	Henry Cohn, 2024, needs more optimization.
6	301	0.735512037518	Henry Cohn, 2024, needs more optimization.
6	302	0.736108068579	Henry Cohn, 2024, needs more optimization.
6	303	0.736949571531	Henry Cohn, 2024, needs more optimization.
6	304	0.736978588110	Henry Cohn, 2024, needs more optimization.
6	305	0.738053007463	Henry Cohn, 2024, needs more optimization.
6	308	0.738240048619	Henry Cohn, 2024, needs more optimization.
6	309	0.739350300303	Henry Cohn, 2024, needs more optimization.
6	310	0.739583717059	Henry Cohn, 2024, needs more optimization.
6	311	0.739673658199	Henry Cohn, 2024, needs more optimization.
6	313	0.739833712572	Henry Cohn, 2024, needs more optimization.
6	314	0.740548906417	Henry Cohn, 2024, needs more optimization.
6	315	0.740982725542	Henry Cohn, 2024, needs more optimization.
6	316	0.741167183307	Henry Cohn, 2024, needs more optimization.
6	318	0.741431566136	Henry Cohn, 2024, needs more optimization.
6	320	0.742285478564	Henry Cohn, 2024, needs more optimization.
6	321	0.742917279370	Henry Cohn, 2024, needs more optimization.
6	322	0.743098945354	Henry Cohn, 2024, needs more optimization.
6	325	0.743525548095	Henry Cohn, 2024, needs more optimization.
6	326	0.744427731553	Henry Cohn, 2024, needs more optimization.
6	327	0.744567421935	Henry Cohn, 2024, needs more optimization.
6	328	0.744857666425	Henry Cohn, 2024, needs more optimization.
6	329	0.745395691586	Henry Cohn, 2024, needs more optimization.
6	330	0.745921431518	Henry Cohn, 2024, needs more optimization.
6	331	0.745944005819	Henry Cohn, 2024, needs more optimization.
6	332	0.746314759104	Henry Cohn, 2024, needs more optimization.
6	342	0.746790391073	Henry Cohn, 2023, needs more optimization.
6	343	0.749879992123	Henry Cohn, 2024, needs more optimization.
6	344	0.750121199015	Henry Cohn, 2024, needs more optimization.
6	345	0.750248876944	Henry Cohn, 2024, needs more optimization.
6	347	0.750849499383	Henry Cohn, 2024, needs more optimization.
6	348	0.751509978211	Henry Cohn, 2024, needs more optimization.
6	349	0.751646998730	Henry Cohn, 2024, needs more optimization.
6	350	0.751889489709	Henry Cohn, 2024, needs more optimization.
6	351	0.752230708498	Henry Cohn, 2024, needs more optimization.
6	352	0.752375130569	Henry Cohn, 2024, needs more optimization.
6	353	0.752986954473	Henry Cohn, 2024, needs more optimization.
6	354	0.753209436636	Henry Cohn, 2024, needs more optimization.
6	355	0.753509977320	Henry Cohn, 2024, needs more optimization.
6	356	0.753634427101	Henry Cohn, 2024, needs more optimization.
6	357	0.753972145157	Henry Cohn, 2024, needs more optimization.
6	358	0.754243460857	Henry Cohn, 2024, needs more optimization.
6	359	0.754370696908	Henry Cohn, 2024, needs more optimization.
6	360	0.754771680847	Henry Cohn, 2024, needs more optimization.
6	361	0.755315833738	Henry Cohn, 2024, needs more optimization.
6	362	0.755436443996	Henry Cohn, 2024, needs more optimization.
6	363	0.755582234120	Henry Cohn, 2024, needs more optimization.
6	366	0.755924204293	Henry Cohn, 2024, needs more optimization.
6	367	0.756425644381	Henry Cohn, 2024, needs more optimization.
6	368	0.757082721090	Henry Cohn, 2024, needs more optimization.
6	369	0.757522056223	Henry Cohn, 2024, needs more optimization.
6	370	0.757657227557	Henry Cohn, 2024, needs more optimization.
6	371	0.757740942260	Henry Cohn, 2024, needs more optimization.
6	372	0.758178283029	Henry Cohn, 2024, needs more optimization.
6	373	0.758406075683	Henry Cohn, 2024, needs more optimization.
6	374	0.758555133489	Henry Cohn, 2024, needs more optimization.
6	376	0.759121209520	Henry Cohn, 2024, needs more optimization.
6	377	0.759463041498	Henry Cohn, 2024, needs more optimization.
6	378	0.759603446451	Henry Cohn, 2024, needs more optimization.
6	379	0.759899674238	Henry Cohn, 2024, needs more optimization.
6	380	0.760179168717	Henry Cohn, 2024, needs more optimization.
6	381	0.760196912898	Henry Cohn, 2024, needs more optimization.
6	384	0.760743441807	Henry Cohn, 2024, needs more optimization.
6	385	0.761301709141	Henry Cohn, 2024, needs more optimization.
6	386	0.761423027034	Henry Cohn, 2024, needs more optimization.
6	387	0.761752012292	Henry Cohn, 2024, needs more optimization.
6	389	0.762275313438	Henry Cohn, 2024, needs more optimization.
6	390	0.762765674321	Henry Cohn, 2024, needs more optimization.
6	391	0.762997719049	Henry Cohn, 2024, needs more optimization.
6	393	0.763227312819	Henry Cohn, 2024, needs more optimization.
6	394	0.763390684936	Henry Cohn, 2024, needs more optimization.
6	395	0.763620430568	Henry Cohn, 2024, needs more optimization.
6	397	0.764127402749	Henry Cohn, 2024, needs more optimization.
6	398	0.764498075350	Henry Cohn, 2024, needs more optimization.
6	399	0.765049644393	Henry Cohn, 2024, needs more optimization.
6	400	0.765139376065	Henry Cohn, 2024, needs more optimization.
6	401	0.765239758920	Henry Cohn, 2024, needs more optimization.
6	402	0.765659810275	Henry Cohn, 2024, needs more optimization.
6	404	0.765786415860	Henry Cohn, 2024, needs more optimization.
6	405	0.766190325157	Henry Cohn, 2024, needs more optimization.
6	406	0.766446439431	Henry Cohn, 2024, needs more optimization.
6	407	0.766458995820	Henry Cohn, 2024, needs more optimization.
6	408	0.766621937326	Henry Cohn, 2024, needs more optimization.
6	409	0.766928809702	Henry Cohn, 2024, needs more optimization.
6	410	0.767257605164	Henry Cohn, 2024, needs more optimization.
6	411	0.767579023898	Henry Cohn, 2024, needs more optimization.
6	412	0.767972897392	Henry Cohn, 2024, needs more optimization.
6	414	0.768018281898	Henry Cohn, 2024, needs more optimization.
6	415	0.768446488411	Henry Cohn, 2024, needs more optimization.
6	416	0.768586039966	Henry Cohn, 2024, needs more optimization.
6	417	0.768816715774	Henry Cohn, 2024, needs more optimization.
6	418	0.769158009690	Henry Cohn, 2024, needs more optimization.
6	419	0.769414078498	Henry Cohn, 2024, needs more optimization.
6	420	0.769431304395	Henry Cohn, 2024, needs more optimization.
6	421	0.769576803387	Henry Cohn, 2024, needs more optimization.
6	422	0.770134735005	Henry Cohn, 2024, needs more optimization.
6	424	0.770142912845	Henry Cohn, 2024, needs more optimization.
6	425	0.770565145673	Henry Cohn, 2024, needs more optimization.
6	427	0.770861569290	Henry Cohn, 2024, needs more optimization.
6	428	0.771329478772	Henry Cohn, 2024, needs more optimization.
6	429	0.771724008502	Henry Cohn, 2024, needs more optimization.
6	430	0.771781110398	Henry Cohn, 2024, needs more optimization.
6	432	0.772150953397	Henry Cohn, 2024, needs more optimization.
6	433	0.772617339141	Henry Cohn, 2024, needs more optimization.
6	435	0.772757860518	Henry Cohn, 2024, needs more optimization.
6	436	0.773091879501	Henry Cohn, 2024, needs more optimization.
6	437	0.773190383767	Henry Cohn, 2024, needs more optimization.
6	439	0.773573258583	Henry Cohn, 2024, needs more optimization.
6	440	0.773680684565	Henry Cohn, 2024, needs more optimization.
6	441	0.773925312184	Henry Cohn, 2024, needs more optimization.
6	442	0.774228654237	Henry Cohn, 2024, needs more optimization.
6	443	0.774538909786	Henry Cohn, 2024, needs more optimization.
6	444	0.774835673896	Henry Cohn, 2024, needs more optimization.
6	445	0.774954753125	Henry Cohn, 2024, needs more optimization.
6	448	0.775092016852	Henry Cohn, 2024, needs more optimization.
6	449	0.775578245753	Henry Cohn, 2024, needs more optimization.
6	450	0.775888171873	Henry Cohn, 2024, needs more optimization.
6	451	0.776121670523	Henry Cohn, 2024, needs more optimization.
6	452	0.776381762753	Henry Cohn, 2024, needs more optimization.
6	454	0.776513452273	Henry Cohn, 2024, needs more optimization.
6	455	0.777021799485	Henry Cohn, 2024, needs more optimization.
6	456	0.777062274044	Henry Cohn, 2024, needs more optimization.
6	457	0.777200611192	Henry Cohn, 2024, needs more optimization.
6	459	0.777520171983	Henry Cohn, 2024, needs more optimization.
6	460	0.777868069146	Henry Cohn, 2024, needs more optimization.
6	462	0.778170807834	Henry Cohn, 2024, needs more optimization.
6	464	0.778489557015	Henry Cohn, 2024, needs more optimization.
6	465	0.778711486135	Henry Cohn, 2024, needs more optimization.
6	466	0.778925230425	Henry Cohn, 2024, needs more optimization.
6	467	0.778979746482	Henry Cohn, 2024, needs more optimization.
6	469	0.779560756746	Henry Cohn, 2024, needs more optimization.
6	470	0.779780910564	Henry Cohn, 2024, needs more optimization.
6	471	0.779983699420	Henry Cohn, 2024, needs more optimization.
6	473	0.780171543918	Henry Cohn, 2024, needs more optimization.
6	474	0.780558857566	Henry Cohn, 2024, needs more optimization.
6	475	0.780574998598	Henry Cohn, 2024, needs more optimization.
6	476	0.780771765302	Henry Cohn, 2024, needs more optimization.
6	477	0.781309565030	Henry Cohn, 2024, needs more optimization.
6	479	0.781349633857	Henry Cohn, 2024, needs more optimization.
6	481	0.781880382005	Henry Cohn, 2024, needs more optimization.
6	482	0.781894752103	Henry Cohn, 2024, needs more optimization.
6	483	0.782088102559	Henry Cohn, 2024, needs more optimization.
6	485	0.782524290320	Henry Cohn, 2024, needs more optimization.
6	486	0.782581618334	Henry Cohn, 2024, needs more optimization.
6	487	0.782783290799	Henry Cohn, 2024, needs more optimization.
6	488	0.783233039233	Henry Cohn, 2024, needs more optimization.
6	489	0.783275331964	Henry Cohn, 2024, needs more optimization.
6	490	0.783578523736	Henry Cohn, 2024, needs more optimization.
6	491	0.783771320650	Henry Cohn, 2024, needs more optimization.
6	492	0.783815869038	Henry Cohn, 2024, needs more optimization.
6	493	0.783830838210	Henry Cohn, 2024, needs more optimization.
6	494	0.784025430368	Henry Cohn, 2024, needs more optimization.
6	495	0.784417494557	Henry Cohn, 2024, needs more optimization.
6	497	0.784588806604	Henry Cohn, 2024, needs more optimization.
6	499	0.784707747423	Henry Cohn, 2024, needs more optimization.
6	501	0.785128241298	Henry Cohn, 2024, needs more optimization.
6	503	0.785514507557	Henry Cohn, 2024, needs more optimization.
6	504	0.785849934747	Henry Cohn, 2024, needs more optimization.
6	505	0.786149207911	Henry Cohn, 2024, needs more optimization.
6	506	0.786407290796	Henry Cohn, 2024, needs more optimization.
6	508	0.786538548637	Henry Cohn, 2024, needs more optimization.
6	510	0.786790552180	Henry Cohn, 2024, needs more optimization.
6	512	0.786833495928	Henry Cohn, 2024, needs more optimization.
6	513	0.787272027541	Henry Cohn, 2024, needs more optimization.
6	516	0.787704319738	Henry Cohn, 2024, needs more optimization.
6	518	0.788165586341	Henry Cohn, 2024, needs more optimization.
6	521	0.788328135631	Henry Cohn, 2024, needs more optimization.
6	523	0.789042690069	Henry Cohn, 2024, needs more optimization.
6	525	0.789220941439	Henry Cohn, 2024, needs more optimization.
6	527	0.789300152202	Henry Cohn, 2024, needs more optimization.
6	528	0.789660081881	Henry Cohn, 2024, needs more optimization.
6	530	0.790032323896	Henry Cohn, 2024, needs more optimization.
6	531	0.790161760337	Henry Cohn, 2024, needs more optimization.
6	532	0.790318339039	Henry Cohn, 2024, needs more optimization.
6	533	0.790592404591	Henry Cohn, 2024, needs more optimization.
6	534	0.790905107891	Henry Cohn, 2024, needs more optimization.
6	535	0.790945763449	Henry Cohn, 2024, needs more optimization.
6	537	0.791255911617	Henry Cohn, 2024, needs more optimization.
6	539	0.791425942755	Henry Cohn, 2024, needs more optimization.
6	540	0.791766367025	Henry Cohn, 2024, needs more optimization.
6	542	0.791964918422	Henry Cohn, 2024, needs more optimization.
6	543	0.792081634216	Henry Cohn, 2024, needs more optimization.
6	545	0.792562346833	Henry Cohn, 2024, needs more optimization.
6	546	0.792775909774	Henry Cohn, 2024, needs more optimization.
6	549	0.793036778341	Henry Cohn, 2024, needs more optimization.
6	551	0.793326577761	Henry Cohn, 2024, needs more optimization.
6	553	0.793404782573	Henry Cohn, 2024, needs more optimization.
6	554	0.793752174481	Henry Cohn, 2024, needs more optimization.
6	555	0.793998545972	Henry Cohn, 2024, needs more optimization.
6	556	0.794149904003	Henry Cohn, 2024, needs more optimization.
6	558	0.794269661975	Henry Cohn, 2024, needs more optimization.
6	559	0.794611140739	Henry Cohn, 2024, needs more optimization.
6	561	0.794970181531	Henry Cohn, 2024, needs more optimization.
6	562	0.795401429472	Henry Cohn, 2024, needs more optimization.
6	565	0.795420953327	Henry Cohn, 2024, needs more optimization.
6	567	0.795617480958	Henry Cohn, 2024, needs more optimization.
6	568	0.795681791942	Henry Cohn, 2024, needs more optimization.
6	569	0.795883821257	Henry Cohn, 2024, needs more optimization.
6	570	0.796147360168	Henry Cohn, 2024, needs more optimization.
6	571	0.796406834836	Henry Cohn, 2024, needs more optimization.
6	574	0.796719181603	Henry Cohn, 2024, needs more optimization.
6	576	0.796870926518	Henry Cohn, 2024, needs more optimization.
6	577	0.797254816465	Henry Cohn, 2024, needs more optimization.
6	578	0.797417937429	Henry Cohn, 2024, needs more optimization.
6	579	0.797716645979	Henry Cohn, 2024, needs more optimization.
6	580	0.797725015318	Henry Cohn, 2024, needs more optimization.
6	581	0.797865682204	Henry Cohn, 2024, needs more optimization.
6	583	0.797923168282	Henry Cohn, 2024, needs more optimization.
6	584	0.798321508403	Henry Cohn, 2024, needs more optimization.
6	586	0.798392606965	Henry Cohn, 2024, needs more optimization.
6	587	0.798497762280	Henry Cohn, 2024, needs more optimization.
6	588	0.798773944776	Henry Cohn, 2024, needs more optimization.
6	590	0.798783796601	Henry Cohn, 2024, needs more optimization.
6	591	0.799186611311	Henry Cohn, 2024, needs more optimization.
6	593	0.799279677702	Henry Cohn, 2024, needs more optimization.
6	594	0.799431353162	Henry Cohn, 2024, needs more optimization.
6	595	0.799749917541	Henry Cohn, 2024, needs more optimization.
6	596	0.799838882310	Henry Cohn, 2024, needs more optimization.
6	597	0.800092453824	Henry Cohn, 2024, needs more optimization.
6	599	0.800146052924	Henry Cohn, 2024, needs more optimization.
6	601	0.800378802385	Henry Cohn, 2024, needs more optimization.
6	602	0.800470557131	Henry Cohn, 2024, needs more optimization.
6	603	0.800973290309	Henry Cohn, 2024, needs more optimization.
6	604	0.801007265645	Henry Cohn, 2024, needs more optimization.
6	605	0.801047409160	Henry Cohn, 2024, needs more optimization.
6	607	0.801330435984	Henry Cohn, 2024, needs more optimization.
6	608	0.801546585635	Henry Cohn, 2024, needs more optimization.
6	610	0.801558206675	Henry Cohn, 2024, needs more optimization.
6	611	0.801651597274	Henry Cohn, 2024, needs more optimization.
6	612	0.801905101705	Henry Cohn, 2024, needs more optimization.
6	613	0.802089915164	Henry Cohn, 2024, needs more optimization.
6	614	0.802310467205	Henry Cohn, 2024, needs more optimization.
6	615	0.802354542134	Henry Cohn, 2024, needs more optimization.
6	616	0.802442064726	Henry Cohn, 2024, needs more optimization.
6	617	0.802661127646	Henry Cohn, 2024, needs more optimization.
6	618	0.802678288480	Henry Cohn, 2024, needs more optimization.
6	619	0.802875465835	Henry Cohn, 2024, needs more optimization.
6	620	0.803058034461	Henry Cohn, 2024, needs more optimization.
6	621	0.803264903270	Henry Cohn, 2024, needs more optimization.
6	622	0.803394763906	Henry Cohn, 2024, needs more optimization.
6	624	0.803528991377	Henry Cohn, 2024, needs more optimization.
6	625	0.803533852398	Henry Cohn, 2024, needs more optimization.
6	627	0.803880431350	Henry Cohn, 2024, needs more optimization.
6	628	0.804102157694	Henry Cohn, 2024, needs more optimization.
6	630	0.804325055030	Henry Cohn, 2024, needs more optimization.
6	632	0.804448274058	Henry Cohn, 2024, needs more optimization.
6	633	0.804623382498	Henry Cohn, 2024, needs more optimization.
6	634	0.804763967494	Henry Cohn, 2024, needs more optimization.
6	635	0.804842380725	Henry Cohn, 2024, needs more optimization.
6	637	0.804901371340	Henry Cohn, 2024, needs more optimization.
6	638	0.805210102041	Henry Cohn, 2024, needs more optimization.
6	640	0.805274739564	Henry Cohn, 2024, needs more optimization.
6	641	0.805642533013	Henry Cohn, 2024, needs more optimization.
6	643	0.805773239367	Henry Cohn, 2024, needs more optimization.
6	644	0.806116053563	Henry Cohn, 2024, needs more optimization.
6	645	0.806233997311	Henry Cohn, 2024, needs more optimization.
6	647	0.806258353502	Henry Cohn, 2024, needs more optimization.
6	649	0.806417386260	Henry Cohn, 2024, needs more optimization.
6	650	0.806754705955	Henry Cohn, 2024, needs more optimization.
6	651	0.806826743761	Henry Cohn, 2024, needs more optimization.
6	652	0.806847407606	Henry Cohn, 2024, needs more optimization.
6	653	0.806929939766	Henry Cohn, 2024, needs more optimization.
6	656	0.807265224351	Henry Cohn, 2024, needs more optimization.
6	657	0.807452344179	Henry Cohn, 2024, needs more optimization.
6	658	0.807696395481	Henry Cohn, 2024, needs more optimization.
6	659	0.807715558675	Henry Cohn, 2024, needs more optimization.
6	661	0.808070087002	Henry Cohn, 2024, needs more optimization.
6	664	0.808338210403	Henry Cohn, 2024, needs more optimization.
6	665	0.808552846549	Henry Cohn, 2024, needs more optimization.
6	668	0.808711714740	Henry Cohn, 2024, needs more optimization.
6	669	0.809036486450	Henry Cohn, 2024, needs more optimization.
6	670	0.809115108237	Henry Cohn, 2024, needs more optimization.
6	671	0.809126717918	Henry Cohn, 2024, needs more optimization.
6	675	0.809415599688	Henry Cohn, 2024, needs more optimization.
6	676	0.809573031769	Henry Cohn, 2024, needs more optimization.
6	678	0.809845843928	Henry Cohn, 2024, needs more optimization.
6	679	0.810096075245	Henry Cohn, 2024, needs more optimization.
6	680	0.810133597607	Henry Cohn, 2024, needs more optimization.
6	681	0.810245994111	Henry Cohn, 2024, needs more optimization.
6	684	0.810416904386	Henry Cohn, 2024, needs more optimization.
6	685	0.810606598968	Henry Cohn, 2024, needs more optimization.
6	686	0.810693231691	Henry Cohn, 2024, needs more optimization.
6	687	0.811046412516	Henry Cohn, 2024, needs more optimization.
6	689	0.811080031219	Henry Cohn, 2024, needs more optimization.
6	690	0.811348551582	Henry Cohn, 2024, needs more optimization.
6	691	0.811419523516	Henry Cohn, 2024, needs more optimization.
6	692	0.811421625033	Henry Cohn, 2024, needs more optimization.
6	694	0.811626838940	Henry Cohn, 2024, needs more optimization.
6	695	0.811705970501	Henry Cohn, 2024, needs more optimization.
6	696	0.812092194767	Henry Cohn, 2024, needs more optimization.
6	697	0.812157466040	Henry Cohn, 2024, needs more optimization.
6	698	0.812171253570	Henry Cohn, 2024, needs more optimization.
6	699	0.812244001250	Henry Cohn, 2024, needs more optimization.
6	702	0.812387031987	Henry Cohn, 2024, needs more optimization.
6	704	0.812509666386	Henry Cohn, 2024, needs more optimization.
6	705	0.813038380876	Henry Cohn, 2024, needs more optimization.
6	707	0.813242856739	Henry Cohn, 2024, needs more optimization.
6	708	0.813297202039	Henry Cohn, 2024, needs more optimization.
6	709	0.813445244651	Henry Cohn, 2024, needs more optimization.
6	710	0.813529148188	Henry Cohn, 2024, needs more optimization.
6	711	0.813684381974	Henry Cohn, 2024, needs more optimization.
6	712	0.813776720839	Henry Cohn, 2024, needs more optimization.
6	713	0.813827140924	Henry Cohn, 2024, needs more optimization.
6	716	0.813899222311	Henry Cohn, 2024, needs more optimization.
6	717	0.814229067553	Henry Cohn, 2024, needs more optimization.
6	718	0.814353303713	Henry Cohn, 2024, needs more optimization.
6	719	0.814416603044	Henry Cohn, 2024, needs more optimization.
6	721	0.814495478412	Henry Cohn, 2024, needs more optimization.
6	722	0.814603783745	Henry Cohn, 2024, needs more optimization.
6	723	0.814625521037	Henry Cohn, 2024, needs more optimization.
6	724	0.814877077758	Henry Cohn, 2024, needs more optimization.
6	725	0.815086369043	Henry Cohn, 2024, needs more optimization.
6	726	0.815114321382	Henry Cohn, 2024, needs more optimization.
6	727	0.815211842574	Henry Cohn, 2024, needs more optimization.
6	728	0.815398405822	Henry Cohn, 2024, needs more optimization.
6	730	0.815435896549	Henry Cohn, 2024, needs more optimization.
6	731	0.815734962742	Henry Cohn, 2024, needs more optimization.
6	733	0.815915260150	Henry Cohn, 2024, needs more optimization.
6	734	0.816024080376	Henry Cohn, 2024, needs more optimization.
6	740	0.816154514992	Henry Cohn, 2024, needs more optimization.
6	741	0.816708868492	Henry Cohn, 2024, needs more optimization.
6	742	0.816826236702	Henry Cohn, 2024, needs more optimization.
6	745	0.816990733769	Henry Cohn, 2024, needs more optimization.
6	746	0.817158099836	Henry Cohn, 2024, needs more optimization.
6	747	0.817352889268	Henry Cohn, 2024, needs more optimization.
6	748	0.817386221644	Henry Cohn, 2024, needs more optimization.
6	749	0.817548721933	Henry Cohn, 2024, needs more optimization.
6	751	0.817562863996	Henry Cohn, 2024, needs more optimization.
6	752	0.817859954095	Henry Cohn, 2024, needs more optimization.
6	753	0.817899970215	Henry Cohn, 2024, needs more optimization.
6	754	0.817905922808	Henry Cohn, 2024, needs more optimization.
6	755	0.818018324420	Henry Cohn, 2024, needs more optimization.
6	756	0.818045427870	Henry Cohn, 2024, needs more optimization.
6	757	0.818206715798	Henry Cohn, 2024, needs more optimization.
6	758	0.818336569538	Henry Cohn, 2024, needs more optimization.
6	760	0.818519057855	Henry Cohn, 2024, needs more optimization.
6	762	0.818639422176	Henry Cohn, 2024, needs more optimization.
6	763	0.818740939977	Henry Cohn, 2024, needs more optimization.
6	764	0.818910698301	Henry Cohn, 2024, needs more optimization.
6	768	0.819086134261	Henry Cohn, 2024, needs more optimization.
6	770	0.819642559799	Henry Cohn, 2024, needs more optimization.
6	771	0.819749955473	Henry Cohn, 2024, needs more optimization.
6	773	0.819783993026	Henry Cohn, 2024, needs more optimization.
6	774	0.819908319943	Henry Cohn, 2024, needs more optimization.
6	775	0.819959086791	Henry Cohn, 2024, needs more optimization.
6	776	0.820053886897	Henry Cohn, 2024, needs more optimization.
6	778	0.820087469567	Henry Cohn, 2024, needs more optimization.
6	779	0.820406055970	Henry Cohn, 2024, needs more optimization.
6	780	0.820543769091	Henry Cohn, 2024, needs more optimization.
6	782	0.820573409469	Henry Cohn, 2024, needs more optimization.
6	784	0.820636659913	Henry Cohn, 2024, needs more optimization.
6	786	0.820998056741	Henry Cohn, 2024, needs more optimization.
6	788	0.821229518257	Henry Cohn, 2024, needs more optimization.
6	789	0.821244496475	Henry Cohn, 2024, needs more optimization.
6	790	0.821459265040	Henry Cohn, 2024, needs more optimization.
6	793	0.821484309876	Henry Cohn, 2024, needs more optimization.
6	795	0.821810793446	Henry Cohn, 2024, needs more optimization.
6	796	0.821868314857	Henry Cohn, 2024, needs more optimization.
6	797	0.822027991969	Henry Cohn, 2024, needs more optimization.
6	798	0.822038484952	Henry Cohn, 2024, needs more optimization.
6	799	0.822372420197	Henry Cohn, 2024, needs more optimization.
6	801	0.822386184894	Henry Cohn, 2024, needs more optimization.
6	803	0.822474224676	Henry Cohn, 2024, needs more optimization.
6	804	0.822613678867	Henry Cohn, 2024, needs more optimization.
6	806	0.822657749333	Henry Cohn, 2024, needs more optimization.
6	808	0.822817696143	Henry Cohn, 2024, needs more optimization.
6	812	0.823023655260	Henry Cohn, 2024, needs more optimization.
6	814	0.823379111105	Henry Cohn, 2024, needs more optimization.
6	815	0.823554938378	Henry Cohn, 2024, needs more optimization.
6	816	0.823686555419	Henry Cohn, 2024, needs more optimization.
6	818	0.823720779428	Henry Cohn, 2024, needs more optimization.
6	819	0.824011336142	Henry Cohn, 2024, needs more optimization.
6	820	0.824038492220	Henry Cohn, 2024, needs more optimization.
6	822	0.824104399397	Henry Cohn, 2024, needs more optimization.
6	823	0.824149617317	Henry Cohn, 2024, needs more optimization.
6	824	0.824452398269	Henry Cohn, 2024, needs more optimization.
6	825	0.824551059542	Henry Cohn, 2024, needs more optimization.
6	826	0.824612711519	Henry Cohn, 2024, needs more optimization.
6	827	0.824656437644	Henry Cohn, 2024, needs more optimization.
6	828	0.824770343713	Henry Cohn, 2024, needs more optimization.
6	830	0.824818002101	Henry Cohn, 2024, needs more optimization.
6	832	0.824928977667	Henry Cohn, 2024, needs more optimization.
6	833	0.824948641172	Henry Cohn, 2024, needs more optimization.
6	834	0.825341013832	Henry Cohn, 2024, needs more optimization.
6	835	0.825400241728	Henry Cohn, 2024, needs more optimization.
6	837	0.825462202860	Henry Cohn, 2024, needs more optimization.
6	839	0.825548458727	Henry Cohn, 2024, needs more optimization.
6	840	0.825914986583	Henry Cohn, 2024, needs more optimization.
6	842	0.825943499306	Henry Cohn, 2024, needs more optimization.
6	843	0.826025263509	Henry Cohn, 2024, needs more optimization.
6	846	0.826149668626	Henry Cohn, 2024, needs more optimization.
6	848	0.826427648852	Henry Cohn, 2024, needs more optimization.
6	849	0.826476079660	Henry Cohn, 2024, needs more optimization.
6	852	0.826596210045	Henry Cohn, 2024, needs more optimization.
6	853	0.826692100376	Henry Cohn, 2024, needs more optimization.
6	855	0.826957368146	Henry Cohn, 2024, needs more optimization.
6	856	0.827010972640	Henry Cohn, 2024, needs more optimization.
6	857	0.827108696752	Henry Cohn, 2024, needs more optimization.
6	858	0.827254017373	Henry Cohn, 2024, needs more optimization.
6	859	0.827325437791	Henry Cohn, 2024, needs more optimization.
6	860	0.827335044113	Henry Cohn, 2024, needs more optimization.
6	864	0.827585678376	Henry Cohn, 2024, needs more optimization.
6	865	0.827784611729	Henry Cohn, 2024, needs more optimization.
6	866	0.827871737665	Henry Cohn, 2024, needs more optimization.
6	867	0.828015887651	Henry Cohn, 2024, needs more optimization.
6	868	0.828110002033	Henry Cohn, 2024, needs more optimization.
6	872	0.828259044836	Henry Cohn, 2024, needs more optimization.
6	873	0.828492416081	Henry Cohn, 2024, needs more optimization.
6	874	0.828514684271	Henry Cohn, 2024, needs more optimization.
6	875	0.828567307860	Henry Cohn, 2024, needs more optimization.
6	878	0.828725865418	Henry Cohn, 2024, needs more optimization.
6	880	0.828794180424	Henry Cohn, 2024, needs more optimization.
6	882	0.828985863176	Henry Cohn, 2024, needs more optimization.
6	883	0.829045635367	Henry Cohn, 2024, needs more optimization.
6	884	0.829312010687	Henry Cohn, 2024, needs more optimization.
6	885	0.829337515925	Henry Cohn, 2024, needs more optimization.
6	886	0.829392531713	Henry Cohn, 2024, needs more optimization.
6	896	0.829494809015	Henry Cohn, 2024, needs more optimization.
6	898	0.830322018300	Henry Cohn, 2024, needs more optimization.
6	899	0.830355791946	Henry Cohn, 2024, needs more optimization.
6	900	0.830475299651	Henry Cohn, 2024, needs more optimization.
6	901	0.830696168887	Henry Cohn, 2024, needs more optimization.
6	902	0.830734330073	Henry Cohn, 2024, needs more optimization.
6	904	0.830817725830	Henry Cohn, 2024, needs more optimization.
6	905	0.830824069322	Henry Cohn, 2024, needs more optimization.
6	908	0.830987585632	Henry Cohn, 2024, needs more optimization.
6	909	0.831243827622	Henry Cohn, 2024, needs more optimization.
6	911	0.831305770421	Henry Cohn, 2024, needs more optimization.
6	912	0.831444909020	Henry Cohn, 2024, needs more optimization.
6	914	0.831516961017	Henry Cohn, 2024, needs more optimization.
6	916	0.831652096730	Henry Cohn, 2024, needs more optimization.
6	917	0.831781177067	Henry Cohn, 2024, needs more optimization.
6	918	0.831866351050	Henry Cohn, 2024, needs more optimization.
6	920	0.831929745566	Henry Cohn, 2024, needs more optimization.
6	923	0.832122655403	Henry Cohn, 2024, needs more optimization.
6	925	0.832286947776	Henry Cohn, 2024, needs more optimization.
6	927	0.832383771671	Henry Cohn, 2024, needs more optimization.
6	928	0.832519540435	Henry Cohn, 2024, needs more optimization.
6	929	0.832801630202	Henry Cohn, 2024, needs more optimization.
6	931	0.832824310117	Henry Cohn, 2024, needs more optimization.
6	933	0.832840558514	Henry Cohn, 2024, needs more optimization.
6	937	0.833049788401	Henry Cohn, 2024, needs more optimization.
6	939	0.833293167428	Henry Cohn, 2024, needs more optimization.
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	991	0.836842330777	Henry Cohn, 2024, needs more optimization.
6	994	0.837010741893	Henry Cohn, 2024, needs more optimization.
6	995	0.837031225550	Henry Cohn, 2024, needs more optimization.
6	996	0.837178926110	Henry Cohn, 2024, needs more optimization.
6	997	0.837279549211	Henry Cohn, 2024, needs more optimization.
6	998	0.837287551904	Henry Cohn, 2024, needs more optimization.
6	999	0.837507311127	Henry Cohn, 2024, needs more optimization.
6	1002	0.837510069244	Henry Cohn, 2024, needs more optimization.
6	1003	0.837726162212	Henry Cohn, 2024, needs more optimization.
6	1004	0.837747524647	Henry Cohn, 2024, needs more optimization.
6	1006	0.837791935654	Henry Cohn, 2024, needs more optimization.
6	1007	0.838045103636	Henry Cohn, 2024, needs more optimization.
6	1008	0.838069816544	Henry Cohn, 2024, needs more optimization.
6	1009	0.838129767394	Henry Cohn, 2024, needs more optimization.
6	1010	0.838214052131	Henry Cohn, 2024, needs more optimization.
6	1013	0.838224914483	Henry Cohn, 2024, needs more optimization.
6	1014	0.838432719538	Henry Cohn, 2024, needs more optimization.
6	1015	0.838453354574	Henry Cohn, 2024, needs more optimization.
6	1016	0.838617457835	Henry Cohn, 2024, needs more optimization.
6	1017	0.838630950919	Henry Cohn, 2024, needs more optimization.
6	1019	0.838714883491	Henry Cohn, 2024, needs more optimization.
6	1020	0.838745985229	Henry Cohn, 2024, needs more optimization.
6	1021	0.838818648101	Henry Cohn, 2024, needs more optimization.
6	1024	0.838887649318	Henry Cohn, 2024, needs more optimization.
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 listed in plain text data
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 listed in plain text data
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	0.248933144681	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7	30	0.249468286876	H. Cohn, Small spherical and projective codes, data set, 2022, 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	0.270027345615	Henry Cohn, 2023.
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	0.310458216649	Henry Cohn, 2023.
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	0.329085633548	Henry Cohn, 2023.
7	43	0.329665776133	Henry Cohn, 2023. Minimal polynomial listed in plain text data
7	44	0.333136872113	Henry Cohn, 2023.
7	45	0.333308788896	Henry Cohn, 2023, needs more optimization.
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	0.389653006570	Henry Cohn, 2024.
7	58	0.393749423280	Henry Cohn, 2023.
7	59	0.403218749805	Henry Cohn, 2023, needs more optimization.
7	60	0.407983549048	Henry Cohn, 2023.
7	61	0.412356098724	Henry Cohn, 2023, needs more optimization.
7	62	0.415090060680	Henry Cohn, 2023.
7	63	0.415655455573	Henry Cohn, 2023, needs more optimization.
7	64	0.420205850438	Henry Cohn, 2024.
7	66	0.421258543571	Henry Cohn, 2023. $622 x^{3} - 771 x^{2} + 288 x - 31$
7	67	0.428242433719	Henry Cohn, 2023, needs more optimization.
7	68	0.428438641205	Henry Cohn, 2023, needs more optimization.
7	78	0.428571428572	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.7.9. There seems to be an error in Appendix D.7: it lists the code as having 80 points, but the construction describes only 78 points. $7 x - 3$
7	79	0.453278430193	Henry Cohn, 2023, needs more optimization.
7	80	0.453908817135	Henry Cohn, 2024, needs more optimization.
7	81	0.460078233657	Henry Cohn, 2024, needs more optimization.
7	82	0.461421957570	Henry Cohn, 2024, needs more optimization.
7	83	0.467230247849	Henry Cohn, 2023, needs more optimization.
7	84	0.474211555233	Henry Cohn, 2024, needs more optimization.
7	85	0.474983055167	Henry Cohn, 2024, needs more optimization.
7	86	0.475588963316	Henry Cohn, 2024, needs more optimization.
7	87	0.475737798418	Henry Cohn, 2024, needs more optimization.
7	88	0.486950871711	Henry Cohn, 2024, needs more optimization.
7	89	0.489784179626	Henry Cohn, 2024, needs more optimization.
7	90	0.491854547760	Henry Cohn, 2024, needs more optimization.
7	91	0.493796710690	Henry Cohn, 2024, needs more optimization.
7	92	0.496238949265	Henry Cohn, 2024, needs more optimization.
7	93	0.497058110209	Henry Cohn, 2024, needs more optimization.
7	94	0.499341540220	Henry Cohn, 2023, needs more optimization.
7	95	0.499756792440	Henry Cohn, 2023, needs more optimization.
7	96	0.499807710730	Henry Cohn, 2023, needs more optimization.
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	0.511248407917	Henry Cohn, 2023. $1875 x^{9} - 27025 x^{8} - 9900 x^{7} + 10500 x^{6} + 14418 x^{5} + 4698 x^{4} - 3564 x^{3} - 1404 x^{2} + 243 x - 81$
7	128	0.519135161519	Henry Cohn, 2024, needs more optimization.
7	130	0.519185040795	Henry Cohn, 2024, needs more optimization.
7	134	0.519751518196	Henry Cohn, 2024, needs more optimization.
7	135	0.520157703745	Henry Cohn, 2024, needs more optimization.
7	136	0.527592255632	Henry Cohn, 2024, needs more optimization.
7	139	0.531977040277	Henry Cohn, 2024, needs more optimization.
7	140	0.532289726626	Henry Cohn, 2024, needs more optimization.
7	141	0.532306905896	Henry Cohn, 2023, needs more optimization.
7	142	0.532480834571	Henry Cohn, 2023, needs more optimization.
7	143	0.532591655227	Henry Cohn, 2024, needs more optimization.
7	144	0.533160876151	Henry Cohn, 2024, needs more optimization.
7	145	0.533193415842	Henry Cohn, 2024, needs more optimization.
7	146	0.533313463252	Henry Cohn, 2024, needs more optimization.
7	147	0.533479867161	Henry Cohn, 2024, needs more optimization.
7	148	0.534209256490	Henry Cohn, 2023. $49 x^{4} - 10 x^{2} - 4 x + 1$
7	149	0.550375415995	Henry Cohn, 2024, needs more optimization.
7	150	0.554695474325	Henry Cohn, 2024, needs more optimization.
7	151	0.557841174915	Henry Cohn, 2024, needs more optimization.
7	152	0.558633265746	Henry Cohn, 2023, needs more optimization.
7	155	0.560557631712	Henry Cohn, 2024, needs more optimization.
7	156	0.561374261848	Henry Cohn, 2023, needs more optimization.
7	157	0.562149317743	Henry Cohn, 2024, needs more optimization.
7	158	0.563106671791	Henry Cohn, 2023, needs more optimization.
7	159	0.563578657147	Henry Cohn, 2023, needs more optimization.
7	160	0.563807705963	Henry Cohn, 2023, needs more optimization.
7	161	0.564007476236	Henry Cohn, 2023, needs more optimization.
7	162	0.564020820373	Henry Cohn, 2023, needs more optimization.
7	163	0.565644570436	Henry Cohn, 2023, needs more optimization.
7	164	0.566628759122	Henry Cohn, 2023, needs more optimization.
7	165	0.567422324448	Henry Cohn, 2023, needs more optimization.
7	166	0.567452419503	Henry Cohn, 2023, needs more optimization.
7	167	0.568998444046	Henry Cohn, 2023, needs more optimization.
7	168	0.569055896175	Henry Cohn, 2023, needs more optimization.
7	169	0.570141557175	Henry Cohn, 2023, needs more optimization.
7	170	0.570171045097	Henry Cohn, 2024, needs more optimization.
7	172	0.570496402190	Henry Cohn, 2024, needs more optimization.
7	173	0.570497810999	Henry Cohn, 2024, needs more optimization.
7	174	0.571720708849	Henry Cohn, 2024, needs more optimization.
7	175	0.572076245180	Henry Cohn, 2023, needs more optimization.
7	176	0.572153011714	Henry Cohn, 2023, needs more optimization.
7	178	0.572385290780	Henry Cohn, 2024, needs more optimization.
7	179	0.572719867454	Henry Cohn, 2023, needs more optimization.
7	180	0.572870839673	Henry Cohn, 2024, needs more optimization.
7	181	0.573147061545	Henry Cohn, 2024, needs more optimization.
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	0.589896154276	Henry Cohn, 2024, needs more optimization.
7	184	0.590855140840	Henry Cohn, 2024, needs more optimization.
7	185	0.592342075537	Henry Cohn, 2024, needs more optimization.
7	186	0.593161472664	Henry Cohn, 2023, needs more optimization.
7	188	0.594044098991	Henry Cohn, 2023, needs more optimization.
7	190	0.594976216200	Henry Cohn, 2024, needs more optimization.
7	191	0.595445545647	Henry Cohn, 2024, needs more optimization.
7	192	0.596263374919	Henry Cohn, 2024, needs more optimization.
7	194	0.599530091620	Henry Cohn, 2024, needs more optimization.
7	195	0.601620188603	Henry Cohn, 2024, needs more optimization.
7	196	0.601904513535	Henry Cohn, 2024, needs more optimization.
7	198	0.604009311472	Henry Cohn, 2024, needs more optimization.
7	199	0.605341397497	Henry Cohn, 2024, needs more optimization.
7	200	0.605908274516	Henry Cohn, 2024, needs more optimization.
7	201	0.607853369983	Henry Cohn, 2024, needs more optimization.
7	202	0.609276584868	Henry Cohn, 2024, needs more optimization.
7	204	0.609519966193	Henry Cohn, 2024, needs more optimization.
7	205	0.611305332481	Henry Cohn, 2024, needs more optimization.
7	206	0.611979700376	Henry Cohn, 2024, needs more optimization.
7	207	0.612756190673	Henry Cohn, 2024, needs more optimization.
7	208	0.613480117466	Henry Cohn, 2024, needs more optimization.
7	209	0.614611665210	Henry Cohn, 2024, needs more optimization.
7	210	0.614915188005	Henry Cohn, 2024, needs more optimization.
7	211	0.616049553683	Henry Cohn, 2024, needs more optimization.
7	212	0.616458104298	Henry Cohn, 2024, needs more optimization.
7	213	0.617085644445	Henry Cohn, 2024, needs more optimization.
7	214	0.618572844155	Henry Cohn, 2024, needs more optimization.
7	215	0.619490793283	Henry Cohn, 2024, needs more optimization.
7	216	0.619614740628	Henry Cohn, 2024, needs more optimization.
7	217	0.620660016562	Henry Cohn, 2024, needs more optimization.
7	218	0.621382806150	Henry Cohn, 2024, needs more optimization.
7	219	0.622001678136	Henry Cohn, 2024, needs more optimization.
7	220	0.622622022607	Henry Cohn, 2024, needs more optimization.
7	221	0.624042061399	Henry Cohn, 2024, needs more optimization.
7	222	0.624643101301	Henry Cohn, 2024, needs more optimization.
7	223	0.625231259632	Henry Cohn, 2024, needs more optimization.
7	224	0.625407131087	Henry Cohn, 2024, needs more optimization.
7	225	0.625888065671	Henry Cohn, 2024, needs more optimization.
7	226	0.627474128397	Henry Cohn, 2024, needs more optimization.
7	227	0.628362645696	Henry Cohn, 2024, needs more optimization.
7	228	0.628580871821	Henry Cohn, 2024, needs more optimization.
7	229	0.629543832196	Henry Cohn, 2024, needs more optimization.
7	230	0.630310025845	Henry Cohn, 2024, needs more optimization.
7	231	0.630564055679	Henry Cohn, 2024, needs more optimization.
7	232	0.631259808434	Henry Cohn, 2024, needs more optimization.
7	233	0.631912453991	Henry Cohn, 2024, needs more optimization.
7	234	0.632651043773	Henry Cohn, 2024, needs more optimization.
7	235	0.633290658051	Henry Cohn, 2024, needs more optimization.
7	236	0.633954332100	Henry Cohn, 2024, needs more optimization.
7	237	0.634396197979	Henry Cohn, 2024, needs more optimization.
7	238	0.634793960348	Henry Cohn, 2024, needs more optimization.
7	239	0.635369298660	Henry Cohn, 2024, needs more optimization.
7	240	0.635696464397	Henry Cohn, 2024, needs more optimization.
7	241	0.636624530546	Henry Cohn, 2024, needs more optimization.
7	242	0.636986536314	Henry Cohn, 2024, needs more optimization.
7	243	0.637526131776	Henry Cohn, 2024, needs more optimization.
7	244	0.638100609519	Henry Cohn, 2024, needs more optimization.
7	245	0.638602200094	Henry Cohn, 2024, needs more optimization.
7	246	0.638787946080	Henry Cohn, 2024, needs more optimization.
7	247	0.639353744539	Henry Cohn, 2024, needs more optimization.
7	248	0.640045346071	Henry Cohn, 2024, needs more optimization.
7	249	0.640412938510	Henry Cohn, 2024, needs more optimization.
7	250	0.640989667765	Henry Cohn, 2024, needs more optimization.
7	251	0.641172114031	Henry Cohn, 2024, needs more optimization.
7	252	0.641660493863	Henry Cohn, 2024, needs more optimization.
7	253	0.641883851623	Henry Cohn, 2024, needs more optimization.
7	254	0.642966537938	Henry Cohn, 2024, needs more optimization.
7	255	0.643277334366	Henry Cohn, 2024, needs more optimization.
7	256	0.643616294186	Henry Cohn, 2024, needs more optimization.
7	257	0.645980204628	Henry Cohn, 2024, needs more optimization.
7	258	0.646623620977	Henry Cohn, 2024, needs more optimization.
7	260	0.647005409022	Henry Cohn, 2024, needs more optimization.
7	261	0.647998175152	Henry Cohn, 2024, needs more optimization.
7	263	0.648352708928	Henry Cohn, 2024, needs more optimization.
7	264	0.648776846522	Henry Cohn, 2024, needs more optimization.
7	265	0.649818151184	Henry Cohn, 2024, needs more optimization.
7	266	0.650045786164	Henry Cohn, 2024, needs more optimization.
7	267	0.650703874234	Henry Cohn, 2024, needs more optimization.
7	268	0.650843662309	Henry Cohn, 2024, needs more optimization.
7	269	0.651069033732	Henry Cohn, 2024, needs more optimization.
7	270	0.651789113329	Henry Cohn, 2024, needs more optimization.
7	271	0.652030430325	Henry Cohn, 2024, needs more optimization.
7	272	0.652384626004	Henry Cohn, 2024, needs more optimization.
7	273	0.652712728515	Henry Cohn, 2024, needs more optimization.
7	274	0.653314122445	Henry Cohn, 2024, needs more optimization.
7	275	0.653504352813	Henry Cohn, 2024, needs more optimization.
7	276	0.654139676350	Henry Cohn, 2024, needs more optimization.
7	277	0.654355978148	Henry Cohn, 2024, needs more optimization.
7	278	0.654485132392	Henry Cohn, 2024, needs more optimization.
7	279	0.654932759344	Henry Cohn, 2024, needs more optimization.
7	280	0.656162862795	Henry Cohn, 2024, needs more optimization.
7	281	0.656287999018	Henry Cohn, 2024, needs more optimization.
7	282	0.656789227726	Henry Cohn, 2024, needs more optimization.
7	283	0.657145132298	Henry Cohn, 2024, needs more optimization.
7	284	0.657315571459	Henry Cohn, 2024, needs more optimization.
7	285	0.657474275960	Henry Cohn, 2024, needs more optimization.
7	286	0.658654724749	Henry Cohn, 2024, needs more optimization.
7	287	0.658869325169	Henry Cohn, 2024, needs more optimization.
7	288	0.659323798682	Henry Cohn, 2024, needs more optimization.
7	289	0.659855021881	Henry Cohn, 2024, needs more optimization.
7	290	0.660392423086	Henry Cohn, 2024, needs more optimization.
7	293	0.660993260201	Henry Cohn, 2024, needs more optimization.
7	295	0.661945481108	Henry Cohn, 2024, needs more optimization.
7	296	0.662160229082	Henry Cohn, 2024, needs more optimization.
7	297	0.662676506953	Henry Cohn, 2024, needs more optimization.
7	298	0.662772327847	Henry Cohn, 2024, needs more optimization.
7	299	0.663116905420	Henry Cohn, 2024, needs more optimization.
7	300	0.663737653209	Henry Cohn, 2024, needs more optimization.
7	301	0.664096575358	Henry Cohn, 2024, needs more optimization.
7	303	0.664784684586	Henry Cohn, 2024, needs more optimization.
7	306	0.665713515109	Henry Cohn, 2024, needs more optimization.
7	307	0.666499347097	Henry Cohn, 2024, needs more optimization.
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	0.683598699275	Henry Cohn, 2024, needs more optimization.
7	360	0.684129828290	Henry Cohn, 2024, needs more optimization.
7	361	0.684430160547	Henry Cohn, 2024, needs more optimization.
7	363	0.684569965607	Henry Cohn, 2024, needs more optimization.
7	364	0.685383946278	Henry Cohn, 2024, needs more optimization.
7	365	0.685560952235	Henry Cohn, 2024, needs more optimization.
7	366	0.685994848503	Henry Cohn, 2024, needs more optimization.
7	367	0.686055499852	Henry Cohn, 2024, needs more optimization.
7	368	0.686407693797	Henry Cohn, 2024, needs more optimization.
7	370	0.686656724310	Henry Cohn, 2024, needs more optimization.
7	371	0.686972747399	Henry Cohn, 2024, needs more optimization.
7	372	0.687130932401	Henry Cohn, 2024, needs more optimization.
7	373	0.687916995588	Henry Cohn, 2024, needs more optimization.
7	375	0.688183357601	Henry Cohn, 2024, needs more optimization.
7	376	0.688641461208	Henry Cohn, 2024, needs more optimization.
7	378	0.689289032391	Henry Cohn, 2024, needs more optimization.
7	379	0.689686743298	Henry Cohn, 2024, needs more optimization.
7	380	0.689714618867	Henry Cohn, 2024, needs more optimization.
7	381	0.689895992272	Henry Cohn, 2024, needs more optimization.
7	382	0.690312308155	Henry Cohn, 2024, needs more optimization.
7	384	0.690573345805	Henry Cohn, 2024, needs more optimization.
7	385	0.690810039814	Henry Cohn, 2024, needs more optimization.
7	388	0.691766837832	Henry Cohn, 2024, needs more optimization.
7	389	0.692205687043	Henry Cohn, 2024, needs more optimization.
7	390	0.692577800851	Henry Cohn, 2024, needs more optimization.
7	391	0.692626676743	Henry Cohn, 2024, needs more optimization.
7	392	0.693183952841	Henry Cohn, 2024, needs more optimization.
7	393	0.693377100541	Henry Cohn, 2024, needs more optimization.
7	394	0.693408898188	Henry Cohn, 2024, needs more optimization.
7	395	0.693964832405	Henry Cohn, 2024, needs more optimization.
7	396	0.694432937441	Henry Cohn, 2024, needs more optimization.
7	397	0.694478848162	Henry Cohn, 2024, needs more optimization.
7	398	0.694823143390	Henry Cohn, 2024, needs more optimization.
7	399	0.694849658274	Henry Cohn, 2024, needs more optimization.
7	400	0.695259690343	Henry Cohn, 2024, needs more optimization.
7	402	0.695463468893	Henry Cohn, 2024, needs more optimization.
7	404	0.696180813804	Henry Cohn, 2024, needs more optimization.
7	405	0.696599992231	Henry Cohn, 2024, needs more optimization.
7	406	0.696677896359	Henry Cohn, 2024, needs more optimization.
7	407	0.697036535848	Henry Cohn, 2024, needs more optimization.
7	408	0.697189486332	Henry Cohn, 2024, needs more optimization.
7	409	0.697356553628	Henry Cohn, 2024, needs more optimization.
7	411	0.697666703937	Henry Cohn, 2024, needs more optimization.
7	412	0.698385005378	Henry Cohn, 2024, needs more optimization.
7	413	0.698593622217	Henry Cohn, 2024, needs more optimization.
7	414	0.699076699748	Henry Cohn, 2024, needs more optimization.
7	415	0.699095330814	Henry Cohn, 2024, needs more optimization.
7	416	0.699398216050	Henry Cohn, 2024, needs more optimization.
7	417	0.699524321582	Henry Cohn, 2024, needs more optimization.
7	418	0.699662801041	Henry Cohn, 2024, needs more optimization.
7	419	0.700053489404	Henry Cohn, 2024, needs more optimization.
7	420	0.700393432817	Henry Cohn, 2024, needs more optimization.
7	421	0.700500893324	Henry Cohn, 2024, needs more optimization.
7	423	0.700793778789	Henry Cohn, 2024, needs more optimization.
7	424	0.701176796581	Henry Cohn, 2024, needs more optimization.
7	425	0.701472290191	Henry Cohn, 2024, needs more optimization.
7	426	0.701614194215	Henry Cohn, 2024, needs more optimization.
7	427	0.701794294830	Henry Cohn, 2024, needs more optimization.
7	428	0.702182334543	Henry Cohn, 2024, needs more optimization.
7	429	0.702557865338	Henry Cohn, 2024, needs more optimization.
7	430	0.702597655086	Henry Cohn, 2024, needs more optimization.
7	431	0.702840076415	Henry Cohn, 2024, needs more optimization.
7	432	0.703091014993	Henry Cohn, 2024, needs more optimization.
7	433	0.703359481859	Henry Cohn, 2024, needs more optimization.
7	434	0.703635781543	Henry Cohn, 2024, needs more optimization.
7	435	0.704027923522	Henry Cohn, 2024, needs more optimization.
7	436	0.704144326787	Henry Cohn, 2024, needs more optimization.
7	437	0.704187761756	Henry Cohn, 2024, needs more optimization.
7	438	0.704483564225	Henry Cohn, 2024, needs more optimization.
7	439	0.704800035800	Henry Cohn, 2024, needs more optimization.
7	440	0.704842088255	Henry Cohn, 2024, needs more optimization.
7	441	0.705181247254	Henry Cohn, 2024, needs more optimization.
7	443	0.705561657319	Henry Cohn, 2024, needs more optimization.
7	444	0.705839318720	Henry Cohn, 2024, needs more optimization.
7	445	0.706061072523	Henry Cohn, 2024, needs more optimization.
7	448	0.706585010245	Henry Cohn, 2024, needs more optimization.
7	449	0.706988355871	Henry Cohn, 2024, needs more optimization.
7	450	0.707025523073	Henry Cohn, 2024, needs more optimization.
7	451	0.707560936506	Henry Cohn, 2024, needs more optimization.
7	452	0.707612942218	Henry Cohn, 2024, needs more optimization.
7	453	0.708332363812	Henry Cohn, 2024, needs more optimization.
7	454	0.708436653988	Henry Cohn, 2024, needs more optimization.
7	455	0.708502089959	Henry Cohn, 2024, needs more optimization.
7	457	0.708599972317	Henry Cohn, 2024, needs more optimization.
7	458	0.709174954933	Henry Cohn, 2024, needs more optimization.
7	459	0.709276780386	Henry Cohn, 2024, needs more optimization.
7	460	0.709283746909	Henry Cohn, 2024, needs more optimization.
7	461	0.709744350313	Henry Cohn, 2024, needs more optimization.
7	462	0.709834925312	Henry Cohn, 2024, needs more optimization.
7	463	0.710244840327	Henry Cohn, 2024, needs more optimization.
7	464	0.710349500170	Henry Cohn, 2024, needs more optimization.
7	465	0.710359694081	Henry Cohn, 2024, needs more optimization.
7	466	0.710859305168	Henry Cohn, 2024, needs more optimization.
7	467	0.711064041645	Henry Cohn, 2024, needs more optimization.
7	468	0.711067399827	Henry Cohn, 2024, needs more optimization.
7	469	0.711500933332	Henry Cohn, 2024, needs more optimization.
7	470	0.711611321332	Henry Cohn, 2024, needs more optimization.
7	472	0.711697362262	Henry Cohn, 2024, needs more optimization.
7	473	0.711947461841	Henry Cohn, 2024, needs more optimization.
7	474	0.712697978937	Henry Cohn, 2024, needs more optimization.
7	475	0.712870085219	Henry Cohn, 2024, needs more optimization.
7	476	0.712988931092	Henry Cohn, 2024, needs more optimization.
7	477	0.713023754860	Henry Cohn, 2024, needs more optimization.
7	478	0.713074394621	Henry Cohn, 2024, needs more optimization.
7	479	0.713552181381	Henry Cohn, 2024, needs more optimization.
7	480	0.713661215479	Henry Cohn, 2024, needs more optimization.
7	481	0.713700184386	Henry Cohn, 2024, needs more optimization.
7	483	0.714170594256	Henry Cohn, 2024, needs more optimization.
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	0.739292715971	Henry Cohn, 2024, needs more optimization.
7	634	0.739508445070	Henry Cohn, 2024, needs more optimization.
7	635	0.739523076449	Henry Cohn, 2024, needs more optimization.
7	636	0.739836218980	Henry Cohn, 2024, needs more optimization.
7	637	0.740016478161	Henry Cohn, 2024, needs more optimization.
7	639	0.740089083409	Henry Cohn, 2024, needs more optimization.
7	640	0.740116617230	Henry Cohn, 2024, needs more optimization.
7	641	0.740640383803	Henry Cohn, 2024, needs more optimization.
7	642	0.740674814577	Henry Cohn, 2024, needs more optimization.
7	643	0.740732436213	Henry Cohn, 2024, needs more optimization.
7	644	0.740834029819	Henry Cohn, 2024, needs more optimization.
7	645	0.740997000264	Henry Cohn, 2024, needs more optimization.
7	646	0.741174214866	Henry Cohn, 2024, needs more optimization.
7	650	0.741369174358	Henry Cohn, 2024, needs more optimization.
7	651	0.741498078951	Henry Cohn, 2024, needs more optimization.
7	652	0.741764283454	Henry Cohn, 2024, needs more optimization.
7	653	0.742084175985	Henry Cohn, 2024, needs more optimization.
7	654	0.742227623123	Henry Cohn, 2024, needs more optimization.
7	657	0.742420901077	Henry Cohn, 2024, needs more optimization.
7	658	0.742833475825	Henry Cohn, 2024, needs more optimization.
7	659	0.742843100184	Henry Cohn, 2024, needs more optimization.
7	661	0.743267499112	Henry Cohn, 2024, needs more optimization.
7	662	0.743301419024	Henry Cohn, 2024, needs more optimization.
7	663	0.743359249005	Henry Cohn, 2024, needs more optimization.
7	664	0.743495676997	Henry Cohn, 2024, needs more optimization.
7	665	0.743524219734	Henry Cohn, 2024, needs more optimization.
7	668	0.743779619515	Henry Cohn, 2024, needs more optimization.
7	669	0.744127088957	Henry Cohn, 2024, needs more optimization.
7	670	0.744203422426	Henry Cohn, 2024, needs more optimization.
7	671	0.744423378706	Henry Cohn, 2024, needs more optimization.
7	673	0.744647066886	Henry Cohn, 2024, needs more optimization.
7	674	0.744862809599	Henry Cohn, 2024, needs more optimization.
7	675	0.744898209016	Henry Cohn, 2024, needs more optimization.
7	676	0.745193054144	Henry Cohn, 2024, needs more optimization.
7	677	0.745364125321	Henry Cohn, 2024, needs more optimization.
7	678	0.745455008248	Henry Cohn, 2024, needs more optimization.
7	680	0.745460450784	Henry Cohn, 2024, needs more optimization.
7	684	0.746000097978	Henry Cohn, 2024, needs more optimization.
7	685	0.746263035070	Henry Cohn, 2024, needs more optimization.
7	687	0.746464406132	Henry Cohn, 2024, needs more optimization.
7	689	0.746713013912	Henry Cohn, 2024, needs more optimization.
7	691	0.747154099488	Henry Cohn, 2024, needs more optimization.
7	693	0.747211598939	Henry Cohn, 2024, needs more optimization.
7	694	0.747300445156	Henry Cohn, 2024, needs more optimization.
7	695	0.747416641959	Henry Cohn, 2024, needs more optimization.
7	696	0.747687832514	Henry Cohn, 2024, needs more optimization.
7	698	0.747810652054	Henry Cohn, 2024, needs more optimization.
7	700	0.748007528804	Henry Cohn, 2024, needs more optimization.
7	701	0.748091038537	Henry Cohn, 2024, needs more optimization.
7	702	0.748390628049	Henry Cohn, 2024, needs more optimization.
7	704	0.748459552018	Henry Cohn, 2024, needs more optimization.
7	705	0.748634666471	Henry Cohn, 2024, needs more optimization.
7	708	0.749050571127	Henry Cohn, 2024, needs more optimization.
7	710	0.749344679741	Henry Cohn, 2024, needs more optimization.
7	713	0.749576633677	Henry Cohn, 2024, needs more optimization.
7	714	0.749866831728	Henry Cohn, 2024, needs more optimization.
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	884	0.767238581074	Henry Cohn, 2024, needs more optimization.
7	887	0.767472153769	Henry Cohn, 2024, needs more optimization.
7	890	0.767596028907	Henry Cohn, 2024, needs more optimization.
7	893	0.767995856674	Henry Cohn, 2024, needs more optimization.
7	894	0.768169302475	Henry Cohn, 2024, needs more optimization.
7	895	0.768300791235	Henry Cohn, 2024, needs more optimization.
7	896	0.768315085115	Henry Cohn, 2024, needs more optimization.
7	897	0.768492122022	Henry Cohn, 2024, needs more optimization.
7	899	0.768612842560	Henry Cohn, 2024, needs more optimization.
7	902	0.768700838570	Henry Cohn, 2024, needs more optimization.
7	903	0.768812942032	Henry Cohn, 2024, needs more optimization.
7	907	0.769201583067	Henry Cohn, 2024, needs more optimization.
7	908	0.769354463444	Henry Cohn, 2024, needs more optimization.
7	910	0.769526704485	Henry Cohn, 2024, needs more optimization.
7	912	0.769615033026	Henry Cohn, 2024, needs more optimization.
7	913	0.769844993405	Henry Cohn, 2024, needs more optimization.
7	914	0.770020319279	Henry Cohn, 2024, needs more optimization.
7	915	0.770078376907	Henry Cohn, 2024, needs more optimization.
7	916	0.770107198587	Henry Cohn, 2024, needs more optimization.
7	918	0.770160918087	Henry Cohn, 2024, needs more optimization.
7	919	0.770412651032	Henry Cohn, 2024, needs more optimization.
7	920	0.770466430282	Henry Cohn, 2024, needs more optimization.
7	923	0.770480877799	Henry Cohn, 2024, needs more optimization.
7	925	0.770870572742	Henry Cohn, 2024, needs more optimization.
7	926	0.771011080366	Henry Cohn, 2024, needs more optimization.
7	927	0.771116865698	Henry Cohn, 2024, needs more optimization.
7	931	0.771313097173	Henry Cohn, 2024, needs more optimization.
7	932	0.771418036781	Henry Cohn, 2024, needs more optimization.
7	935	0.771599846854	Henry Cohn, 2024, needs more optimization.
7	937	0.771615740458	Henry Cohn, 2024, needs more optimization.
7	938	0.771976714213	Henry Cohn, 2024, needs more optimization.
7	939	0.772023691824	Henry Cohn, 2024, needs more optimization.
7	940	0.772100090275	Henry Cohn, 2024, needs more optimization.
7	942	0.772210712544	Henry Cohn, 2024, needs more optimization.
7	944	0.772297958334	Henry Cohn, 2024, needs more optimization.
7	945	0.772561870281	Henry Cohn, 2024, needs more optimization.
7	946	0.772617625309	Henry Cohn, 2024, needs more optimization.
7	948	0.772740120557	Henry Cohn, 2024, needs more optimization.
7	951	0.772906672486	Henry Cohn, 2024, needs more optimization.
7	952	0.772953143848	Henry Cohn, 2024, needs more optimization.
7	953	0.773231400299	Henry Cohn, 2024, needs more optimization.
7	954	0.773302222768	Henry Cohn, 2024, needs more optimization.
7	957	0.773347122306	Henry Cohn, 2024, needs more optimization.
7	958	0.773487818740	Henry Cohn, 2024, needs more optimization.
7	960	0.773623874685	Henry Cohn, 2024, needs more optimization.
7	961	0.773832900752	Henry Cohn, 2024, needs more optimization.
7	963	0.773871780630	Henry Cohn, 2024, needs more optimization.
7	964	0.774006425747	Henry Cohn, 2024, needs more optimization.
7	965	0.774050445987	Henry Cohn, 2024, needs more optimization.
7	966	0.774088853994	Henry Cohn, 2024, needs more optimization.
7	967	0.774169467478	Henry Cohn, 2024, needs more optimization.
7	968	0.774218886802	Henry Cohn, 2024, needs more optimization.
7	969	0.774457350410	Henry Cohn, 2024, needs more optimization.
7	971	0.774544687420	Henry Cohn, 2024, needs more optimization.
7	972	0.774618589112	Henry Cohn, 2024, needs more optimization.
7	973	0.774732791296	Henry Cohn, 2024, needs more optimization.
7	975	0.774766518635	Henry Cohn, 2024, needs more optimization.
7	977	0.775025977566	Henry Cohn, 2024, needs more optimization.
7	980	0.775139652843	Henry Cohn, 2024, needs more optimization.
7	982	0.775392446609	Henry Cohn, 2024, needs more optimization.
7	984	0.775543893687	Henry Cohn, 2024, needs more optimization.
7	986	0.775708628890	Henry Cohn, 2024, needs more optimization.
7	987	0.775780504643	Henry Cohn, 2024, needs more optimization.
7	988	0.775851787049	Henry Cohn, 2024, needs more optimization.
7	989	0.775973171479	Henry Cohn, 2024, needs more optimization.
7	992	0.776064644899	Henry Cohn, 2024, needs more optimization.
7	994	0.776317074545	Henry Cohn, 2024, needs more optimization.
7	996	0.776526667767	Henry Cohn, 2024, needs more optimization.
7	997	0.776804530363	Henry Cohn, 2024, needs more optimization.
7	998	0.776812029626	Henry Cohn, 2024, needs more optimization.
7	1000	0.776893100041	Henry Cohn, 2024, needs more optimization.
7	1001	0.776941017209	Henry Cohn, 2024, needs more optimization.
7	1002	0.777080725698	Henry Cohn, 2024, needs more optimization.
7	1006	0.777104886076	Henry Cohn, 2024, needs more optimization.
7	1008	0.777333015028	Henry Cohn, 2024, needs more optimization.
7	1010	0.777413707073	Henry Cohn, 2024, needs more optimization.
7	1011	0.777548776751	Henry Cohn, 2024, needs more optimization.
7	1012	0.777818155531	Henry Cohn, 2024, needs more optimization.
7	1015	0.777919592938	Henry Cohn, 2024, needs more optimization.
7	1016	0.778029251833	Henry Cohn, 2024, needs more optimization.
7	1017	0.778135524939	Henry Cohn, 2024, needs more optimization.
7	1019	0.778251999034	Henry Cohn, 2024, needs more optimization.
7	1020	0.778291251091	Henry Cohn, 2024, needs more optimization.
7	1021	0.778470198183	Henry Cohn, 2024, needs more optimization.
7	1024	0.778503809700	Henry Cohn, 2024, needs more optimization.
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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 listed in plain text data
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	0.187927415590	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial listed in plain text data
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	0.219706574300	H. Cohn, Small spherical and projective codes, data set, 2022, 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	0.265123725370	Henry Cohn, 2023.
8	41	0.269595854246	Henry Cohn, 2023.
8	42	0.276791074187	Henry Cohn, 2023.
8	43	0.285393498373	Henry Cohn, 2023.
8	44	0.288917068041	Henry Cohn, 2024.
8	45	0.293536733640	Henry Cohn, 2023, needs more optimization.
8	46	0.298272580160	Henry Cohn, 2024.
8	47	0.301071641398	Henry Cohn, 2024.
8	48	0.306887170190	Henry Cohn, 2023, needs more optimization.
8	49	0.310567741349	Henry Cohn, 2024.
8	50	0.315289580845	Henry Cohn, 2023.
8	51	0.316850575857	Henry Cohn, 2023.
8	52	0.317163413684	Henry Cohn, 2023.
8	53	0.323178575759	Henry Cohn, 2023.
8	54	0.326168059066	Henry Cohn, 2023.
8	55	0.328647504145	Henry Cohn, 2023, needs more optimization.
8	56	0.330635804030	Henry Cohn, 2023, needs more optimization.
8	57	0.332158961759	Henry Cohn, 2023, needs more optimization.
8	58	0.332764127620	Henry Cohn, 2024, needs more optimization.
8	59	0.333074434005	Henry Cohn, 2023, needs more optimization.
8	60	0.333203866874	Henry Cohn, 2024, needs more optimization.
8	61	0.333268915119	Henry Cohn, 2024, needs more optimization.
8	62	0.333284021412	Henry Cohn, 2023, needs more optimization.
8	63	0.333331595003	Henry Cohn, 2024, needs more optimization.
8	64	0.333333333334	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. $3 x - 1$
8	65	0.340297749224	Henry Cohn, 2023, needs more optimization.
8	66	0.348779612155	Henry Cohn, 2023.
8	67	0.350802261971	Henry Cohn, 2023, needs more optimization.
8	68	0.352462830866	Henry Cohn, 2023, needs more optimization.
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	0.374360545517	Henry Cohn, 2023.
8	74	0.375030122156	Henry Cohn, 2023, needs more optimization.
8	75	0.380147256279	Henry Cohn, 2023, needs more optimization.
8	76	0.383280469013	Henry Cohn, 2023.
8	77	0.386336872825	Henry Cohn, 2023, needs more optimization.
8	78	0.387879818212	Henry Cohn, 2023, needs more optimization.
8	79	0.395049514669	Henry Cohn, 2023, needs more optimization.
8	80	0.399272876863	Henry Cohn, 2023, needs more optimization.
8	81	0.402676855091	Henry Cohn, 2023, needs more optimization.
8	82	0.405264834580	Henry Cohn, 2023, needs more optimization.
8	83	0.409144258225	Henry Cohn, 2023, needs more optimization.
8	84	0.409508840421	Henry Cohn, 2023, needs more optimization.
8	85	0.414246295839	Henry Cohn, 2024, needs more optimization.
8	86	0.417446345241	Henry Cohn, 2024, needs more optimization.
8	88	0.418782717642	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. $32 x^{3} - 8 x + 1$
8	89	0.424850819596	Henry Cohn, 2023, needs more optimization.
8	90	0.425710077949	Henry Cohn, 2023, needs more optimization.
8	91	0.426007165883	Henry Cohn, 2023, needs more optimization.
8	92	0.426045497553	Henry Cohn, 2023, needs more optimization.
8	93	0.426385173741	Henry Cohn, 2023, needs more optimization.
8	94	0.426828493917	Henry Cohn, 2023, needs more optimization.
8	95	0.427086350340	Henry Cohn, 2023, needs more optimization.
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	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	0.495057518460	Henry Cohn, 2024, needs more optimization.
8	138	0.495307574277	Henry Cohn, 2024, needs more optimization.
8	139	0.495466305462	Henry Cohn, 2024, needs more optimization.
8	140	0.495651610459	Henry Cohn, 2024, needs more optimization.
8	141	0.495930558188	Henry Cohn, 2024, needs more optimization.
8	142	0.496054490323	Henry Cohn, 2024, needs more optimization.
8	143	0.496204618307	Henry Cohn, 2024, needs more optimization.
8	144	0.496365612728	Henry Cohn, 2024, needs more optimization.
8	145	0.497315599079	Henry Cohn, 2024, needs more optimization.
8	146	0.497516215874	Henry Cohn, 2024, needs more optimization.
8	147	0.497641762457	Henry Cohn, 2024, needs more optimization.
8	148	0.497962148212	Henry Cohn, 2024, needs more optimization.
8	149	0.498168458853	Henry Cohn, 2024, needs more optimization.
8	150	0.498340219249	Henry Cohn, 2024, needs more optimization.
8	151	0.498485599500	Henry Cohn, 2024, needs more optimization.
8	152	0.498597832374	Henry Cohn, 2024, needs more optimization.
8	153	0.498661604118	Henry Cohn, 2024, needs more optimization.
8	154	0.498744385679	Henry Cohn, 2024, needs more optimization.
8	155	0.498806488626	Henry Cohn, 2024, needs more optimization.
8	156	0.498868527070	Henry Cohn, 2024, needs more optimization.
8	157	0.498912048924	Henry Cohn, 2024, needs more optimization.
8	158	0.498972735492	Henry Cohn, 2024, needs more optimization.
8	159	0.499035979491	Henry Cohn, 2024, needs more optimization.
8	160	0.499098134735	Henry Cohn, 2024, needs more optimization.
8	161	0.499156103043	Henry Cohn, 2024, needs more optimization.
8	162	0.499228440064	Henry Cohn, 2024, needs more optimization.
8	163	0.499311893467	Henry Cohn, 2024, needs more optimization.
8	164	0.499396322688	Henry Cohn, 2024, needs more optimization.
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	0.539503939581	Bram Cohen, 2023.
8	242	0.545336939828	Henry Cohn, 2024, needs more optimization.
8	243	0.548057898976	Henry Cohn, 2024, needs more optimization.
8	244	0.550954188218	Henry Cohn, 2024, needs more optimization.
8	245	0.554170171832	Henry Cohn, 2024, needs more optimization.
8	246	0.554780227594	Henry Cohn, 2024, needs more optimization.
8	247	0.557476263049	Henry Cohn, 2024, needs more optimization.
8	248	0.558436003585	Henry Cohn, 2024, needs more optimization.
8	249	0.559791294021	Henry Cohn, 2024, needs more optimization.
8	250	0.561384867308	Henry Cohn, 2024, needs more optimization.
8	251	0.562313426667	Henry Cohn, 2024, needs more optimization.
8	252	0.564960366219	Henry Cohn, 2024, needs more optimization.
8	254	0.565974682831	Henry Cohn, 2024, needs more optimization.
8	255	0.567647127651	Henry Cohn, 2024, needs more optimization.
8	256	0.568990360141	Henry Cohn, 2024, needs more optimization.
8	267	0.581535858738	Henry Cohn, 2024, needs more optimization.
8	268	0.587342297819	Henry Cohn, 2024, needs more optimization.
8	271	0.588541120980	Henry Cohn, 2024, needs more optimization.
8	273	0.590603929589	Henry Cohn, 2024, needs more optimization.
8	275	0.590817716117	Henry Cohn, 2024, needs more optimization.
8	277	0.591422608089	Henry Cohn, 2024, needs more optimization.
8	278	0.591713618663	Henry Cohn, 2024, needs more optimization.
8	310	0.592250069349	Henry Cohn, 2024, needs more optimization.
8	312	0.606555260296	Henry Cohn, 2024, needs more optimization.
8	313	0.606774086273	Henry Cohn, 2024, needs more optimization.
8	314	0.607415522481	Henry Cohn, 2024, needs more optimization.
8	315	0.607471912045	Henry Cohn, 2024, needs more optimization.
8	319	0.607936086933	Henry Cohn, 2024, needs more optimization.
8	320	0.609150991920	Henry Cohn, 2024, needs more optimization.
8	321	0.610099524394	Henry Cohn, 2024, needs more optimization.
8	322	0.610220545255	Henry Cohn, 2024, needs more optimization.
8	323	0.610492872869	Henry Cohn, 2024, needs more optimization.
8	324	0.610950175534	Henry Cohn, 2024, needs more optimization.
8	326	0.611598268237	Henry Cohn, 2024, needs more optimization.
8	327	0.611773278571	Henry Cohn, 2024, needs more optimization.
8	329	0.612810613872	Henry Cohn, 2024, needs more optimization.
8	330	0.612883430828	Henry Cohn, 2024, needs more optimization.
8	331	0.613599740948	Henry Cohn, 2024, needs more optimization.
8	333	0.614498461358	Henry Cohn, 2024, needs more optimization.
8	334	0.614808784463	Henry Cohn, 2024, needs more optimization.
8	335	0.615079834019	Henry Cohn, 2024, needs more optimization.
8	336	0.615502333834	Henry Cohn, 2024, needs more optimization.
8	337	0.615566018686	Henry Cohn, 2024, needs more optimization.
8	339	0.616125937791	Henry Cohn, 2024, needs more optimization.
8	340	0.616857883445	Henry Cohn, 2024, needs more optimization.
8	341	0.617285255062	Henry Cohn, 2024, needs more optimization.
8	343	0.617774220203	Henry Cohn, 2024, needs more optimization.
8	344	0.618170241059	Henry Cohn, 2024, needs more optimization.
8	345	0.618610248346	Henry Cohn, 2024, needs more optimization.
8	346	0.619106438573	Henry Cohn, 2024, needs more optimization.
8	347	0.619233274732	Henry Cohn, 2024, needs more optimization.
8	348	0.619762354233	Henry Cohn, 2024, needs more optimization.
8	349	0.620088968150	Henry Cohn, 2024, needs more optimization.
8	351	0.620434795573	Henry Cohn, 2024, needs more optimization.
8	352	0.621259142120	Henry Cohn, 2024, needs more optimization.
8	353	0.621590038646	Henry Cohn, 2024, needs more optimization.
8	355	0.621788618423	Henry Cohn, 2024, needs more optimization.
8	356	0.622499284233	Henry Cohn, 2024, needs more optimization.
8	358	0.622816239560	Henry Cohn, 2024, needs more optimization.
8	359	0.623214078558	Henry Cohn, 2024, needs more optimization.
8	360	0.623648253030	Henry Cohn, 2024, needs more optimization.
8	362	0.623963307212	Henry Cohn, 2024, needs more optimization.
8	363	0.624447555106	Henry Cohn, 2024, needs more optimization.
8	364	0.625024326462	Henry Cohn, 2024, needs more optimization.
8	365	0.625263518341	Henry Cohn, 2024, needs more optimization.
8	366	0.625327456288	Henry Cohn, 2024, needs more optimization.
8	367	0.625767122291	Henry Cohn, 2024, needs more optimization.
8	368	0.626040496057	Henry Cohn, 2024, needs more optimization.
8	369	0.626318657433	Henry Cohn, 2024, needs more optimization.
8	371	0.626826902566	Henry Cohn, 2024, needs more optimization.
8	373	0.627104718576	Henry Cohn, 2024, needs more optimization.
8	375	0.628004964681	Henry Cohn, 2024, needs more optimization.
8	376	0.628361562453	Henry Cohn, 2024, needs more optimization.
8	378	0.628496953656	Henry Cohn, 2024, needs more optimization.
8	379	0.629331924399	Henry Cohn, 2024, needs more optimization.
8	380	0.629697072219	Henry Cohn, 2024, needs more optimization.
8	381	0.630018293852	Henry Cohn, 2024, needs more optimization.
8	382	0.630123698447	Henry Cohn, 2024, needs more optimization.
8	383	0.630352667134	Henry Cohn, 2024, needs more optimization.
8	384	0.630579441955	Henry Cohn, 2024, needs more optimization.
8	386	0.631133875234	Henry Cohn, 2024, needs more optimization.
8	388	0.631820525283	Henry Cohn, 2024, needs more optimization.
8	391	0.632523058051	Henry Cohn, 2024, needs more optimization.
8	394	0.633212224277	Henry Cohn, 2024, needs more optimization.
8	395	0.633724521566	Henry Cohn, 2024, needs more optimization.
8	396	0.634392143101	Henry Cohn, 2024, needs more optimization.
8	398	0.634592316005	Henry Cohn, 2024, needs more optimization.
8	400	0.634662910613	Henry Cohn, 2024, needs more optimization.
8	401	0.635448836822	Henry Cohn, 2024, needs more optimization.
8	402	0.635895106527	Henry Cohn, 2024, needs more optimization.
8	403	0.636032299770	Henry Cohn, 2024, needs more optimization.
8	404	0.636675606654	Henry Cohn, 2024, needs more optimization.
8	406	0.636785638147	Henry Cohn, 2024, needs more optimization.
8	408	0.637529335910	Henry Cohn, 2024, needs more optimization.
8	416	0.637917796226	Henry Cohn, 2024, needs more optimization.
8	417	0.639557548907	Henry Cohn, 2024, needs more optimization.
8	418	0.639644680913	Henry Cohn, 2024, needs more optimization.
8	420	0.640358100336	Henry Cohn, 2024, needs more optimization.
8	422	0.640925558470	Henry Cohn, 2024, needs more optimization.
8	423	0.641403626005	Henry Cohn, 2024, needs more optimization.
8	425	0.641444466419	Henry Cohn, 2024, needs more optimization.
8	426	0.642145374911	Henry Cohn, 2024, needs more optimization.
8	427	0.642152791393	Henry Cohn, 2024, needs more optimization.
8	429	0.642326434683	Henry Cohn, 2024, needs more optimization.
8	430	0.642624295910	Henry Cohn, 2024, needs more optimization.
8	432	0.643489527870	Henry Cohn, 2024, needs more optimization.
8	433	0.643975210051	Henry Cohn, 2024, needs more optimization.
8	434	0.644103860225	Henry Cohn, 2024, needs more optimization.
8	435	0.644359747454	Henry Cohn, 2024, needs more optimization.
8	436	0.644421796905	Henry Cohn, 2024, needs more optimization.
8	437	0.644616336280	Henry Cohn, 2024, needs more optimization.
8	438	0.644644010247	Henry Cohn, 2024, needs more optimization.
8	439	0.644927670845	Henry Cohn, 2024, needs more optimization.
8	441	0.645397515823	Henry Cohn, 2024, needs more optimization.
8	442	0.646101100448	Henry Cohn, 2024, needs more optimization.
8	446	0.646320201756	Henry Cohn, 2024, needs more optimization.
8	448	0.646914003433	Henry Cohn, 2024, needs more optimization.
8	449	0.647708699824	Henry Cohn, 2024, needs more optimization.
8	450	0.647856185959	Henry Cohn, 2024, needs more optimization.
8	451	0.648037462877	Henry Cohn, 2024, needs more optimization.
8	452	0.648245111564	Henry Cohn, 2024, needs more optimization.
8	455	0.648612340129	Henry Cohn, 2024, needs more optimization.
8	456	0.649337040360	Henry Cohn, 2024, needs more optimization.
8	457	0.649377474908	Henry Cohn, 2024, needs more optimization.
8	458	0.649386597465	Henry Cohn, 2024, needs more optimization.
8	460	0.649811095129	Henry Cohn, 2024, needs more optimization.
8	461	0.650196221781	Henry Cohn, 2024, needs more optimization.
8	464	0.650564071432	Henry Cohn, 2024, needs more optimization.
8	465	0.651058568791	Henry Cohn, 2024, needs more optimization.
8	467	0.651473888096	Henry Cohn, 2024, needs more optimization.
8	468	0.651872797504	Henry Cohn, 2024, needs more optimization.
8	469	0.652107027901	Henry Cohn, 2024, needs more optimization.
8	470	0.652242454240	Henry Cohn, 2024, needs more optimization.
8	471	0.652352358326	Henry Cohn, 2024, needs more optimization.
8	473	0.652627527427	Henry Cohn, 2024, needs more optimization.
8	475	0.653297187658	Henry Cohn, 2024, needs more optimization.
8	476	0.653513975909	Henry Cohn, 2024, needs more optimization.
8	478	0.653883669782	Henry Cohn, 2024, needs more optimization.
8	480	0.654283731981	Henry Cohn, 2024, needs more optimization.
8	481	0.654732416343	Henry Cohn, 2024, needs more optimization.
8	482	0.654845248860	Henry Cohn, 2024, needs more optimization.
8	483	0.655193007104	Henry Cohn, 2024, needs more optimization.
8	484	0.655526565272	Henry Cohn, 2024, needs more optimization.
8	486	0.655608574913	Henry Cohn, 2024, needs more optimization.
8	487	0.656137162392	Henry Cohn, 2024, needs more optimization.
8	488	0.656181556315	Henry Cohn, 2024, needs more optimization.
8	489	0.656429297460	Henry Cohn, 2024, needs more optimization.
8	491	0.656450876216	Henry Cohn, 2024, needs more optimization.
8	492	0.656611679455	Henry Cohn, 2024, needs more optimization.
8	493	0.656959843788	Henry Cohn, 2024, needs more optimization.
8	494	0.657052159544	Henry Cohn, 2024, needs more optimization.
8	495	0.657287720626	Henry Cohn, 2024, needs more optimization.
8	496	0.657603953822	Henry Cohn, 2024, needs more optimization.
8	497	0.658099274191	Henry Cohn, 2024, needs more optimization.
8	499	0.658264262947	Henry Cohn, 2024, needs more optimization.
8	500	0.658455885781	Henry Cohn, 2024, needs more optimization.
8	501	0.658809877048	Henry Cohn, 2024, needs more optimization.
8	502	0.659148528896	Henry Cohn, 2024, needs more optimization.
8	504	0.659454391137	Henry Cohn, 2024, needs more optimization.
8	505	0.659518417447	Henry Cohn, 2024, needs more optimization.
8	506	0.659916934408	Henry Cohn, 2024, needs more optimization.
8	508	0.660198102557	Henry Cohn, 2024, needs more optimization.
8	510	0.660534939054	Henry Cohn, 2024, needs more optimization.
8	511	0.660737681639	Henry Cohn, 2024, needs more optimization.
8	512	0.660883799091	Henry Cohn, 2024, needs more optimization.
8	513	0.661247033274	Henry Cohn, 2024, needs more optimization.
8	514	0.661573543922	Henry Cohn, 2024, needs more optimization.
8	515	0.661672337915	Henry Cohn, 2024, needs more optimization.
8	516	0.661681002402	Henry Cohn, 2024, needs more optimization.
8	517	0.662076944299	Henry Cohn, 2024, needs more optimization.
8	518	0.662295612713	Henry Cohn, 2024, needs more optimization.
8	519	0.662516854205	Henry Cohn, 2024, needs more optimization.
8	520	0.662590948857	Henry Cohn, 2024, needs more optimization.
8	521	0.662819267121	Henry Cohn, 2024, needs more optimization.
8	522	0.662823480048	Henry Cohn, 2024, needs more optimization.
8	523	0.663097264908	Henry Cohn, 2024, needs more optimization.
8	524	0.663105137621	Henry Cohn, 2024, needs more optimization.
8	525	0.663620350014	Henry Cohn, 2024, needs more optimization.
8	527	0.663654485585	Henry Cohn, 2024, needs more optimization.
8	528	0.663899602518	Henry Cohn, 2024, needs more optimization.
8	530	0.664110598247	Henry Cohn, 2024, needs more optimization.
8	531	0.664396350968	Henry Cohn, 2024, needs more optimization.
8	532	0.664845785883	Henry Cohn, 2024, needs more optimization.
8	534	0.665042712640	Henry Cohn, 2024, needs more optimization.
8	535	0.665188203709	Henry Cohn, 2024, needs more optimization.
8	536	0.665428556585	Henry Cohn, 2024, needs more optimization.
8	537	0.665759409131	Henry Cohn, 2024, needs more optimization.
8	538	0.665826070768	Henry Cohn, 2024, needs more optimization.
8	539	0.665962830029	Henry Cohn, 2024, needs more optimization.
8	540	0.666168697101	Henry Cohn, 2024, needs more optimization.
8	592	0.666666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 2$
8	595	0.675498380667	Henry Cohn, 2024, needs more optimization.
8	597	0.675810710310	Henry Cohn, 2024, needs more optimization.
8	598	0.676196262250	Henry Cohn, 2024, needs more optimization.
8	599	0.676484670605	Henry Cohn, 2024, needs more optimization.
8	600	0.676524754238	Henry Cohn, 2024, needs more optimization.
8	601	0.676577347595	Henry Cohn, 2024, needs more optimization.
8	602	0.676905847219	Henry Cohn, 2024, needs more optimization.
8	606	0.677235384527	Henry Cohn, 2024, needs more optimization.
8	607	0.677536105789	Henry Cohn, 2024, needs more optimization.
8	608	0.677840537270	Henry Cohn, 2024, needs more optimization.
8	610	0.678076222061	Henry Cohn, 2024, needs more optimization.
8	611	0.678264585796	Henry Cohn, 2024, needs more optimization.
8	613	0.678345949664	Henry Cohn, 2024, needs more optimization.
8	615	0.678838392958	Henry Cohn, 2024, needs more optimization.
8	616	0.679057676281	Henry Cohn, 2024, needs more optimization.
8	617	0.679265294606	Henry Cohn, 2024, needs more optimization.
8	618	0.679395324185	Henry Cohn, 2024, needs more optimization.
8	621	0.679506532027	Henry Cohn, 2024, needs more optimization.
8	622	0.679848151046	Henry Cohn, 2024, needs more optimization.
8	623	0.680082175175	Henry Cohn, 2024, needs more optimization.
8	625	0.680180058207	Henry Cohn, 2024, needs more optimization.
8	626	0.680370595289	Henry Cohn, 2024, needs more optimization.
8	627	0.680617599048	Henry Cohn, 2024, needs more optimization.
8	629	0.680779104082	Henry Cohn, 2024, needs more optimization.
8	630	0.680989561514	Henry Cohn, 2024, needs more optimization.
8	631	0.681359079223	Henry Cohn, 2024, needs more optimization.
8	632	0.681443307963	Henry Cohn, 2024, needs more optimization.
8	634	0.681539572040	Henry Cohn, 2024, needs more optimization.
8	635	0.681689548471	Henry Cohn, 2024, needs more optimization.
8	636	0.681957300787	Henry Cohn, 2024, needs more optimization.
8	638	0.682186142540	Henry Cohn, 2024, needs more optimization.
8	640	0.682252960387	Henry Cohn, 2024, needs more optimization.
8	642	0.682699436586	Henry Cohn, 2024, needs more optimization.
8	644	0.682987511844	Henry Cohn, 2024, needs more optimization.
8	646	0.683343588105	Henry Cohn, 2024, needs more optimization.
8	647	0.683592918825	Henry Cohn, 2024, needs more optimization.
8	648	0.683668902312	Henry Cohn, 2024, needs more optimization.
8	649	0.684122657628	Henry Cohn, 2024, needs more optimization.
8	650	0.684123776531	Henry Cohn, 2024, needs more optimization.
8	651	0.684230781991	Henry Cohn, 2024, needs more optimization.
8	652	0.684607590953	Henry Cohn, 2024, needs more optimization.
8	653	0.684614838815	Henry Cohn, 2024, needs more optimization.
8	654	0.684744643325	Henry Cohn, 2024, needs more optimization.
8	655	0.684768029063	Henry Cohn, 2024, needs more optimization.
8	657	0.685010819949	Henry Cohn, 2024, needs more optimization.
8	658	0.685066223726	Henry Cohn, 2024, needs more optimization.
8	660	0.685289468253	Henry Cohn, 2024, needs more optimization.
8	661	0.685485403370	Henry Cohn, 2024, needs more optimization.
8	662	0.685782461241	Henry Cohn, 2024, needs more optimization.
8	663	0.685816695445	Henry Cohn, 2024, needs more optimization.
8	665	0.685980754867	Henry Cohn, 2024, needs more optimization.
8	668	0.686406080965	Henry Cohn, 2024, needs more optimization.
8	669	0.686721022132	Henry Cohn, 2024, needs more optimization.
8	672	0.686742479256	Henry Cohn, 2024, needs more optimization.
8	673	0.687306107718	Henry Cohn, 2024, needs more optimization.
8	674	0.687386703264	Henry Cohn, 2024, needs more optimization.
8	676	0.687479849470	Henry Cohn, 2024, needs more optimization.
8	677	0.687762322951	Henry Cohn, 2024, needs more optimization.
8	678	0.687869048948	Henry Cohn, 2024, needs more optimization.
8	679	0.688009232816	Henry Cohn, 2024, needs more optimization.
8	681	0.688251500529	Henry Cohn, 2024, needs more optimization.
8	682	0.688380140917	Henry Cohn, 2024, needs more optimization.
8	684	0.688582976835	Henry Cohn, 2024, needs more optimization.
8	686	0.688685461787	Henry Cohn, 2024, needs more optimization.
8	687	0.689196574165	Henry Cohn, 2024, needs more optimization.
8	688	0.689323771753	Henry Cohn, 2024, needs more optimization.
8	690	0.689591562700	Henry Cohn, 2024, needs more optimization.
8	691	0.689600251253	Henry Cohn, 2024, needs more optimization.
8	693	0.689804699875	Henry Cohn, 2024, needs more optimization.
8	697	0.690104243892	Henry Cohn, 2024, needs more optimization.
8	698	0.690366596482	Henry Cohn, 2024, needs more optimization.
8	699	0.690689439707	Henry Cohn, 2024, needs more optimization.
8	700	0.690946967246	Henry Cohn, 2024, needs more optimization.
8	702	0.690954076138	Henry Cohn, 2024, needs more optimization.
8	704	0.691128712663	Henry Cohn, 2024, needs more optimization.
8	705	0.691522116096	Henry Cohn, 2024, needs more optimization.
8	706	0.691662208308	Henry Cohn, 2024, needs more optimization.
8	707	0.691772665232	Henry Cohn, 2024, needs more optimization.
8	708	0.691897818392	Henry Cohn, 2024, needs more optimization.
8	709	0.692097188730	Henry Cohn, 2024, needs more optimization.
8	711	0.692229320227	Henry Cohn, 2024, needs more optimization.
8	712	0.692344643066	Henry Cohn, 2024, needs more optimization.
8	713	0.692404929482	Henry Cohn, 2024, needs more optimization.
8	716	0.692843644999	Henry Cohn, 2024, needs more optimization.
8	717	0.693198157198	Henry Cohn, 2024, needs more optimization.
8	719	0.693287491254	Henry Cohn, 2024, needs more optimization.
8	720	0.693419338374	Henry Cohn, 2024, needs more optimization.
8	721	0.693673429990	Henry Cohn, 2024, needs more optimization.
8	722	0.693915901142	Henry Cohn, 2024, needs more optimization.
8	724	0.693955088252	Henry Cohn, 2024, needs more optimization.
8	726	0.693978284685	Henry Cohn, 2024, needs more optimization.
8	727	0.694332674478	Henry Cohn, 2024, needs more optimization.
8	728	0.694485706560	Henry Cohn, 2024, needs more optimization.
8	729	0.694544028736	Henry Cohn, 2024, needs more optimization.
8	732	0.694829339692	Henry Cohn, 2024, needs more optimization.
8	734	0.694929835698	Henry Cohn, 2024, needs more optimization.
8	735	0.695182554084	Henry Cohn, 2024, needs more optimization.
8	737	0.695567556342	Henry Cohn, 2024, needs more optimization.
8	738	0.695613055090	Henry Cohn, 2024, needs more optimization.
8	739	0.695774351034	Henry Cohn, 2024, needs more optimization.
8	740	0.695983841289	Henry Cohn, 2024, needs more optimization.
8	741	0.696137362917	Henry Cohn, 2024, needs more optimization.
8	743	0.696179001708	Henry Cohn, 2024, needs more optimization.
8	744	0.696417972427	Henry Cohn, 2024, needs more optimization.
8	745	0.696531149672	Henry Cohn, 2024, needs more optimization.
8	746	0.696824864286	Henry Cohn, 2024, needs more optimization.
8	748	0.696847922106	Henry Cohn, 2024, needs more optimization.
8	749	0.696999300117	Henry Cohn, 2024, needs more optimization.
8	752	0.697244357985	Henry Cohn, 2024, needs more optimization.
8	754	0.697622031782	Henry Cohn, 2024, needs more optimization.
8	755	0.697638896592	Henry Cohn, 2024, needs more optimization.
8	756	0.697890367930	Henry Cohn, 2024, needs more optimization.
8	759	0.698026611230	Henry Cohn, 2024, needs more optimization.
8	760	0.698161579155	Henry Cohn, 2024, needs more optimization.
8	761	0.698582852499	Henry Cohn, 2024, needs more optimization.
8	762	0.698743084620	Henry Cohn, 2024, needs more optimization.
8	764	0.698854258315	Henry Cohn, 2024, needs more optimization.
8	766	0.698914540508	Henry Cohn, 2024, needs more optimization.
8	768	0.699041203232	Henry Cohn, 2024, needs more optimization.
8	770	0.699213704487	Henry Cohn, 2024, needs more optimization.
8	773	0.699760157847	Henry Cohn, 2024, needs more optimization.
8	774	0.699892790834	Henry Cohn, 2024, needs more optimization.
8	775	0.700125205880	Henry Cohn, 2024, needs more optimization.
8	776	0.700231322126	Henry Cohn, 2024, needs more optimization.
8	777	0.700474482651	Henry Cohn, 2024, needs more optimization.
8	779	0.700541883086	Henry Cohn, 2024, needs more optimization.
8	782	0.700676780515	Henry Cohn, 2024, needs more optimization.
8	783	0.701092369576	Henry Cohn, 2024, needs more optimization.
8	784	0.701122141249	Henry Cohn, 2024, needs more optimization.
8	785	0.701182670622	Henry Cohn, 2024, needs more optimization.
8	786	0.701302609116	Henry Cohn, 2024, needs more optimization.
8	787	0.701414201548	Henry Cohn, 2024, needs more optimization.
8	788	0.701633286554	Henry Cohn, 2024, needs more optimization.
8	790	0.701693446647	Henry Cohn, 2024, needs more optimization.
8	794	0.701981884601	Henry Cohn, 2024, needs more optimization.
8	795	0.702436342477	Henry Cohn, 2024, needs more optimization.
8	796	0.702520503165	Henry Cohn, 2024, needs more optimization.
8	797	0.702729683468	Henry Cohn, 2024, needs more optimization.
8	798	0.702863386499	Henry Cohn, 2024, needs more optimization.
8	800	0.702867328037	Henry Cohn, 2024, needs more optimization.
8	801	0.702960665077	Henry Cohn, 2024, needs more optimization.
8	802	0.703014783053	Henry Cohn, 2024, needs more optimization.
8	803	0.703222213932	Henry Cohn, 2024, needs more optimization.
8	804	0.703280479958	Henry Cohn, 2024, needs more optimization.
8	805	0.703484482331	Henry Cohn, 2024, needs more optimization.
8	808	0.703648546764	Henry Cohn, 2024, needs more optimization.
8	810	0.703880328560	Henry Cohn, 2024, needs more optimization.
8	811	0.703914027805	Henry Cohn, 2024, needs more optimization.
8	813	0.704188859863	Henry Cohn, 2024, needs more optimization.
8	814	0.704421512898	Henry Cohn, 2024, needs more optimization.
8	815	0.704542839937	Henry Cohn, 2024, needs more optimization.
8	816	0.704676277564	Henry Cohn, 2024, needs more optimization.
8	818	0.704976471613	Henry Cohn, 2024, needs more optimization.
8	819	0.705115953869	Henry Cohn, 2024, needs more optimization.
8	821	0.705143543456	Henry Cohn, 2024, needs more optimization.
8	822	0.705163227426	Henry Cohn, 2024, needs more optimization.
8	823	0.705425387443	Henry Cohn, 2024, needs more optimization.
8	825	0.705478606384	Henry Cohn, 2024, needs more optimization.
8	827	0.705727615911	Henry Cohn, 2024, needs more optimization.
8	828	0.705745655315	Henry Cohn, 2024, needs more optimization.
8	830	0.705980317644	Henry Cohn, 2024, needs more optimization.
8	832	0.706102758424	Henry Cohn, 2024, needs more optimization.
8	833	0.706679716191	Henry Cohn, 2024, needs more optimization.
8	834	0.706693387195	Henry Cohn, 2024, needs more optimization.
8	837	0.706732340551	Henry Cohn, 2024, needs more optimization.
8	838	0.707024279558	Henry Cohn, 2024, needs more optimization.
8	839	0.707088176369	Henry Cohn, 2024, needs more optimization.
8	841	0.707094791620	Henry Cohn, 2024, needs more optimization.
8	843	0.707329359656	Henry Cohn, 2024, needs more optimization.
8	845	0.707524642138	Henry Cohn, 2024, needs more optimization.
8	848	0.707898195403	Henry Cohn, 2024, needs more optimization.
8	849	0.707993677101	Henry Cohn, 2024, needs more optimization.
8	851	0.708254238289	Henry Cohn, 2024, needs more optimization.
8	852	0.708298657545	Henry Cohn, 2024, needs more optimization.
8	853	0.708342994877	Henry Cohn, 2024, needs more optimization.
8	855	0.708528400227	Henry Cohn, 2024, needs more optimization.
8	856	0.708676511130	Henry Cohn, 2024, needs more optimization.
8	857	0.708763100635	Henry Cohn, 2024, needs more optimization.
8	858	0.709046698608	Henry Cohn, 2024, needs more optimization.
8	859	0.709107789912	Henry Cohn, 2024, needs more optimization.
8	860	0.709109705541	Henry Cohn, 2024, needs more optimization.
8	862	0.709202082110	Henry Cohn, 2024, needs more optimization.
8	863	0.709568989775	Henry Cohn, 2024, needs more optimization.
8	866	0.709645987696	Henry Cohn, 2024, needs more optimization.
8	868	0.709793536548	Henry Cohn, 2024, needs more optimization.
8	869	0.710164616573	Henry Cohn, 2024, needs more optimization.
8	873	0.710181415164	Henry Cohn, 2024, needs more optimization.
8	878	0.710670608535	Henry Cohn, 2024, needs more optimization.
8	879	0.710894072815	Henry Cohn, 2024, needs more optimization.
8	880	0.710971751108	Henry Cohn, 2024, needs more optimization.
8	881	0.711035091217	Henry Cohn, 2024, needs more optimization.
8	883	0.711265768983	Henry Cohn, 2024, needs more optimization.
8	885	0.711470245496	Henry Cohn, 2024, needs more optimization.
8	887	0.711579089927	Henry Cohn, 2024, needs more optimization.
8	888	0.711705514764	Henry Cohn, 2024, needs more optimization.
8	890	0.712005035187	Henry Cohn, 2024, needs more optimization.
8	892	0.712368646933	Henry Cohn, 2024, needs more optimization.
8	893	0.712483376841	Henry Cohn, 2024, needs more optimization.
8	894	0.712551692793	Henry Cohn, 2024, needs more optimization.
8	896	0.712602599804	Henry Cohn, 2024, needs more optimization.
8	897	0.712757100954	Henry Cohn, 2024, needs more optimization.
8	898	0.712855040004	Henry Cohn, 2024, needs more optimization.
8	900	0.712915572089	Henry Cohn, 2024, needs more optimization.
8	901	0.713032848309	Henry Cohn, 2024, needs more optimization.
8	903	0.713245940522	Henry Cohn, 2024, needs more optimization.
8	904	0.713314564922	Henry Cohn, 2024, needs more optimization.
8	906	0.713473718852	Henry Cohn, 2024, needs more optimization.
8	907	0.713700897865	Henry Cohn, 2024, needs more optimization.
8	909	0.713829458200	Henry Cohn, 2024, needs more optimization.
8	912	0.713859430184	Henry Cohn, 2024, needs more optimization.
8	913	0.714192730639	Henry Cohn, 2024, needs more optimization.
8	996	0.714269304535	Henry Cohn, 2024, needs more optimization.
8	1024	0.714285714286	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $7 x - 5$
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 listed in plain text data
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	0.149975121908	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9	28	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	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, 2023, needs more optimization.
9	36	0.2	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 1$
9	37	0.213783378445	Henry Cohn, 2024, needs more optimization.
9	38	0.217711380183	Henry Cohn, 2023, needs more optimization.
9	39	0.222837046412	Henry Cohn, 2023.
9	40	0.225704407232	Henry Cohn, 2023.
9	41	0.230353619603	Henry Cohn, 2023.
9	42	0.231125268456	Henry Cohn, 2023, needs more optimization.
9	43	0.231201190091	Henry Cohn, 2023.
9	44	0.233560116870	Henry Cohn, 2024.
9	47	0.238172399483	Henry Cohn, 2023. $335 x^{2} - 42 x - 9$
9	48	0.254741941811	Henry Cohn, 2023.
9	49	0.261827927697	Henry Cohn, 2023.
9	52	0.267191024627	Henry Cohn, 2023. $71 x^{2} - 4 x - 4$
9	53	0.269834758170	Henry Cohn, 2023. Minimal polynomial listed in plain text data
9	54	0.271688945915	Henry Cohn, 2023, needs more optimization.
9	55	0.281821472987	Henry Cohn, 2023, needs more optimization.
9	56	0.287378710663	Henry Cohn, 2023.
9	57	0.290508376520	Henry Cohn, 2023, needs more optimization.
9	58	0.294116447906	Henry Cohn, 2023, needs more optimization.
9	59	0.294328630820	Henry Cohn, 2023, needs more optimization.
9	60	0.297651969467	Henry Cohn, 2023.
9	61	0.297700422270	Henry Cohn, 2023.
9	62	0.299808194811	Henry Cohn, 2023, needs more optimization.
9	63	0.304556123336	Henry Cohn, 2023, needs more optimization.
9	64	0.306653313780	Henry Cohn, 2023.
9	65	0.310866635545	Henry Cohn, 2024, needs more optimization.
9	66	0.314231726732	Henry Cohn, 2024, needs more optimization.
9	67	0.320299009148	Henry Cohn, 2024, needs more optimization.
9	68	0.323366516425	Henry Cohn, 2024, needs more optimization.
9	69	0.327407821351	Henry Cohn, 2024, needs more optimization.
9	70	0.329018632832	Henry Cohn, 2023, needs more optimization.
9	71	0.329921685621	Henry Cohn, 2023, needs more optimization.
9	77	0.330113020449	Henry Cohn, 2023, needs more optimization.
9	79	0.330918632949	Henry Cohn, 2023, needs more optimization.
9	80	0.333109756286	Henry Cohn, 2023, needs more optimization.
9	96	0.333333333334	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. $3 x - 1$
9	97	0.371214682351	Henry Cohn, 2023, needs more optimization.
9	98	0.372095120083	Henry Cohn, 2023, needs more optimization.
9	100	0.378761465674	Henry Cohn, 2023, needs more optimization.
9	102	0.385636880073	Henry Cohn, 2024, needs more optimization.
9	103	0.390830032928	Henry Cohn, 2024, needs more optimization.
9	104	0.393551485031	Henry Cohn, 2023, needs more optimization.
9	105	0.395716616931	Henry Cohn, 2024, needs more optimization.
9	106	0.397079642430	Henry Cohn, 2024, needs more optimization.
9	107	0.398216738131	Henry Cohn, 2024, needs more optimization.
9	108	0.400552037396	Henry Cohn, 2024, needs more optimization.
9	109	0.403741325303	Henry Cohn, 2024, needs more optimization.
9	110	0.406532302427	Henry Cohn, 2024, needs more optimization.
9	111	0.409974308273	Henry Cohn, 2024, needs more optimization.
9	112	0.411759661871	Henry Cohn, 2024, needs more optimization.
9	113	0.413984309052	Henry Cohn, 2024, needs more optimization.
9	114	0.415397732794	Henry Cohn, 2024, needs more optimization.
9	115	0.417527894038	Henry Cohn, 2024, needs more optimization.
9	116	0.418911096012	Henry Cohn, 2023, needs more optimization.
9	117	0.421190744037	Henry Cohn, 2024, needs more optimization.
9	118	0.422844834571	Henry Cohn, 2023, needs more optimization.
9	119	0.424470642757	Henry Cohn, 2024, needs more optimization.
9	120	0.425593260421	Henry Cohn, 2023, needs more optimization.
9	121	0.427386167977	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, arXiv:2403.04330. $7 x - 3$
9	165	0.454545454546	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 5$
9	166	0.472195862354	Henry Cohn, 2024, needs more optimization.
9	167	0.473657198942	Henry Cohn, 2024, needs more optimization.
9	168	0.474746985749	Henry Cohn, 2024, needs more optimization.
9	169	0.475497755965	Henry Cohn, 2024, needs more optimization.
9	170	0.476236325351	Henry Cohn, 2024, needs more optimization.
9	171	0.477105202501	Henry Cohn, 2024, needs more optimization.
9	172	0.478086023503	Henry Cohn, 2024, needs more optimization.
9	173	0.478632980781	Henry Cohn, 2024, needs more optimization.
9	174	0.479905787659	Henry Cohn, 2024, needs more optimization.
9	175	0.480287367385	Henry Cohn, 2024, needs more optimization.
9	176	0.481175286341	Henry Cohn, 2024, needs more optimization.
9	177	0.481718144205	Henry Cohn, 2024, needs more optimization.
9	178	0.482619811355	Henry Cohn, 2024, needs more optimization.
9	179	0.483253416194	Henry Cohn, 2024, needs more optimization.
9	180	0.484433396999	Henry Cohn, 2024, needs more optimization.
9	181	0.485125025408	Henry Cohn, 2024, needs more optimization.
9	182	0.485771150867	Henry Cohn, 2024, needs more optimization.
9	183	0.486840018575	Henry Cohn, 2024, needs more optimization.
9	184	0.487357265694	Henry Cohn, 2024, needs more optimization.
9	185	0.488016561646	Henry Cohn, 2024, needs more optimization.
9	186	0.488769445204	Henry Cohn, 2024, needs more optimization.
9	187	0.489235797414	Henry Cohn, 2024, needs more optimization.
9	188	0.490465014311	Henry Cohn, 2024, needs more optimization.
9	189	0.491271176824	Henry Cohn, 2024, needs more optimization.
9	190	0.491717185588	Henry Cohn, 2024, needs more optimization.
9	191	0.492457306995	Henry Cohn, 2024, needs more optimization.
9	192	0.493257491390	Henry Cohn, 2024, needs more optimization.
9	193	0.493800763718	Henry Cohn, 2024, needs more optimization.
9	194	0.494573518575	Henry Cohn, 2024, needs more optimization.
9	195	0.495127968925	Henry Cohn, 2024, needs more optimization.
9	196	0.497060957217	Henry Cohn, 2024, needs more optimization.
9	197	0.497262220796	Henry Cohn, 2024, needs more optimization.
9	198	0.498081896687	Henry Cohn, 2024, needs more optimization.
9	200	0.498311538234	Henry Cohn, 2024, needs more optimization.
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. $2 x - 1$
9	307	0.517341896236	Henry Cohn, 2024, needs more optimization.
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	612	0.6	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $5 x - 3$
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	724	0.644179272583	Henry Cohn, 2024, needs more optimization.
9	725	0.644212458445	Henry Cohn, 2024, needs more optimization.
9	726	0.644249367090	Henry Cohn, 2024, needs more optimization.
9	727	0.644542794331	Henry Cohn, 2024, needs more optimization.
9	730	0.644695139658	Henry Cohn, 2024, needs more optimization.
9	731	0.644854938092	Henry Cohn, 2024, needs more optimization.
9	732	0.644966583730	Henry Cohn, 2024, needs more optimization.
9	734	0.645119660256	Henry Cohn, 2024, needs more optimization.
9	737	0.645453329339	Henry Cohn, 2024, needs more optimization.
9	739	0.645867269960	Henry Cohn, 2024, needs more optimization.
9	740	0.645985941381	Henry Cohn, 2024, needs more optimization.
9	741	0.646191900119	Henry Cohn, 2024, needs more optimization.
9	743	0.646357130982	Henry Cohn, 2024, needs more optimization.
9	744	0.646485978527	Henry Cohn, 2024, needs more optimization.
9	745	0.646734337068	Henry Cohn, 2024, needs more optimization.
9	747	0.647031615771	Henry Cohn, 2024, needs more optimization.
9	748	0.647091288441	Henry Cohn, 2024, needs more optimization.
9	749	0.647144041905	Henry Cohn, 2024, needs more optimization.
9	750	0.647283339314	Henry Cohn, 2024, needs more optimization.
9	751	0.647426851530	Henry Cohn, 2024, needs more optimization.
9	753	0.647827960271	Henry Cohn, 2024, needs more optimization.
9	754	0.647929874640	Henry Cohn, 2024, needs more optimization.
9	755	0.648012305821	Henry Cohn, 2024, needs more optimization.
9	756	0.648064707396	Henry Cohn, 2024, needs more optimization.
9	757	0.648241440802	Henry Cohn, 2024, needs more optimization.
9	758	0.648273181630	Henry Cohn, 2024, needs more optimization.
9	761	0.648376413271	Henry Cohn, 2024, needs more optimization.
9	763	0.649017420143	Henry Cohn, 2024, needs more optimization.
9	764	0.649082931965	Henry Cohn, 2024, needs more optimization.
9	766	0.649169093609	Henry Cohn, 2024, needs more optimization.
9	768	0.649306283622	Henry Cohn, 2024, needs more optimization.
9	769	0.649692705914	Henry Cohn, 2024, needs more optimization.
9	771	0.649810705995	Henry Cohn, 2024, needs more optimization.
9	772	0.650133691770	Henry Cohn, 2024, needs more optimization.
9	774	0.650167309814	Henry Cohn, 2024, needs more optimization.
9	775	0.650275985769	Henry Cohn, 2024, needs more optimization.
9	776	0.650411712326	Henry Cohn, 2024, needs more optimization.
9	778	0.650606981905	Henry Cohn, 2024, needs more optimization.
9	781	0.650957869498	Henry Cohn, 2024, needs more optimization.
9	783	0.651202853867	Henry Cohn, 2024, needs more optimization.
9	787	0.651486297799	Henry Cohn, 2024, needs more optimization.
9	791	0.651890794327	Henry Cohn, 2024, needs more optimization.
9	792	0.652094300866	Henry Cohn, 2024, needs more optimization.
9	793	0.652274236266	Henry Cohn, 2024, needs more optimization.
9	794	0.652514536378	Henry Cohn, 2024, needs more optimization.
9	795	0.652723462340	Henry Cohn, 2024, needs more optimization.
9	797	0.652813597859	Henry Cohn, 2024, needs more optimization.
9	798	0.653107067481	Henry Cohn, 2024, needs more optimization.
9	801	0.653172264394	Henry Cohn, 2024, needs more optimization.
9	803	0.653439807670	Henry Cohn, 2024, needs more optimization.
9	806	0.653720152322	Henry Cohn, 2024, needs more optimization.
9	807	0.653728337065	Henry Cohn, 2024, needs more optimization.
9	808	0.653910967965	Henry Cohn, 2024, needs more optimization.
9	809	0.654125667081	Henry Cohn, 2024, needs more optimization.
9	810	0.654362995301	Henry Cohn, 2024, needs more optimization.
9	812	0.654623274981	Henry Cohn, 2024, needs more optimization.
9	813	0.654729844039	Henry Cohn, 2024, needs more optimization.
9	814	0.654779734980	Henry Cohn, 2024, needs more optimization.
9	815	0.654815272716	Henry Cohn, 2024, needs more optimization.
9	818	0.655063808020	Henry Cohn, 2024, needs more optimization.
9	820	0.655251045755	Henry Cohn, 2024, needs more optimization.
9	821	0.655640515881	Henry Cohn, 2024, needs more optimization.
9	823	0.655889777840	Henry Cohn, 2024, needs more optimization.
9	824	0.655937633968	Henry Cohn, 2024, needs more optimization.
9	825	0.656124390794	Henry Cohn, 2024, needs more optimization.
9	826	0.656147363900	Henry Cohn, 2024, needs more optimization.
9	828	0.656309541762	Henry Cohn, 2024, needs more optimization.
9	830	0.656441164225	Henry Cohn, 2024, needs more optimization.
9	832	0.656633197669	Henry Cohn, 2024, needs more optimization.
9	833	0.656835790396	Henry Cohn, 2024, needs more optimization.
9	835	0.656996805600	Henry Cohn, 2024, needs more optimization.
9	836	0.657092271473	Henry Cohn, 2024, needs more optimization.
9	837	0.657338127927	Henry Cohn, 2024, needs more optimization.
9	839	0.657425064436	Henry Cohn, 2024, needs more optimization.
9	840	0.657630612915	Henry Cohn, 2024, needs more optimization.
9	842	0.657832396156	Henry Cohn, 2024, needs more optimization.
9	843	0.658001773430	Henry Cohn, 2024, needs more optimization.
9	844	0.658189238333	Henry Cohn, 2024, needs more optimization.
9	846	0.658233669581	Henry Cohn, 2024, needs more optimization.
9	848	0.658383758638	Henry Cohn, 2024, needs more optimization.
9	850	0.658462811548	Henry Cohn, 2024, needs more optimization.
9	852	0.658766697216	Henry Cohn, 2024, needs more optimization.
9	853	0.659090703858	Henry Cohn, 2024, needs more optimization.
9	854	0.659367170535	Henry Cohn, 2024, needs more optimization.
9	856	0.659375912475	Henry Cohn, 2024, needs more optimization.
9	858	0.659484013418	Henry Cohn, 2024, needs more optimization.
9	860	0.659727020220	Henry Cohn, 2024, needs more optimization.
9	861	0.659910043343	Henry Cohn, 2024, needs more optimization.
9	863	0.659924015022	Henry Cohn, 2024, needs more optimization.
9	864	0.660166123542	Henry Cohn, 2024, needs more optimization.
9	865	0.660241024158	Henry Cohn, 2024, needs more optimization.
9	867	0.660382785925	Henry Cohn, 2024, needs more optimization.
9	868	0.660473163175	Henry Cohn, 2024, needs more optimization.
9	871	0.660696779866	Henry Cohn, 2024, needs more optimization.
9	872	0.661007842716	Henry Cohn, 2024, needs more optimization.
9	874	0.661089042491	Henry Cohn, 2024, needs more optimization.
9	875	0.661305050811	Henry Cohn, 2024, needs more optimization.
9	876	0.661485790243	Henry Cohn, 2024, needs more optimization.
9	879	0.661597030428	Henry Cohn, 2024, needs more optimization.
9	880	0.661887233858	Henry Cohn, 2024, needs more optimization.
9	882	0.661904445425	Henry Cohn, 2024, needs more optimization.
9	884	0.662187483976	Henry Cohn, 2024, needs more optimization.
9	885	0.662383614647	Henry Cohn, 2024, needs more optimization.
9	887	0.662407495138	Henry Cohn, 2024, needs more optimization.
9	888	0.662622602605	Henry Cohn, 2024, needs more optimization.
9	889	0.662770732589	Henry Cohn, 2024, needs more optimization.
9	891	0.662879436196	Henry Cohn, 2024, needs more optimization.
9	892	0.662881008458	Henry Cohn, 2024, needs more optimization.
9	893	0.663030819107	Henry Cohn, 2024, needs more optimization.
9	894	0.663143394893	Henry Cohn, 2024, needs more optimization.
9	896	0.663144355264	Henry Cohn, 2024, needs more optimization.
9	897	0.663489084069	Henry Cohn, 2024, needs more optimization.
9	898	0.663603157882	Henry Cohn, 2024, needs more optimization.
9	899	0.663822075305	Henry Cohn, 2024, needs more optimization.
9	901	0.663869274003	Henry Cohn, 2024, needs more optimization.
9	902	0.664020935179	Henry Cohn, 2024, needs more optimization.
9	904	0.664188946159	Henry Cohn, 2024, needs more optimization.
9	905	0.664225582925	Henry Cohn, 2024, needs more optimization.
9	907	0.664419510748	Henry Cohn, 2024, needs more optimization.
9	908	0.664721859975	Henry Cohn, 2024, needs more optimization.
9	910	0.664815633074	Henry Cohn, 2024, needs more optimization.
9	911	0.664869570667	Henry Cohn, 2024, needs more optimization.
9	914	0.664910283908	Henry Cohn, 2024, needs more optimization.
9	915	0.665374249396	Henry Cohn, 2024, needs more optimization.
9	916	0.665386063861	Henry Cohn, 2024, needs more optimization.
9	917	0.665535838506	Henry Cohn, 2024, needs more optimization.
9	922	0.665635047740	Henry Cohn, 2024, needs more optimization.
9	923	0.665997191391	Henry Cohn, 2024, needs more optimization.
9	924	0.666122996139	Henry Cohn, 2024, needs more optimization.
9	925	0.666307532176	Henry Cohn, 2024, needs more optimization.
9	927	0.666336436562	Henry Cohn, 2024, needs more optimization.
9	931	0.666565908284	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, 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	0.086857326541	H. Cohn, Small spherical and projective codes, data set, 2022, 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	0.130634295944	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial listed in plain text data
10	30	0.138439560893	H. Cohn, Small spherical and projective codes, data set, updated 2023, 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 listed in plain text data
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	0.150154626306	Henry Cohn, 2024, needs more optimization.
10	34	0.150194121283	Henry Cohn, 2024, needs more optimization.
10	35	0.157418897528	Henry Cohn, 2024, needs more optimization.
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	0.196239848492	Henry Cohn, 2024, needs more optimization.
10	43	0.205907349245	Henry Cohn, 2023.
10	44	0.210560489799	Henry Cohn, 2023.
10	45	0.210852889344	Henry Cohn, 2023, needs more optimization.
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	0.223348296065	Henry Cohn, 2023.
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	0.253642861547	Henry Cohn, 2023.
10	59	0.253695768487	Henry Cohn, 2023, needs more optimization.
10	60	0.256704396577	Henry Cohn, 2023.
10	61	0.260972170006	Henry Cohn, 2024, needs more optimization.
10	66	0.266666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $15 x - 4$
10	72	0.275987133320	Henry Cohn, 2024.
10	73	0.279856896354	Henry Cohn, 2024, needs more optimization.
10	74	0.279859243767	Henry Cohn, 2023, needs more optimization.
10	75	0.285402755367	Henry Cohn, 2024, needs more optimization.
10	77	0.288336175448	Henry Cohn, 2024, needs more optimization.
10	78	0.298140175134	Henry Cohn, 2024, needs more optimization.
10	80	0.307240914168	Henry Cohn, 2024, needs more optimization.
10	81	0.316243720476	Henry Cohn, 2024, needs more optimization.
10	82	0.319460740622	Henry Cohn, 2024, needs more optimization.
10	83	0.322982294251	Henry Cohn, 2024, needs more optimization.
10	84	0.323691974972	Henry Cohn, 2024, needs more optimization.
10	88	0.325104342618	Henry Cohn, 2023, needs more optimization.
10	89	0.325816989936	Henry Cohn, 2024, needs more optimization.
10	90	0.326817895739	Henry Cohn, 2024, needs more optimization.
10	91	0.329016915942	Henry Cohn, 2024, needs more optimization.
10	92	0.329046876953	Henry Cohn, 2024, needs more optimization.
10	93	0.329552669891	Henry Cohn, 2024, needs more optimization.
10	95	0.329855189192	Henry Cohn, 2023, needs more optimization.
10	96	0.330516800207	Henry Cohn, 2023, needs more optimization.
10	97	0.330990146889	Henry Cohn, 2024, needs more optimization.
10	98	0.331076198649	Henry Cohn, 2024, needs more optimization.
10	99	0.331203339480	Henry Cohn, 2023, needs more optimization.
10	100	0.331255831064	Henry Cohn, 2023, needs more optimization.
10	101	0.331771958564	Henry Cohn, 2023, needs more optimization.
10	102	0.331786638364	Henry Cohn, 2023, needs more optimization.
10	104	0.333263143208	Henry Cohn, 2023, needs more optimization.
10	105	0.333276771176	Henry Cohn, 2023, needs more optimization.
10	107	0.333327625778	Henry Cohn, 2023, needs more optimization.
10	108	0.333329834036	Henry Cohn, 2023, needs more optimization.
10	109	0.335318650634	Henry Cohn, 2024, needs more optimization.
10	110	0.340620761632	Henry Cohn, 2023, needs more optimization.
10	111	0.342369261176	Henry Cohn, 2024, needs more optimization.
10	112	0.347037575649	Henry Cohn, 2023, needs more optimization.
10	113	0.348684613501	Henry Cohn, 2024, needs more optimization.
10	114	0.350518187162	Henry Cohn, 2024, needs more optimization.
10	115	0.352629567807	Henry Cohn, 2023, needs more optimization.
10	116	0.354276388556	Henry Cohn, 2023, needs more optimization.
10	117	0.361921116926	Henry Cohn, 2023, needs more optimization.
10	118	0.362516515684	Henry Cohn, 2023, needs more optimization.
10	119	0.366359521775	Henry Cohn, 2023, needs more optimization.
10	120	0.366489099663	Henry Cohn, 2023, needs more optimization.
10	121	0.367503616250	Henry Cohn, 2023, needs more optimization.
10	122	0.367643854488	Henry Cohn, 2023, needs more optimization.
10	128	0.368206341619	Henry Cohn, 2024, needs more optimization.
10	130	0.371651719461	Henry Cohn, 2024, needs more optimization.
10	132	0.372272319936	Henry Cohn, 2024, needs more optimization.
10	133	0.388929900475	Henry Cohn, 2024, needs more optimization.
10	134	0.390551958515	Henry Cohn, 2024, needs more optimization.
10	136	0.393903053006	Henry Cohn, 2024, needs more optimization.
10	137	0.397228376296	Henry Cohn, 2024, needs more optimization.
10	138	0.398867227085	Henry Cohn, 2024, needs more optimization.
10	139	0.400975278368	Henry Cohn, 2024, needs more optimization.
10	140	0.401957047501	Henry Cohn, 2024, needs more optimization.
10	141	0.403164423710	Henry Cohn, 2024, needs more optimization.
10	142	0.404804248933	Henry Cohn, 2024, needs more optimization.
10	156	0.405827419558	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x^{2} - 2 x - 1$
10	157	0.421786177148	Henry Cohn, 2024, needs more optimization.
10	158	0.422120176183	Henry Cohn, 2024, needs more optimization.
10	159	0.423638895631	Henry Cohn, 2024, needs more optimization.
10	160	0.424121835638	Henry Cohn, 2024, needs more optimization.
10	161	0.425583706171	Henry Cohn, 2024, needs more optimization.
10	162	0.425893154698	Henry Cohn, 2024, needs more optimization.
10	163	0.426082965893	Henry Cohn, 2024, needs more optimization.
10	164	0.427249190766	Henry Cohn, 2024, needs more optimization.
10	165	0.428193812153	Henry Cohn, 2024, needs more optimization.
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	196	0.451065176210	Henry Cohn, 2024, needs more optimization.
10	197	0.453343037913	Henry Cohn, 2024, needs more optimization.
10	198	0.453847329851	Henry Cohn, 2024, needs more optimization.
10	199	0.454782150001	Henry Cohn, 2024, needs more optimization.
10	200	0.455457543462	Henry Cohn, 2024, needs more optimization.
10	201	0.456132602612	Henry Cohn, 2024, needs more optimization.
10	202	0.456612439167	Henry Cohn, 2024, needs more optimization.
10	203	0.457186435441	Henry Cohn, 2024, needs more optimization.
10	204	0.458103712287	Henry Cohn, 2024, needs more optimization.
10	205	0.458699979474	Henry Cohn, 2024, needs more optimization.
10	206	0.459110298718	Henry Cohn, 2024, needs more optimization.
10	207	0.459807858367	Henry Cohn, 2024, needs more optimization.
10	208	0.460455080076	Henry Cohn, 2024, needs more optimization.
10	209	0.461088694075	Henry Cohn, 2024, needs more optimization.
10	210	0.461908979543	Henry Cohn, 2024, needs more optimization.
10	211	0.462156364202	Henry Cohn, 2024, needs more optimization.
10	212	0.463050410861	Henry Cohn, 2024, needs more optimization.
10	213	0.463834386470	Henry Cohn, 2024, needs more optimization.
10	214	0.464563532001	Henry Cohn, 2024, needs more optimization.
10	215	0.464817293629	Henry Cohn, 2024, needs more optimization.
10	216	0.465839971105	Henry Cohn, 2024, needs more optimization.
10	217	0.466321417269	Henry Cohn, 2024, needs more optimization.
10	218	0.466652379663	Henry Cohn, 2024, needs more optimization.
10	219	0.467251601258	Henry Cohn, 2024, needs more optimization.
10	220	0.467847584478	Henry Cohn, 2024, needs more optimization.
10	221	0.468517831486	Henry Cohn, 2024, needs more optimization.
10	222	0.469204116037	Henry Cohn, 2024, needs more optimization.
10	223	0.469665578577	Henry Cohn, 2024, needs more optimization.
10	224	0.470131562598	Henry Cohn, 2024, needs more optimization.
10	225	0.470920820047	Henry Cohn, 2024, needs more optimization.
10	226	0.471799876211	Henry Cohn, 2024, needs more optimization.
10	227	0.472160440215	Henry Cohn, 2024, needs more optimization.
10	228	0.472632518342	Henry Cohn, 2024, needs more optimization.
10	229	0.473190697588	Henry Cohn, 2024, needs more optimization.
10	230	0.473751339745	Henry Cohn, 2024, needs more optimization.
10	231	0.474161399902	Henry Cohn, 2024, needs more optimization.
10	232	0.475076644021	Henry Cohn, 2024, needs more optimization.
10	233	0.475516346926	Henry Cohn, 2024, needs more optimization.
10	234	0.475838563007	Henry Cohn, 2024, needs more optimization.
10	235	0.476509099639	Henry Cohn, 2024, needs more optimization.
10	236	0.476761264100	Henry Cohn, 2024, needs more optimization.
10	237	0.477693685225	Henry Cohn, 2024, needs more optimization.
10	238	0.478229813400	Henry Cohn, 2024, needs more optimization.
10	239	0.478549102190	Henry Cohn, 2024, needs more optimization.
10	240	0.478969110129	Henry Cohn, 2024, needs more optimization.
10	241	0.479634668090	Henry Cohn, 2024, needs more optimization.
10	242	0.480119379745	Henry Cohn, 2024, needs more optimization.
10	243	0.480477411508	Henry Cohn, 2024, needs more optimization.
10	244	0.481323918563	Henry Cohn, 2024, needs more optimization.
10	245	0.481574042016	Henry Cohn, 2024, needs more optimization.
10	246	0.481966087648	Henry Cohn, 2024, needs more optimization.
10	247	0.482672520306	Henry Cohn, 2024, needs more optimization.
10	248	0.483144745362	Henry Cohn, 2024, needs more optimization.
10	249	0.483736558233	Henry Cohn, 2024, needs more optimization.
10	250	0.484150516913	Henry Cohn, 2024, needs more optimization.
10	251	0.484558802701	Henry Cohn, 2024, needs more optimization.
10	252	0.485342959854	Henry Cohn, 2024, needs more optimization.
10	253	0.485642897140	Henry Cohn, 2024, needs more optimization.
10	254	0.486283472919	Henry Cohn, 2024, needs more optimization.
10	255	0.486542838105	Henry Cohn, 2024, needs more optimization.
10	256	0.486834341924	Henry Cohn, 2024, needs more optimization.
10	257	0.488418556277	Henry Cohn, 2024, needs more optimization.
10	258	0.488916567371	Henry Cohn, 2024, needs more optimization.
10	259	0.489262212604	Henry Cohn, 2024, needs more optimization.
10	260	0.489545050931	Henry Cohn, 2024, needs more optimization.
10	261	0.490010303948	Henry Cohn, 2024, needs more optimization.
10	263	0.490547385241	Henry Cohn, 2024, needs more optimization.
10	265	0.491632611620	Henry Cohn, 2024, needs more optimization.
10	266	0.492303932750	Henry Cohn, 2024, needs more optimization.
10	267	0.492459650786	Henry Cohn, 2024, needs more optimization.
10	268	0.492999933689	Henry Cohn, 2024, needs more optimization.
10	269	0.493581466905	Henry Cohn, 2024, needs more optimization.
10	270	0.494067984353	Henry Cohn, 2024, needs more optimization.
10	271	0.494285752984	Henry Cohn, 2024, needs more optimization.
10	272	0.494728526835	Henry Cohn, 2024, needs more optimization.
10	273	0.495639259362	Henry Cohn, 2024, needs more optimization.
10	274	0.495703928087	Henry Cohn, 2024, needs more optimization.
10	276	0.496293844595	Henry Cohn, 2024, needs more optimization.
10	277	0.497306270003	Henry Cohn, 2024, needs more optimization.
10	278	0.497402425687	Henry Cohn, 2024, needs more optimization.
10	279	0.498285566476	Henry Cohn, 2024, needs more optimization.
10	280	0.498313276042	Henry Cohn, 2024, needs more optimization.
10	281	0.498594079316	Henry Cohn, 2024, needs more optimization.
10	283	0.499428814053	Henry Cohn, 2024, needs more optimization.
10	510	0.5	M. Ganzhinov, Highly symmetric lines, preprint, 2022, arXiv:2207.08266. $2 x - 1$
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	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	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	0.077296880695	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661. Minimal polynomial listed in plain text data
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	0.108571944195	H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
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	39	0.142857142858	Henry Cohn, 2023. $7 x - 1$
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, 2023, needs more optimization.
11	44	0.164387348702	Henry Cohn, 2023.
11	45	0.167764862361	Henry Cohn, 2023.
11	46	0.173024920814	Henry Cohn, 2023.
11	47	0.193277477549	Henry Cohn, 2023.
11	48	0.198581200103	Henry Cohn, 2023, needs more optimization.
11	49	0.202537656414	Henry Cohn, 2024, needs more optimization.
11	51	0.204957387535	Henry Cohn, 2023. Minimal polynomial listed in plain text data
11	52	0.208220167705	Henry Cohn, 2023, needs more optimization.
11	53	0.209837940547	Henry Cohn, 2023, needs more optimization.
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	62	0.238334838338	Henry Cohn, 2024, needs more optimization.
11	63	0.239536005912	Henry Cohn, 2024, needs more optimization.
11	64	0.246037771298	Henry Cohn, 2024, needs more optimization.
11	65	0.249186205889	Henry Cohn, 2024, needs more optimization.
11	66	0.251954710476	Henry Cohn, 2024, needs more optimization.
11	67	0.254866280297	Henry Cohn, 2024, needs more optimization.
11	68	0.257382753783	Henry Cohn, 2024, needs more optimization.
11	69	0.259999205701	Henry Cohn, 2024, needs more optimization.
11	70	0.262581295575	Henry Cohn, 2024, needs more optimization.
11	71	0.264394227069	Henry Cohn, 2024, needs more optimization.
11	88	0.267191024627	Henry Cohn, 2023. $71 x^{2} - 4 x - 4$
11	92	0.296535165409	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $8 x^{2} + x - 1$
11	94	0.298848806260	Henry Cohn, 2023, needs more optimization.
11	95	0.308634061371	Henry Cohn, 2024, needs more optimization.
11	96	0.311430784592	Henry Cohn, 2024, needs more optimization.
11	97	0.313303937249	Henry Cohn, 2024, needs more optimization.
11	98	0.314782431804	Henry Cohn, 2024, needs more optimization.
11	99	0.316926566238	Henry Cohn, 2024, needs more optimization.
11	100	0.318422272166	Henry Cohn, 2024, needs more optimization.
11	101	0.319894149498	Henry Cohn, 2024, needs more optimization.
11	102	0.320919893448	Henry Cohn, 2024, needs more optimization.
11	103	0.322037121017	Henry Cohn, 2024, needs more optimization.
11	104	0.323093185610	Henry Cohn, 2024, needs more optimization.
11	105	0.323367705576	Henry Cohn, 2024, needs more optimization.
11	106	0.324111693584	Henry Cohn, 2024, needs more optimization.
11	107	0.325108181912	Henry Cohn, 2024, needs more optimization.
11	109	0.326088702676	Henry Cohn, 2024, needs more optimization.
11	111	0.327513996750	Henry Cohn, 2023, needs more optimization.
11	112	0.327752515271	Henry Cohn, 2023, needs more optimization.
11	113	0.329803040552	Henry Cohn, 2023, needs more optimization.
11	114	0.330031659816	Henry Cohn, 2023, needs more optimization.
11	115	0.330406388060	Henry Cohn, 2024, needs more optimization.
11	118	0.330883912607	Henry Cohn, 2023, needs more optimization.
11	119	0.331116854340	Henry Cohn, 2023, needs more optimization.
11	120	0.331150136199	Henry Cohn, 2023, needs more optimization.
11	121	0.331853848381	Henry Cohn, 2023, needs more optimization.
11	122	0.331861095984	Henry Cohn, 2023, needs more optimization.
11	123	0.332954236962	Henry Cohn, 2023, needs more optimization.
11	124	0.332964924971	Henry Cohn, 2023, needs more optimization.
11	125	0.333212924685	Henry Cohn, 2023, needs more optimization.
11	126	0.333227865413	Henry Cohn, 2023, needs more optimization.
11	127	0.333270861920	Henry Cohn, 2024, needs more optimization.
11	128	0.333273747639	Henry Cohn, 2024, needs more optimization.
11	129	0.333274996083	Henry Cohn, 2024, needs more optimization.
11	130	0.333276029314	Henry Cohn, 2024, needs more optimization.
11	150	0.333333333334	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. $3 x - 1$
11	151	0.367698002159	Henry Cohn, 2024, needs more optimization.
11	152	0.368415563653	Henry Cohn, 2024, needs more optimization.
11	153	0.370107055341	Henry Cohn, 2024, needs more optimization.
11	154	0.370208976197	Henry Cohn, 2024, needs more optimization.
11	156	0.370549724720	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, arXiv:2403.04330. $8 x - 3$
11	167	0.387954541819	Henry Cohn, 2024, needs more optimization.
11	168	0.389391527379	Henry Cohn, 2024, needs more optimization.
11	169	0.390170475796	Henry Cohn, 2024, needs more optimization.
11	170	0.391490429618	Henry Cohn, 2024, needs more optimization.
11	171	0.392850460696	Henry Cohn, 2024, needs more optimization.
11	172	0.393657569226	Henry Cohn, 2024, needs more optimization.
11	173	0.395033954695	Henry Cohn, 2024, needs more optimization.
11	174	0.395869456955	Henry Cohn, 2024, needs more optimization.
11	175	0.396736838203	Henry Cohn, 2024, needs more optimization.
11	176	0.398352796192	Henry Cohn, 2024, needs more optimization.
11	177	0.399060629924	Henry Cohn, 2024, needs more optimization.
11	178	0.400114944611	Henry Cohn, 2024, needs more optimization.
11	179	0.401212948825	Henry Cohn, 2024, needs more optimization.
11	180	0.402008054713	Henry Cohn, 2024, needs more optimization.
11	181	0.402840226809	Henry Cohn, 2024, needs more optimization.
11	182	0.404028845859	Henry Cohn, 2024, needs more optimization.
11	183	0.404487593290	Henry Cohn, 2024, needs more optimization.
11	184	0.405668684622	Henry Cohn, 2024, needs more optimization.
11	185	0.406634952271	Henry Cohn, 2024, needs more optimization.
11	186	0.407358366607	Henry Cohn, 2024, needs more optimization.
11	187	0.407944918047	Henry Cohn, 2024, needs more optimization.
11	188	0.409296595777	Henry Cohn, 2024, needs more optimization.
11	189	0.410191685023	Henry Cohn, 2024, needs more optimization.
11	190	0.410306850585	Henry Cohn, 2024, needs more optimization.
11	192	0.411485699691	Henry Cohn, 2024, needs more optimization.
11	193	0.413378748639	Henry Cohn, 2024, needs more optimization.
11	195	0.413896438364	Henry Cohn, 2024, needs more optimization.
11	197	0.415324616108	Henry Cohn, 2024, needs more optimization.
11	198	0.416354538896	Henry Cohn, 2024, needs more optimization.
11	199	0.417326320806	Henry Cohn, 2024, needs more optimization.
11	200	0.418263694693	Henry Cohn, 2024, needs more optimization.
11	201	0.418681913506	Henry Cohn, 2024, needs more optimization.
11	202	0.418878054921	Henry Cohn, 2024, needs more optimization.
11	203	0.419837663507	Henry Cohn, 2024, needs more optimization.
11	204	0.420357592190	Henry Cohn, 2024, needs more optimization.
11	205	0.421039166147	Henry Cohn, 2024, needs more optimization.
11	206	0.421927426130	Henry Cohn, 2024, needs more optimization.
11	207	0.422267989692	Henry Cohn, 2024, needs more optimization.
11	208	0.422991069138	Henry Cohn, 2024, needs more optimization.
11	209	0.423603161901	Henry Cohn, 2024, needs more optimization.
11	210	0.424230096890	Henry Cohn, 2024, needs more optimization.
11	211	0.424502284272	Henry Cohn, 2024, needs more optimization.
11	212	0.425256410379	Henry Cohn, 2024, needs more optimization.
11	213	0.425927883152	Henry Cohn, 2024, needs more optimization.
11	214	0.426497729953	Henry Cohn, 2024, needs more optimization.
11	215	0.426993046561	Henry Cohn, 2024, needs more optimization.
11	216	0.427946928447	Henry Cohn, 2024, needs more optimization.
11	217	0.428064317464	Henry Cohn, 2024, needs more optimization.
11	224	0.428571428572	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $7 x - 3$
11	225	0.432940867273	Henry Cohn, 2024, needs more optimization.
11	226	0.433190232594	Henry Cohn, 2024, needs more optimization.
11	227	0.433859701409	Henry Cohn, 2024, needs more optimization.
11	228	0.434680277837	Henry Cohn, 2024, needs more optimization.
11	229	0.434851999871	Henry Cohn, 2024, needs more optimization.
11	230	0.435665072539	Henry Cohn, 2024, needs more optimization.
11	231	0.436417432126	Henry Cohn, 2024, needs more optimization.
11	232	0.436712434095	Henry Cohn, 2024, needs more optimization.
11	233	0.437432692210	Henry Cohn, 2024, needs more optimization.
11	234	0.437964973156	Henry Cohn, 2024, needs more optimization.
11	235	0.438119446578	Henry Cohn, 2024, needs more optimization.
11	236	0.438981008629	Henry Cohn, 2024, needs more optimization.
11	237	0.439435035851	Henry Cohn, 2024, needs more optimization.
11	238	0.439748187375	Henry Cohn, 2024, needs more optimization.
11	239	0.440010753003	Henry Cohn, 2024, needs more optimization.
11	240	0.440743834790	Henry Cohn, 2024, needs more optimization.
11	241	0.441687883593	Henry Cohn, 2024, needs more optimization.
11	242	0.442089678135	Henry Cohn, 2024, needs more optimization.
11	243	0.442588626915	Henry Cohn, 2024, needs more optimization.
11	244	0.442919239800	Henry Cohn, 2024, needs more optimization.
11	245	0.443754542483	Henry Cohn, 2024, needs more optimization.
11	246	0.444334810743	Henry Cohn, 2024, needs more optimization.
11	247	0.444752050211	Henry Cohn, 2024, needs more optimization.
11	248	0.445217636654	Henry Cohn, 2024, needs more optimization.
11	249	0.445619004777	Henry Cohn, 2024, needs more optimization.
11	250	0.446178628838	Henry Cohn, 2024, needs more optimization.
11	251	0.446311480044	Henry Cohn, 2024, needs more optimization.
11	252	0.447497088895	Henry Cohn, 2024, needs more optimization.
11	253	0.447729800756	Henry Cohn, 2024, needs more optimization.
11	254	0.447988346809	Henry Cohn, 2024, needs more optimization.
11	255	0.448688900161	Henry Cohn, 2024, needs more optimization.
11	256	0.448904365202	Henry Cohn, 2024, needs more optimization.
11	258	0.450476838680	Henry Cohn, 2024, needs more optimization.
11	259	0.450936305667	Henry Cohn, 2024, needs more optimization.
11	261	0.451661716055	Henry Cohn, 2024, needs more optimization.
11	263	0.452133925068	Henry Cohn, 2024, needs more optimization.
11	264	0.453356589419	Henry Cohn, 2024, needs more optimization.
11	266	0.453749946828	Henry Cohn, 2024, needs more optimization.
11	293	0.454545454546	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 5$
11	295	0.466608079217	Henry Cohn, 2024, needs more optimization.
11	296	0.466877720002	Henry Cohn, 2024, needs more optimization.
11	297	0.467234703160	Henry Cohn, 2024, needs more optimization.
11	298	0.467902801896	Henry Cohn, 2024, needs more optimization.
11	299	0.468330655732	Henry Cohn, 2024, needs more optimization.
11	300	0.468741394856	Henry Cohn, 2024, needs more optimization.
11	301	0.469529619157	Henry Cohn, 2024, needs more optimization.
11	302	0.469560447294	Henry Cohn, 2024, needs more optimization.
11	303	0.469922685620	Henry Cohn, 2024, needs more optimization.
11	305	0.470617019492	Henry Cohn, 2024, needs more optimization.
11	306	0.471064303525	Henry Cohn, 2024, needs more optimization.
11	307	0.471292800064	Henry Cohn, 2024, needs more optimization.
11	308	0.471550751368	Henry Cohn, 2024, needs more optimization.
11	309	0.471935907073	Henry Cohn, 2024, needs more optimization.
11	310	0.472124415972	Henry Cohn, 2024, needs more optimization.
11	311	0.472821639564	Henry Cohn, 2024, needs more optimization.
11	312	0.473443973679	Henry Cohn, 2024, needs more optimization.
11	313	0.473582104923	Henry Cohn, 2024, needs more optimization.
11	314	0.473695960739	Henry Cohn, 2024, needs more optimization.
11	315	0.474265087738	Henry Cohn, 2024, needs more optimization.
11	316	0.474585879154	Henry Cohn, 2024, needs more optimization.
11	317	0.474714845839	Henry Cohn, 2024, needs more optimization.
11	318	0.475652305707	Henry Cohn, 2024, needs more optimization.
11	319	0.475714840486	Henry Cohn, 2024, needs more optimization.
11	320	0.475759312614	Henry Cohn, 2024, needs more optimization.
11	321	0.476584682442	Henry Cohn, 2024, needs more optimization.
11	322	0.476664855522	Henry Cohn, 2024, needs more optimization.
11	323	0.477421945978	Henry Cohn, 2024, needs more optimization.
11	324	0.477742838383	Henry Cohn, 2024, needs more optimization.
11	325	0.478283257592	Henry Cohn, 2024, needs more optimization.
11	327	0.478442841090	Henry Cohn, 2024, needs more optimization.
11	329	0.479035042709	Henry Cohn, 2024, needs more optimization.
11	331	0.479788239041	Henry Cohn, 2024, needs more optimization.
11	332	0.480294101282	Henry Cohn, 2024, needs more optimization.
11	333	0.480700637374	Henry Cohn, 2024, needs more optimization.
11	334	0.481675191637	Henry Cohn, 2024, needs more optimization.
11	335	0.481996055280	Henry Cohn, 2024, needs more optimization.
11	336	0.482092036064	Henry Cohn, 2024, needs more optimization.
11	339	0.482336976927	Henry Cohn, 2024, needs more optimization.
11	340	0.483146683753	Henry Cohn, 2024, needs more optimization.
11	341	0.483497327631	Henry Cohn, 2024, needs more optimization.
11	343	0.484005467007	Henry Cohn, 2024, needs more optimization.
11	345	0.484429935956	Henry Cohn, 2024, needs more optimization.
11	347	0.485077176155	Henry Cohn, 2024, needs more optimization.
11	348	0.485456240606	Henry Cohn, 2024, needs more optimization.
11	349	0.486356357888	Henry Cohn, 2024, needs more optimization.
11	350	0.486388380010	Henry Cohn, 2024, needs more optimization.
11	352	0.486673860686	Henry Cohn, 2024, needs more optimization.
11	353	0.487550800955	Henry Cohn, 2024, needs more optimization.
11	355	0.487908218101	Henry Cohn, 2024, needs more optimization.
11	356	0.488592070815	Henry Cohn, 2024, needs more optimization.
11	357	0.488620095747	Henry Cohn, 2024, needs more optimization.
11	359	0.489129367474	Henry Cohn, 2024, needs more optimization.
11	360	0.489157371350	Henry Cohn, 2024, needs more optimization.
11	361	0.490070957063	Henry Cohn, 2024, needs more optimization.
11	362	0.490332158670	Henry Cohn, 2024, needs more optimization.
11	364	0.490558217258	Henry Cohn, 2024, needs more optimization.
11	365	0.491145514845	Henry Cohn, 2024, needs more optimization.
11	367	0.491862392470	Henry Cohn, 2024, needs more optimization.
11	369	0.492269094349	Henry Cohn, 2024, needs more optimization.
11	370	0.492520899573	Henry Cohn, 2024, needs more optimization.
11	371	0.492826927101	Henry Cohn, 2024, needs more optimization.
11	372	0.493137157287	Henry Cohn, 2024, needs more optimization.
11	373	0.493838307322	Henry Cohn, 2024, needs more optimization.
11	376	0.494177334613	Henry Cohn, 2024, needs more optimization.
11	377	0.494560974317	Henry Cohn, 2024, needs more optimization.
11	378	0.494836548858	Henry Cohn, 2024, needs more optimization.
11	379	0.495496900589	Henry Cohn, 2024, needs more optimization.
11	380	0.495800917252	Henry Cohn, 2024, needs more optimization.
11	381	0.495830007550	Henry Cohn, 2024, needs more optimization.
11	382	0.495846036218	Henry Cohn, 2024, needs more optimization.
11	384	0.496455231277	Henry Cohn, 2024, needs more optimization.
11	387	0.497355937207	Henry Cohn, 2024, needs more optimization.
11	389	0.497509189194	Henry Cohn, 2024, needs more optimization.
11	391	0.498855264847	Henry Cohn, 2024, needs more optimization.
11	393	0.499373920979	Henry Cohn, 2024, needs more optimization.
11	394	0.499420673608	Henry Cohn, 2024, needs more optimization.
11	396	0.499949742670	Henry Cohn, 2024, needs more optimization.
11	592	0.5	M. Ganzhinov, Highly symmetric lines, preprint, 2022, arXiv:2207.08266. $2 x - 1$
11	593	0.542166805849	Henry Cohn, 2024, needs more optimization.
11	595	0.542636788628	Henry Cohn, 2024, needs more optimization.
11	596	0.542880232473	Henry Cohn, 2024, needs more optimization.
11	597	0.542965137370	Henry Cohn, 2024, needs more optimization.
11	598	0.543089938752	Henry Cohn, 2024, needs more optimization.
11	599	0.543196722572	Henry Cohn, 2024, needs more optimization.
11	600	0.543536297706	Henry Cohn, 2024, needs more optimization.
11	604	0.544082398293	Henry Cohn, 2024, needs more optimization.
11	606	0.544581411516	Henry Cohn, 2024, needs more optimization.
11	607	0.544852782801	Henry Cohn, 2024, needs more optimization.
11	610	0.545050020798	Henry Cohn, 2024, needs more optimization.
11	612	0.545479985058	Henry Cohn, 2024, needs more optimization.
11	614	0.545809363828	Henry Cohn, 2024, needs more optimization.
11	617	0.546166884274	Henry Cohn, 2024, needs more optimization.
11	618	0.546588496875	Henry Cohn, 2024, needs more optimization.
11	619	0.546664063283	Henry Cohn, 2024, needs more optimization.
11	620	0.546806604898	Henry Cohn, 2024, needs more optimization.
11	621	0.547107713150	Henry Cohn, 2024, needs more optimization.
11	625	0.547143874126	Henry Cohn, 2024, needs more optimization.
11	626	0.547597493108	Henry Cohn, 2024, needs more optimization.
11	628	0.547836317787	Henry Cohn, 2024, needs more optimization.
11	631	0.548569445989	Henry Cohn, 2024, needs more optimization.
11	633	0.548597434778	Henry Cohn, 2024, needs more optimization.
11	636	0.549126999037	Henry Cohn, 2024, needs more optimization.
11	639	0.549619645465	Henry Cohn, 2024, needs more optimization.
11	640	0.549731596793	Henry Cohn, 2024, needs more optimization.
11	641	0.550139962982	Henry Cohn, 2024, needs more optimization.
11	643	0.550215282830	Henry Cohn, 2024, needs more optimization.
11	644	0.550732300938	Henry Cohn, 2024, needs more optimization.
11	646	0.550747990637	Henry Cohn, 2024, needs more optimization.
11	647	0.551088089130	Henry Cohn, 2024, needs more optimization.
11	651	0.551407870920	Henry Cohn, 2024, needs more optimization.
11	652	0.551674877670	Henry Cohn, 2024, needs more optimization.
11	653	0.551886885566	Henry Cohn, 2024, needs more optimization.
11	654	0.552054870309	Henry Cohn, 2024, needs more optimization.
11	656	0.552301337830	Henry Cohn, 2024, needs more optimization.
11	658	0.552518542193	Henry Cohn, 2024, needs more optimization.
11	660	0.552935937988	Henry Cohn, 2024, needs more optimization.
11	662	0.553191190730	Henry Cohn, 2024, needs more optimization.
11	664	0.553475800421	Henry Cohn, 2024, needs more optimization.
11	665	0.553824515724	Henry Cohn, 2024, needs more optimization.
11	666	0.554031927552	Henry Cohn, 2024, needs more optimization.
11	667	0.554065744337	Henry Cohn, 2024, needs more optimization.
11	669	0.554265784694	Henry Cohn, 2024, needs more optimization.
11	670	0.554347638064	Henry Cohn, 2024, needs more optimization.
11	671	0.554513994180	Henry Cohn, 2024, needs more optimization.
11	672	0.554742555812	Henry Cohn, 2024, needs more optimization.
11	673	0.555006293329	Henry Cohn, 2024, needs more optimization.
11	675	0.555115562931	Henry Cohn, 2024, needs more optimization.
11	676	0.555375880758	Henry Cohn, 2024, needs more optimization.
11	677	0.555462637644	Henry Cohn, 2024, needs more optimization.
11	679	0.555521427561	Henry Cohn, 2024, needs more optimization.
11	982	0.555555555556	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 5$
11	984	0.590123877427	Henry Cohn, 2024, needs more optimization.
11	987	0.590187435878	Henry Cohn, 2024, needs more optimization.
11	988	0.590614015574	Henry Cohn, 2024, needs more optimization.
11	992	0.590818885180	Henry Cohn, 2024, needs more optimization.
11	994	0.590972623258	Henry Cohn, 2024, needs more optimization.
11	997	0.591232020965	Henry Cohn, 2024, needs more optimization.
11	999	0.591493727317	Henry Cohn, 2024, needs more optimization.
11	1000	0.591677828212	Henry Cohn, 2024, needs more optimization.
11	1001	0.591790839816	Henry Cohn, 2024, needs more optimization.
11	1005	0.592017801301	Henry Cohn, 2024, needs more optimization.
11	1007	0.592169408952	Henry Cohn, 2024, needs more optimization.
11	1009	0.592308571380	Henry Cohn, 2024, needs more optimization.
11	1010	0.592642341029	Henry Cohn, 2024, needs more optimization.
11	1013	0.592940378626	Henry Cohn, 2024, needs more optimization.
11	1014	0.592953982077	Henry Cohn, 2024, needs more optimization.
11	1016	0.593011586794	Henry Cohn, 2024, needs more optimization.
11	1018	0.593073484314	Henry Cohn, 2024, needs more optimization.
11	1019	0.593268293797	Henry Cohn, 2024, needs more optimization.
11	1021	0.593528325981	Henry Cohn, 2024, needs more optimization.
11	1023	0.593579862187	Henry Cohn, 2024, needs more optimization.
11	1024	0.593657884661	Henry Cohn, 2024, needs more optimization.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $14 x - 1$
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	0.119914148449	Henry Cohn, 2023.
12	36	0.121737723964	Henry Cohn, 2023, needs more optimization.
12	37	0.121971459128	Henry Cohn, 2023. $359 x^{2} + 30 x - 9$
12	38	0.130788914737	Henry Cohn, 2023. $63002864 x^{4} + 17841888 x^{3} - 1199448 x^{2} - 239112 x - 6561$
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.
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, 2023, needs more optimization.
12	46	0.150221894103	Henry Cohn, 2023, needs more optimization.
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	0.180095499631	Henry Cohn, 2023.
12	53	0.187411675260	Henry Cohn, 2023, needs more optimization.
12	54	0.189749455904	Henry Cohn, 2024, needs more optimization.
12	55	0.193781308327	Henry Cohn, 2024, needs more optimization.
12	56	0.201391028643	Henry Cohn, 2024, needs more optimization.
12	57	0.202003502638	Henry Cohn, 2024, needs more optimization.
12	58	0.204406167593	Henry Cohn, 2024, needs more optimization.
12	59	0.205178221918	Henry Cohn, 2024, needs more optimization.
12	60	0.207676097674	Henry Cohn, 2024, needs more optimization.
12	61	0.211406503811	Henry Cohn, 2024, needs more optimization.
12	63	0.214216749906	Henry Cohn, 2024, needs more optimization.
12	64	0.219220818853	Henry Cohn, 2024, needs more optimization.
12	65	0.221466479472	Henry Cohn, 2024, needs more optimization.
12	66	0.223515942635	Henry Cohn, 2024, needs more optimization.
12	67	0.226140593215	Henry Cohn, 2024, needs more optimization.
12	68	0.228089002614	Henry Cohn, 2024, needs more optimization.
12	69	0.230608063853	Henry Cohn, 2024, needs more optimization.
12	70	0.233442872593	Henry Cohn, 2024, needs more optimization.
12	71	0.235845198196	Henry Cohn, 2024, needs more optimization.
12	72	0.238006330597	Henry Cohn, 2024, needs more optimization.
12	73	0.240866904684	Henry Cohn, 2024, needs more optimization.
12	74	0.242798361760	Henry Cohn, 2024, needs more optimization.
12	75	0.245891679629	Henry Cohn, 2024, needs more optimization.
12	76	0.247643438077	Henry Cohn, 2024, needs more optimization.
12	78	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. $4 x - 1$
12	79	0.253645713815	Henry Cohn, 2024, needs more optimization.
12	80	0.254149331489	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. $96 x^{3} + 33 x^{2} - 50 x + 9$
12	81	0.258107681427	Henry Cohn, 2024, needs more optimization.
12	82	0.259351314878	Henry Cohn, 2024, needs more optimization.
12	83	0.261226378829	Henry Cohn, 2024, needs more optimization.
12	84	0.263223605137	Henry Cohn, 2024, needs more optimization.
12	85	0.265050744978	Henry Cohn, 2024, needs more optimization.
12	86	0.266330913284	Henry Cohn, 2024, needs more optimization.
12	87	0.267085685590	Henry Cohn, 2024, needs more optimization.
12	88	0.267145967434	Henry Cohn, 2023, needs more optimization.
12	95	0.267190848624	Henry Cohn, 2023, needs more optimization.
12	96	0.272727272728	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $11 x - 3$
12	97	0.282670131669	Henry Cohn, 2024, needs more optimization.
12	98	0.283506518179	Henry Cohn, 2024, needs more optimization.
12	99	0.284900489273	Henry Cohn, 2024, needs more optimization.
12	100	0.286213185392	Henry Cohn, 2024, needs more optimization.
12	101	0.287420746198	Henry Cohn, 2024, needs more optimization.
12	102	0.289229781201	Henry Cohn, 2024, needs more optimization.
12	103	0.290425178995	Henry Cohn, 2024, needs more optimization.
12	104	0.291679828197	Henry Cohn, 2024, needs more optimization.
12	105	0.293118138196	Henry Cohn, 2024, needs more optimization.
12	106	0.295397531389	Henry Cohn, 2024, needs more optimization.
12	107	0.296856845079	Henry Cohn, 2024, needs more optimization.
12	108	0.297753546117	Henry Cohn, 2024, needs more optimization.
12	109	0.299341803086	Henry Cohn, 2024, needs more optimization.
12	110	0.301543655035	Henry Cohn, 2024, needs more optimization.
12	111	0.302746929192	Henry Cohn, 2024, needs more optimization.
12	112	0.304209400673	Henry Cohn, 2024, needs more optimization.
12	113	0.306330087884	Henry Cohn, 2024, needs more optimization.
12	114	0.307262831341	Henry Cohn, 2024, needs more optimization.
12	115	0.309123178923	Henry Cohn, 2024, needs more optimization.
12	116	0.310010373474	Henry Cohn, 2024, needs more optimization.
12	117	0.311046380507	Henry Cohn, 2024, needs more optimization.
12	118	0.312603711294	Henry Cohn, 2024, needs more optimization.
12	119	0.313831156765	Henry Cohn, 2024, needs more optimization.
12	120	0.314945670877	Henry Cohn, 2024, needs more optimization.
12	121	0.316350650601	Henry Cohn, 2024, needs more optimization.
12	122	0.317244464584	Henry Cohn, 2024, needs more optimization.
12	123	0.318230249485	Henry Cohn, 2024, needs more optimization.
12	124	0.319006331671	Henry Cohn, 2024, needs more optimization.
12	125	0.319203499874	Henry Cohn, 2024, needs more optimization.
12	126	0.319540071975	Henry Cohn, 2024, needs more optimization.
12	128	0.321897014963	Henry Cohn, 2024, needs more optimization.
12	129	0.322215091435	Henry Cohn, 2024, needs more optimization.
12	130	0.323167983388	Henry Cohn, 2023, needs more optimization.
12	131	0.323807670453	Henry Cohn, 2024, needs more optimization.
12	132	0.323837665230	Henry Cohn, 2024, needs more optimization.
12	134	0.325266129278	Henry Cohn, 2024, needs more optimization.
12	136	0.325662703593	Henry Cohn, 2024, needs more optimization.
12	138	0.326445516369	Henry Cohn, 2024, needs more optimization.
12	142	0.327356972064	Henry Cohn, 2024, needs more optimization.
12	144	0.330234201645	Henry Cohn, 2024, needs more optimization.
12	146	0.330572430433	Henry Cohn, 2024, needs more optimization.
12	148	0.330906347293	Henry Cohn, 2024, needs more optimization.
12	150	0.332832983276	Henry Cohn, 2024, needs more optimization.
12	168	0.333330721215	Henry Cohn, 2024, needs more optimization.
12	169	0.350299733477	Henry Cohn, 2024, needs more optimization.
12	170	0.350708162762	Henry Cohn, 2024, needs more optimization.
12	171	0.351893627839	Henry Cohn, 2024, needs more optimization.
12	172	0.352074102099	Henry Cohn, 2024, needs more optimization.
12	173	0.353496936378	Henry Cohn, 2024, needs more optimization.
12	174	0.353968793093	Henry Cohn, 2024, needs more optimization.
12	176	0.355113812809	Henry Cohn, 2024, needs more optimization.
12	177	0.357329338267	Henry Cohn, 2024, needs more optimization.
12	178	0.357427812261	Henry Cohn, 2024, needs more optimization.
12	179	0.358393335972	Henry Cohn, 2024, needs more optimization.
12	180	0.359212120924	Henry Cohn, 2024, needs more optimization.
12	182	0.360485176813	Henry Cohn, 2024, needs more optimization.
12	183	0.362489681855	Henry Cohn, 2024, needs more optimization.
12	184	0.363101281633	Henry Cohn, 2024, needs more optimization.
12	186	0.364676550537	Henry Cohn, 2024, needs more optimization.
12	187	0.366231387876	Henry Cohn, 2024, needs more optimization.
12	188	0.367440902339	Henry Cohn, 2024, needs more optimization.
12	189	0.368850434550	Henry Cohn, 2024, needs more optimization.
12	190	0.370125489408	Henry Cohn, 2024, needs more optimization.
12	191	0.370846431497	Henry Cohn, 2024, needs more optimization.
12	192	0.373615418047	Henry Cohn, 2024, needs more optimization.
12	195	0.374732044928	Henry Cohn, 2024, needs more optimization.
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	0.391125107378	Henry Cohn, 2024, needs more optimization.
12	212	0.391989189456	Henry Cohn, 2024, needs more optimization.
12	213	0.392380591728	Henry Cohn, 2024, needs more optimization.
12	214	0.393180943440	Henry Cohn, 2024, needs more optimization.
12	215	0.394173522127	Henry Cohn, 2024, needs more optimization.
12	216	0.394680251593	Henry Cohn, 2024, needs more optimization.
12	217	0.395496989843	Henry Cohn, 2024, needs more optimization.
12	218	0.396116275182	Henry Cohn, 2024, needs more optimization.
12	219	0.396890867296	Henry Cohn, 2024, needs more optimization.
12	220	0.397342893115	Henry Cohn, 2024, needs more optimization.
12	221	0.397879791702	Henry Cohn, 2024, needs more optimization.
12	222	0.398445595559	Henry Cohn, 2024, needs more optimization.
12	223	0.399113634835	Henry Cohn, 2024, needs more optimization.
12	224	0.399535286445	Henry Cohn, 2024, needs more optimization.
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	289	0.430967632965	Henry Cohn, 2024, needs more optimization.
12	290	0.431749857746	Henry Cohn, 2024, needs more optimization.
12	291	0.432111407792	Henry Cohn, 2024, needs more optimization.
12	292	0.432548474709	Henry Cohn, 2024, needs more optimization.
12	293	0.432590672374	Henry Cohn, 2024, needs more optimization.
12	294	0.432772369006	Henry Cohn, 2024, needs more optimization.
12	295	0.433130415918	Henry Cohn, 2024, needs more optimization.
12	296	0.433849478079	Henry Cohn, 2024, needs more optimization.
12	297	0.434553273664	Henry Cohn, 2024, needs more optimization.
12	298	0.434850037301	Henry Cohn, 2024, needs more optimization.
12	300	0.435277394193	Henry Cohn, 2024, needs more optimization.
12	302	0.435739667238	Henry Cohn, 2024, needs more optimization.
12	303	0.436661679991	Henry Cohn, 2024, needs more optimization.
12	304	0.436962715749	Henry Cohn, 2024, needs more optimization.
12	305	0.437173454198	Henry Cohn, 2024, needs more optimization.
12	306	0.437581602736	Henry Cohn, 2024, needs more optimization.
12	307	0.438388192877	Henry Cohn, 2024, needs more optimization.
12	309	0.438664002933	Henry Cohn, 2024, needs more optimization.
12	310	0.438987558575	Henry Cohn, 2024, needs more optimization.
12	311	0.439841622038	Henry Cohn, 2024, needs more optimization.
12	312	0.440226735636	Henry Cohn, 2024, needs more optimization.
12	313	0.440515039072	Henry Cohn, 2024, needs more optimization.
12	316	0.441160873604	Henry Cohn, 2024, needs more optimization.
12	317	0.441522002689	Henry Cohn, 2024, needs more optimization.
12	318	0.442034498452	Henry Cohn, 2024, needs more optimization.
12	320	0.442335638652	Henry Cohn, 2024, needs more optimization.
12	321	0.442961402803	Henry Cohn, 2024, needs more optimization.
12	322	0.443864859925	Henry Cohn, 2024, needs more optimization.
12	324	0.444086353366	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, arXiv:2403.04330. $9 x - 4$
12	409	0.470332798528	Henry Cohn, 2024, needs more optimization.
12	410	0.470697677708	Henry Cohn, 2024, needs more optimization.
12	412	0.470886977502	Henry Cohn, 2024, needs more optimization.
12	413	0.471109171996	Henry Cohn, 2024, needs more optimization.
12	416	0.471887046336	Henry Cohn, 2024, needs more optimization.
12	417	0.472626537165	Henry Cohn, 2024, needs more optimization.
12	418	0.472946043146	Henry Cohn, 2024, needs more optimization.
12	419	0.473021372741	Henry Cohn, 2024, needs more optimization.
12	420	0.473138813931	Henry Cohn, 2024, needs more optimization.
12	421	0.473193576067	Henry Cohn, 2024, needs more optimization.
12	423	0.473713916057	Henry Cohn, 2024, needs more optimization.
12	424	0.474111889418	Henry Cohn, 2024, needs more optimization.
12	426	0.474502485853	Henry Cohn, 2024, needs more optimization.
12	427	0.474744764366	Henry Cohn, 2024, needs more optimization.
12	428	0.475093494992	Henry Cohn, 2024, needs more optimization.
12	430	0.475657455820	Henry Cohn, 2024, needs more optimization.
12	431	0.475709143660	Henry Cohn, 2024, needs more optimization.
12	432	0.476056806733	Henry Cohn, 2024, needs more optimization.
12	433	0.476404662948	Henry Cohn, 2024, needs more optimization.
12	434	0.476734306387	Henry Cohn, 2024, needs more optimization.
12	435	0.476947994754	Henry Cohn, 2024, needs more optimization.
12	436	0.477408296657	Henry Cohn, 2024, needs more optimization.
12	437	0.477533262170	Henry Cohn, 2024, needs more optimization.
12	438	0.477616527655	Henry Cohn, 2024, needs more optimization.
12	440	0.478325738194	Henry Cohn, 2024, needs more optimization.
12	441	0.478394199834	Henry Cohn, 2024, needs more optimization.
12	443	0.478614280458	Henry Cohn, 2024, needs more optimization.
12	444	0.479246750994	Henry Cohn, 2024, needs more optimization.
12	446	0.479450115806	Henry Cohn, 2024, needs more optimization.
12	448	0.479581777973	Henry Cohn, 2024, needs more optimization.
12	449	0.480447931315	Henry Cohn, 2024, needs more optimization.
12	452	0.480839465272	Henry Cohn, 2024, needs more optimization.
12	455	0.481336804101	Henry Cohn, 2024, needs more optimization.
12	456	0.482275315453	Henry Cohn, 2024, needs more optimization.
12	458	0.482370631717	Henry Cohn, 2024, needs more optimization.
12	459	0.482748044312	Henry Cohn, 2024, needs more optimization.
12	460	0.482963163484	Henry Cohn, 2024, needs more optimization.
12	463	0.483224943998	Henry Cohn, 2024, needs more optimization.
12	464	0.483873521943	Henry Cohn, 2024, needs more optimization.
12	465	0.483992897316	Henry Cohn, 2024, needs more optimization.
12	467	0.484447304638	Henry Cohn, 2024, needs more optimization.
12	468	0.484610171554	Henry Cohn, 2024, needs more optimization.
12	469	0.484883777859	Henry Cohn, 2024, needs more optimization.
12	470	0.485066227305	Henry Cohn, 2024, needs more optimization.
12	472	0.485382649785	Henry Cohn, 2024, needs more optimization.
12	473	0.485486305212	Henry Cohn, 2024, needs more optimization.
12	475	0.485915432152	Henry Cohn, 2024, needs more optimization.
12	477	0.486274758483	Henry Cohn, 2024, needs more optimization.
12	478	0.487043609175	Henry Cohn, 2024, needs more optimization.
12	480	0.487224345381	Henry Cohn, 2024, needs more optimization.
12	481	0.487273119890	Henry Cohn, 2024, needs more optimization.
12	482	0.487803552952	Henry Cohn, 2024, needs more optimization.
12	483	0.488093134003	Henry Cohn, 2024, needs more optimization.
12	485	0.488107911292	Henry Cohn, 2024, needs more optimization.
12	486	0.488596193740	Henry Cohn, 2024, needs more optimization.
12	487	0.488634501612	Henry Cohn, 2024, needs more optimization.
12	488	0.488704644890	Henry Cohn, 2024, needs more optimization.
12	489	0.489361454703	Henry Cohn, 2024, needs more optimization.
12	490	0.489450913037	Henry Cohn, 2024, needs more optimization.
12	492	0.489518308411	Henry Cohn, 2024, needs more optimization.
12	494	0.489733128551	Henry Cohn, 2024, needs more optimization.
12	496	0.490722033580	Henry Cohn, 2024, needs more optimization.
12	499	0.491191926719	Henry Cohn, 2024, needs more optimization.
12	500	0.491526626815	Henry Cohn, 2024, needs more optimization.
12	501	0.491609069289	Henry Cohn, 2024, needs more optimization.
12	502	0.492056859739	Henry Cohn, 2024, needs more optimization.
12	503	0.492111536300	Henry Cohn, 2024, needs more optimization.
12	505	0.492148706743	Henry Cohn, 2024, needs more optimization.
12	507	0.492889094151	Henry Cohn, 2024, needs more optimization.
12	509	0.493044407420	Henry Cohn, 2024, needs more optimization.
12	512	0.493527633116	Henry Cohn, 2024, needs more optimization.
12	513	0.493829300943	Henry Cohn, 2024, needs more optimization.
12	514	0.494324478680	Henry Cohn, 2024, needs more optimization.
12	516	0.494563332060	Henry Cohn, 2024, needs more optimization.
12	518	0.495025211259	Henry Cohn, 2024, needs more optimization.
12	519	0.495496612867	Henry Cohn, 2024, needs more optimization.
12	520	0.495638053610	Henry Cohn, 2024, needs more optimization.
12	521	0.495903042871	Henry Cohn, 2024, needs more optimization.
12	522	0.495906890279	Henry Cohn, 2024, needs more optimization.
12	523	0.496189073128	Henry Cohn, 2024, needs more optimization.
12	527	0.496473567601	Henry Cohn, 2024, needs more optimization.
12	528	0.497301734335	Henry Cohn, 2024, needs more optimization.
12	530	0.497415087994	Henry Cohn, 2024, needs more optimization.
12	531	0.497605363726	Henry Cohn, 2024, needs more optimization.
12	532	0.497976426069	Henry Cohn, 2024, needs more optimization.
12	533	0.498030070615	Henry Cohn, 2024, needs more optimization.
12	534	0.498093443417	Henry Cohn, 2024, needs more optimization.
12	535	0.498264594161	Henry Cohn, 2024, needs more optimization.
12	536	0.498635066605	Henry Cohn, 2024, needs more optimization.
12	538	0.498709656277	Henry Cohn, 2024, needs more optimization.
12	539	0.499005958419	Henry Cohn, 2024, needs more optimization.
12	540	0.499184169956	Henry Cohn, 2024, needs more optimization.
12	541	0.499351474139	Henry Cohn, 2024, needs more optimization.
12	542	0.499479630529	Henry Cohn, 2024, needs more optimization.
12	756	0.499999999946	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, needs more optimization.
12	840	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, 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. $2 x - 1$
12	841	0.542293388496	Henry Cohn, 2024, needs more optimization.
12	842	0.542409079728	Henry Cohn, 2024, needs more optimization.
12	843	0.542646064974	Henry Cohn, 2024, needs more optimization.
12	845	0.542750138365	Henry Cohn, 2024, needs more optimization.
12	847	0.542950805710	Henry Cohn, 2024, needs more optimization.
12	850	0.543044768814	Henry Cohn, 2024, needs more optimization.
12	853	0.543361858883	Henry Cohn, 2024, needs more optimization.
12	854	0.543581316065	Henry Cohn, 2024, needs more optimization.
12	856	0.543774630376	Henry Cohn, 2024, needs more optimization.
12	859	0.544106068443	Henry Cohn, 2024, needs more optimization.
12	861	0.544609888874	Henry Cohn, 2024, needs more optimization.
12	863	0.544826276596	Henry Cohn, 2024, needs more optimization.
12	865	0.544827027625	Henry Cohn, 2024, needs more optimization.
12	870	0.545056255118	Henry Cohn, 2024, needs more optimization.
12	871	0.545304277618	Henry Cohn, 2024, needs more optimization.
12	872	0.545678277534	Henry Cohn, 2024, needs more optimization.
12	874	0.545789444019	Henry Cohn, 2024, needs more optimization.
12	877	0.546055933264	Henry Cohn, 2024, needs more optimization.
12	878	0.546302551624	Henry Cohn, 2024, needs more optimization.
12	879	0.546385316552	Henry Cohn, 2024, needs more optimization.
12	883	0.546681952237	Henry Cohn, 2024, needs more optimization.
12	884	0.546858150696	Henry Cohn, 2024, needs more optimization.
12	885	0.546989217963	Henry Cohn, 2024, needs more optimization.
12	887	0.547092786098	Henry Cohn, 2024, needs more optimization.
12	889	0.547158576851	Henry Cohn, 2024, needs more optimization.
12	891	0.547636244755	Henry Cohn, 2024, needs more optimization.
12	892	0.547648908375	Henry Cohn, 2024, needs more optimization.
12	893	0.547715113467	Henry Cohn, 2024, needs more optimization.
12	894	0.547943895596	Henry Cohn, 2024, needs more optimization.
12	896	0.547965819808	Henry Cohn, 2024, needs more optimization.
12	900	0.548469163199	Henry Cohn, 2024, needs more optimization.
12	902	0.548521588728	Henry Cohn, 2024, needs more optimization.
12	904	0.548699008412	Henry Cohn, 2024, needs more optimization.
12	907	0.549026255238	Henry Cohn, 2024, needs more optimization.
12	909	0.549284044819	Henry Cohn, 2024, needs more optimization.
12	912	0.549452689108	Henry Cohn, 2024, needs more optimization.
12	915	0.549822424241	Henry Cohn, 2024, needs more optimization.
12	917	0.550088218942	Henry Cohn, 2024, needs more optimization.
12	918	0.550172692884	Henry Cohn, 2024, needs more optimization.
12	919	0.550314520626	Henry Cohn, 2024, needs more optimization.
12	920	0.550335705427	Henry Cohn, 2024, needs more optimization.
12	921	0.550661529916	Henry Cohn, 2024, needs more optimization.
12	925	0.550818889096	Henry Cohn, 2024, needs more optimization.
12	927	0.551084681936	Henry Cohn, 2024, needs more optimization.
12	928	0.551213071913	Henry Cohn, 2024, needs more optimization.
12	929	0.551514644166	Henry Cohn, 2024, needs more optimization.
12	931	0.551635286830	Henry Cohn, 2024, needs more optimization.
12	933	0.551683109780	Henry Cohn, 2024, needs more optimization.
12	935	0.551787832455	Henry Cohn, 2024, needs more optimization.
12	936	0.552037381879	Henry Cohn, 2024, needs more optimization.
12	937	0.552109303436	Henry Cohn, 2024, needs more optimization.
12	939	0.552236034908	Henry Cohn, 2024, needs more optimization.
12	940	0.552429819856	Henry Cohn, 2024, needs more optimization.
12	941	0.552534281258	Henry Cohn, 2024, needs more optimization.
12	943	0.552657390390	Henry Cohn, 2024, needs more optimization.
12	944	0.552831118917	Henry Cohn, 2024, needs more optimization.
12	945	0.552963063037	Henry Cohn, 2024, needs more optimization.
12	950	0.553187398772	Henry Cohn, 2024, needs more optimization.
12	954	0.553511296656	Henry Cohn, 2024, needs more optimization.
12	957	0.553907411229	Henry Cohn, 2024, needs more optimization.
12	960	0.554095747124	Henry Cohn, 2024, needs more optimization.
12	963	0.554457625979	Henry Cohn, 2024, needs more optimization.
12	965	0.554594577365	Henry Cohn, 2024, needs more optimization.
12	966	0.554979404250	Henry Cohn, 2024, needs more optimization.
12	967	0.555032181157	Henry Cohn, 2024, needs more optimization.
12	968	0.555077441044	Henry Cohn, 2024, needs more optimization.
12	971	0.555109663664	Henry Cohn, 2024, needs more optimization.
12	1024	0.555555555556	Subcode of a code of size 1144 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 5$
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $15 x - 1$
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	0.089954457132	Henry Cohn, 2023.
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	0.119453869186	Henry Cohn, 2023.
13	40	0.121482933612	Henry Cohn, 2023, needs more optimization.
13	42	0.125	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $8 x - 1$
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	0.141255994068	Henry Cohn, 2023. $486 x^{4} + 174 x^{3} + 30 x^{2} - 2 x - 1$
13	50	0.142459427551	Henry Cohn, 2023. Minimal polynomial listed in plain text data
13	51	0.145120831484	Henry Cohn, 2023. Minimal polynomial listed in plain text data
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	0.147908234754	Henry Cohn, 2023, needs more optimization.
13	54	0.148576024647	Henry Cohn, 2023, needs more optimization.
13	55	0.148805253270	Henry Cohn, 2023, needs more optimization.
13	56	0.148975682089	Henry Cohn, 2023.
13	57	0.166162190421	Henry Cohn, 2023, needs more optimization.
13	58	0.173474302723	Henry Cohn, 2023.
13	59	0.180546114082	Henry Cohn, 2024, needs more optimization.
13	60	0.189232418822	Henry Cohn, 2024, needs more optimization.
13	61	0.192485586711	Henry Cohn, 2024, needs more optimization.
13	62	0.195452989479	Henry Cohn, 2024, needs more optimization.
13	63	0.197591643362	Henry Cohn, 2024, needs more optimization.
13	64	0.200010209361	Henry Cohn, 2024, needs more optimization.
13	65	0.201096675588	Henry Cohn, 2024, needs more optimization.
13	66	0.201532997898	Henry Cohn, 2024, needs more optimization.
13	67	0.204272557340	Henry Cohn, 2024, needs more optimization.
13	68	0.207724662756	Henry Cohn, 2024, needs more optimization.
13	69	0.208439951240	Henry Cohn, 2024, needs more optimization.
13	70	0.210869472873	Henry Cohn, 2024, needs more optimization.
13	71	0.212588870217	Henry Cohn, 2024, needs more optimization.
13	72	0.214211025221	Henry Cohn, 2024, needs more optimization.
13	73	0.216212522522	Henry Cohn, 2024, needs more optimization.
13	74	0.218091527380	Henry Cohn, 2024, needs more optimization.
13	75	0.220390883539	Henry Cohn, 2024, needs more optimization.
13	76	0.222173972908	Henry Cohn, 2024, needs more optimization.
13	77	0.224170804123	Henry Cohn, 2024, needs more optimization.
13	78	0.226471448488	Henry Cohn, 2024, needs more optimization.
13	79	0.228158299450	Henry Cohn, 2024, needs more optimization.
13	80	0.230745749130	Henry Cohn, 2024, needs more optimization.
13	81	0.232789702878	Henry Cohn, 2024, needs more optimization.
13	82	0.235062878637	Henry Cohn, 2024, needs more optimization.
13	83	0.236620965828	Henry Cohn, 2024, needs more optimization.
13	84	0.238406841015	Henry Cohn, 2024, needs more optimization.
13	85	0.240498544639	Henry Cohn, 2024, needs more optimization.
13	86	0.242184870432	Henry Cohn, 2024, needs more optimization.
13	87	0.243822440517	Henry Cohn, 2024, needs more optimization.
13	88	0.245756498859	Henry Cohn, 2024, needs more optimization.
13	89	0.247335375917	Henry Cohn, 2024, needs more optimization.
13	90	0.248992396729	Henry Cohn, 2024, needs more optimization.
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	0.265757903710	Henry Cohn, 2023, needs more optimization.
13	107	0.270978248661	Henry Cohn, 2024, needs more optimization.
13	108	0.272504317670	Henry Cohn, 2024, needs more optimization.
13	112	0.272727272728	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $11 x - 3$
13	113	0.278243037496	Henry Cohn, 2024, needs more optimization.
13	114	0.279384767260	Henry Cohn, 2024, needs more optimization.
13	115	0.280231349612	Henry Cohn, 2024, needs more optimization.
13	116	0.281727556932	Henry Cohn, 2024, needs more optimization.
13	117	0.282253166421	Henry Cohn, 2024, needs more optimization.
13	118	0.283873052566	Henry Cohn, 2024, needs more optimization.
13	119	0.285356793354	Henry Cohn, 2024, needs more optimization.
13	120	0.286161135987	Henry Cohn, 2024, needs more optimization.
13	121	0.287756172691	Henry Cohn, 2024, needs more optimization.
13	122	0.288742202136	Henry Cohn, 2024, needs more optimization.
13	123	0.290001071561	Henry Cohn, 2024, needs more optimization.
13	124	0.291992083580	Henry Cohn, 2024, needs more optimization.
13	125	0.293140528823	Henry Cohn, 2024, needs more optimization.
13	126	0.294165135084	Henry Cohn, 2024, needs more optimization.
13	127	0.295362948602	Henry Cohn, 2024, needs more optimization.
13	128	0.296563827278	Henry Cohn, 2024, needs more optimization.
13	129	0.298122159345	Henry Cohn, 2024, needs more optimization.
13	130	0.299105657017	Henry Cohn, 2024, needs more optimization.
13	131	0.300760170042	Henry Cohn, 2024, needs more optimization.
13	132	0.301837057739	Henry Cohn, 2024, needs more optimization.
13	133	0.302043942244	Henry Cohn, 2024, needs more optimization.
13	134	0.303901796528	Henry Cohn, 2024, needs more optimization.
13	135	0.304159948150	Henry Cohn, 2024, needs more optimization.
13	136	0.305846338818	Henry Cohn, 2024, needs more optimization.
13	137	0.307092216487	Henry Cohn, 2024, needs more optimization.
13	138	0.308414689795	Henry Cohn, 2024, needs more optimization.
13	139	0.308705043059	Henry Cohn, 2024, needs more optimization.
13	140	0.309112687439	Henry Cohn, 2024, needs more optimization.
13	141	0.310608562438	Henry Cohn, 2024, needs more optimization.
13	142	0.311625994989	Henry Cohn, 2024, needs more optimization.
13	143	0.312019579575	Henry Cohn, 2024, needs more optimization.
13	144	0.313472377210	Henry Cohn, 2024, needs more optimization.
13	145	0.313629006895	Henry Cohn, 2024, needs more optimization.
13	146	0.314710548608	Henry Cohn, 2024, needs more optimization.
13	147	0.314912107220	Henry Cohn, 2024, needs more optimization.
13	148	0.316115796939	Henry Cohn, 2024, needs more optimization.
13	150	0.316535464116	Henry Cohn, 2024, needs more optimization.
13	153	0.318817759714	Henry Cohn, 2024, needs more optimization.
13	154	0.319541669317	Henry Cohn, 2024, needs more optimization.
13	155	0.320516414170	Henry Cohn, 2024, needs more optimization.
13	156	0.320835724126	Henry Cohn, 2024, needs more optimization.
13	157	0.320859593240	Henry Cohn, 2024, needs more optimization.
13	159	0.321479537381	Henry Cohn, 2024, needs more optimization.
13	160	0.323206058218	Henry Cohn, 2024, needs more optimization.
13	161	0.323570816829	Henry Cohn, 2024, needs more optimization.
13	163	0.323769041275	Henry Cohn, 2024, needs more optimization.
13	164	0.323829442033	Henry Cohn, 2024, needs more optimization.
13	166	0.325219252867	Henry Cohn, 2024, needs more optimization.
13	169	0.325719753978	Henry Cohn, 2024, needs more optimization.
13	170	0.327187161008	Henry Cohn, 2024, needs more optimization.
13	171	0.327747227298	Henry Cohn, 2024, needs more optimization.
13	172	0.327804980780	Henry Cohn, 2024, needs more optimization.
13	173	0.327937112293	Henry Cohn, 2024, needs more optimization.
13	174	0.328212205737	Henry Cohn, 2024, needs more optimization.
13	176	0.328700350021	Henry Cohn, 2024, needs more optimization.
13	178	0.328710103653	Henry Cohn, 2024, needs more optimization.
13	179	0.329568963625	Henry Cohn, 2024, needs more optimization.
13	180	0.330116076191	Henry Cohn, 2024, needs more optimization.
13	182	0.330456254659	Henry Cohn, 2024, needs more optimization.
13	183	0.331714214552	Henry Cohn, 2024, needs more optimization.
13	184	0.332048647677	Henry Cohn, 2024, needs more optimization.
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	0.352053326651	Henry Cohn, 2024, needs more optimization.
13	210	0.353503109482	Henry Cohn, 2024, needs more optimization.
13	211	0.354146048385	Henry Cohn, 2024, needs more optimization.
13	212	0.355347000676	Henry Cohn, 2024, needs more optimization.
13	213	0.355945199456	Henry Cohn, 2024, needs more optimization.
13	214	0.356134916619	Henry Cohn, 2024, needs more optimization.
13	216	0.357593553778	Henry Cohn, 2024, needs more optimization.
13	217	0.359106056299	Henry Cohn, 2024, needs more optimization.
13	218	0.360542835026	Henry Cohn, 2024, needs more optimization.
13	219	0.361222714288	Henry Cohn, 2024, needs more optimization.
13	220	0.361698996601	Henry Cohn, 2024, needs more optimization.
13	221	0.362103847615	Henry Cohn, 2024, needs more optimization.
13	222	0.363210865067	Henry Cohn, 2024, needs more optimization.
13	224	0.364100100297	Henry Cohn, 2024, needs more optimization.
13	225	0.365748615110	Henry Cohn, 2024, needs more optimization.
13	226	0.366510114777	Henry Cohn, 2024, needs more optimization.
13	227	0.366849621098	Henry Cohn, 2024, needs more optimization.
13	228	0.369121724709	Henry Cohn, 2024, needs more optimization.
13	229	0.369352055442	Henry Cohn, 2024, needs more optimization.
13	230	0.370431486343	Henry Cohn, 2024, needs more optimization.
13	231	0.370940738047	Henry Cohn, 2024, needs more optimization.
13	232	0.371603149846	Henry Cohn, 2024, needs more optimization.
13	233	0.372326615289	Henry Cohn, 2024, needs more optimization.
13	234	0.373476131833	Henry Cohn, 2024, needs more optimization.
13	235	0.373740867602	Henry Cohn, 2024, needs more optimization.
13	236	0.374723637533	Henry Cohn, 2024, needs more optimization.
13	237	0.375076765371	Henry Cohn, 2024, needs more optimization.
13	238	0.376278629115	Henry Cohn, 2024, needs more optimization.
13	239	0.376703094924	Henry Cohn, 2024, needs more optimization.
13	240	0.376865228352	Henry Cohn, 2024, needs more optimization.
13	241	0.377477110743	Henry Cohn, 2024, needs more optimization.
13	242	0.378495298095	Henry Cohn, 2024, needs more optimization.
13	243	0.379805545183	Henry Cohn, 2024, needs more optimization.
13	244	0.380239404677	Henry Cohn, 2024, needs more optimization.
13	245	0.380694618725	Henry Cohn, 2024, needs more optimization.
13	246	0.381226012336	Henry Cohn, 2024, needs more optimization.
13	252	0.381963272515	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, arXiv:2403.04330. $13 x - 5$
13	315	0.411789036929	Henry Cohn, 2024, needs more optimization.
13	318	0.412751038567	Henry Cohn, 2024, needs more optimization.
13	320	0.413623388057	Henry Cohn, 2024, needs more optimization.
13	321	0.413785881193	Henry Cohn, 2024, needs more optimization.
13	322	0.414624458250	Henry Cohn, 2024, needs more optimization.
13	323	0.415008362431	Henry Cohn, 2024, needs more optimization.
13	324	0.415286913035	Henry Cohn, 2024, needs more optimization.
13	326	0.415821218130	Henry Cohn, 2024, needs more optimization.
13	327	0.416103291612	Henry Cohn, 2024, needs more optimization.
13	328	0.416322125722	Henry Cohn, 2024, needs more optimization.
13	329	0.416367357079	Henry Cohn, 2024, needs more optimization.
13	330	0.417777094939	Henry Cohn, 2024, needs more optimization.
13	331	0.417778312114	Henry Cohn, 2024, needs more optimization.
13	332	0.417968502403	Henry Cohn, 2024, needs more optimization.
13	333	0.418491597740	Henry Cohn, 2024, needs more optimization.
13	334	0.418608202257	Henry Cohn, 2024, needs more optimization.
13	335	0.418944369179	Henry Cohn, 2024, needs more optimization.
13	336	0.419532213891	Henry Cohn, 2024, needs more optimization.
13	338	0.419661495032	Henry Cohn, 2024, needs more optimization.
13	339	0.420269807569	Henry Cohn, 2024, needs more optimization.
13	340	0.420284324419	Henry Cohn, 2024, needs more optimization.
13	341	0.420955658815	Henry Cohn, 2024, needs more optimization.
13	342	0.421127627528	Henry Cohn, 2024, needs more optimization.
13	343	0.421676169218	Henry Cohn, 2024, needs more optimization.
13	345	0.421943128023	Henry Cohn, 2024, needs more optimization.
13	346	0.422297394239	Henry Cohn, 2024, needs more optimization.
13	348	0.423141908122	Henry Cohn, 2024, needs more optimization.
13	349	0.423853893646	Henry Cohn, 2024, needs more optimization.
13	350	0.423902155677	Henry Cohn, 2024, needs more optimization.
13	352	0.424142346906	Henry Cohn, 2024, needs more optimization.
13	353	0.424954062003	Henry Cohn, 2024, needs more optimization.
13	354	0.425057675414	Henry Cohn, 2024, needs more optimization.
13	355	0.425509259398	Henry Cohn, 2024, needs more optimization.
13	356	0.425748427328	Henry Cohn, 2024, needs more optimization.
13	357	0.426334312182	Henry Cohn, 2024, needs more optimization.
13	358	0.426390639427	Henry Cohn, 2024, needs more optimization.
13	359	0.426644169196	Henry Cohn, 2024, needs more optimization.
13	361	0.427283309800	Henry Cohn, 2024, needs more optimization.
13	362	0.427521694469	Henry Cohn, 2024, needs more optimization.
13	363	0.427889366976	Henry Cohn, 2024, needs more optimization.
13	364	0.427983932257	Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, arXiv:2403.04330. $7 x - 3$
13	578	0.454545454546	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $11 x - 5$
13	579	0.476814008086	Henry Cohn, 2024, needs more optimization.
13	580	0.477016048195	Henry Cohn, 2024, needs more optimization.
13	582	0.477127383639	Henry Cohn, 2024, needs more optimization.
13	584	0.477355444725	Henry Cohn, 2024, needs more optimization.
13	585	0.477854283886	Henry Cohn, 2024, needs more optimization.
13	586	0.477898167731	Henry Cohn, 2024, needs more optimization.
13	587	0.478301052327	Henry Cohn, 2024, needs more optimization.
13	588	0.478375715813	Henry Cohn, 2024, needs more optimization.
13	589	0.478561886570	Henry Cohn, 2024, needs more optimization.
13	590	0.478590964434	Henry Cohn, 2024, needs more optimization.
13	591	0.478761436572	Henry Cohn, 2024, needs more optimization.
13	593	0.478874297165	Henry Cohn, 2024, needs more optimization.
13	594	0.478968671991	Henry Cohn, 2024, needs more optimization.
13	595	0.479275909549	Henry Cohn, 2024, needs more optimization.
13	596	0.479431916606	Henry Cohn, 2024, needs more optimization.
13	597	0.479954939141	Henry Cohn, 2024, needs more optimization.
13	598	0.480078969898	Henry Cohn, 2024, needs more optimization.
13	599	0.480089756730	Henry Cohn, 2024, needs more optimization.
13	601	0.480284514561	Henry Cohn, 2024, needs more optimization.
13	602	0.480665735209	Henry Cohn, 2024, needs more optimization.
13	606	0.480821480611	Henry Cohn, 2024, needs more optimization.
13	607	0.481276586680	Henry Cohn, 2024, needs more optimization.
13	608	0.481366890226	Henry Cohn, 2024, needs more optimization.
13	609	0.481889126134	Henry Cohn, 2024, needs more optimization.
13	612	0.482004739754	Henry Cohn, 2024, needs more optimization.
13	614	0.482252008488	Henry Cohn, 2024, needs more optimization.
13	616	0.482582973880	Henry Cohn, 2024, needs more optimization.
13	617	0.482660838508	Henry Cohn, 2024, needs more optimization.
13	618	0.482879856445	Henry Cohn, 2024, needs more optimization.
13	621	0.483651269097	Henry Cohn, 2024, needs more optimization.
13	622	0.483829409501	Henry Cohn, 2024, needs more optimization.
13	623	0.483892491992	Henry Cohn, 2024, needs more optimization.
13	624	0.484082997023	Henry Cohn, 2024, needs more optimization.
13	627	0.484101949259	Henry Cohn, 2024, needs more optimization.
13	628	0.484622666191	Henry Cohn, 2024, needs more optimization.
13	630	0.485090064447	Henry Cohn, 2024, needs more optimization.
13	631	0.485260873780	Henry Cohn, 2024, needs more optimization.
13	633	0.485332577461	Henry Cohn, 2024, needs more optimization.
13	635	0.485581032178	Henry Cohn, 2024, needs more optimization.
13	636	0.485903516255	Henry Cohn, 2024, needs more optimization.
13	637	0.486104423446	Henry Cohn, 2024, needs more optimization.
13	640	0.486206313250	Henry Cohn, 2024, needs more optimization.
13	641	0.486620901925	Henry Cohn, 2024, needs more optimization.
13	642	0.486794908843	Henry Cohn, 2024, needs more optimization.
13	645	0.486980901765	Henry Cohn, 2024, needs more optimization.
13	646	0.487409254026	Henry Cohn, 2024, needs more optimization.
13	649	0.487717466390	Henry Cohn, 2024, needs more optimization.
13	650	0.488190153882	Henry Cohn, 2024, needs more optimization.
13	652	0.488236254675	Henry Cohn, 2024, needs more optimization.
13	654	0.488588199747	Henry Cohn, 2024, needs more optimization.
13	655	0.488598039501	Henry Cohn, 2024, needs more optimization.
13	656	0.488995624284	Henry Cohn, 2024, needs more optimization.
13	658	0.489057555640	Henry Cohn, 2024, needs more optimization.
13	659	0.489303552736	Henry Cohn, 2024, needs more optimization.
13	662	0.489562883666	Henry Cohn, 2024, needs more optimization.
13	664	0.489945322790	Henry Cohn, 2024, needs more optimization.
13	666	0.490343003462	Henry Cohn, 2024, needs more optimization.
13	667	0.490353307924	Henry Cohn, 2024, needs more optimization.
13	668	0.490666068859	Henry Cohn, 2024, needs more optimization.
13	671	0.490855539067	Henry Cohn, 2024, needs more optimization.
13	672	0.490953365212	Henry Cohn, 2024, needs more optimization.
13	673	0.491444660001	Henry Cohn, 2024, needs more optimization.
13	674	0.491445143839	Henry Cohn, 2024, needs more optimization.
13	676	0.491708212130	Henry Cohn, 2024, needs more optimization.
13	677	0.491780855325	Henry Cohn, 2024, needs more optimization.
13	678	0.491973278752	Henry Cohn, 2024, needs more optimization.
13	679	0.492164378840	Henry Cohn, 2024, needs more optimization.
13	682	0.492318409784	Henry Cohn, 2024, needs more optimization.
13	683	0.492679577894	Henry Cohn, 2024, needs more optimization.
13	685	0.492975685235	Henry Cohn, 2024, needs more optimization.
13	686	0.493037409557	Henry Cohn, 2024, needs more optimization.
13	688	0.493155771578	Henry Cohn, 2024, needs more optimization.
13	689	0.493503888162	Henry Cohn, 2024, needs more optimization.
13	691	0.493692735433	Henry Cohn, 2024, needs more optimization.
13	692	0.493986499296	Henry Cohn, 2024, needs more optimization.
13	693	0.494182339504	Henry Cohn, 2024, needs more optimization.
13	694	0.494205463781	Henry Cohn, 2024, needs more optimization.
13	696	0.494625119065	Henry Cohn, 2024, needs more optimization.
13	697	0.494871872778	Henry Cohn, 2024, needs more optimization.
13	698	0.494886601499	Henry Cohn, 2024, needs more optimization.
13	699	0.495107660979	Henry Cohn, 2024, needs more optimization.
13	701	0.495209605108	Henry Cohn, 2024, needs more optimization.
13	704	0.495281841050	Henry Cohn, 2024, needs more optimization.
13	705	0.495537338518	Henry Cohn, 2024, needs more optimization.
13	707	0.495986958208	Henry Cohn, 2024, needs more optimization.
13	708	0.496028964002	Henry Cohn, 2024, needs more optimization.
13	710	0.496332871965	Henry Cohn, 2024, needs more optimization.
13	711	0.496422430830	Henry Cohn, 2024, needs more optimization.
13	712	0.496796508131	Henry Cohn, 2024, needs more optimization.
13	713	0.496838462563	Henry Cohn, 2024, needs more optimization.
13	715	0.497037842841	Henry Cohn, 2024, needs more optimization.
13	717	0.497162954387	Henry Cohn, 2024, needs more optimization.
13	718	0.497393548760	Henry Cohn, 2024, needs more optimization.
13	719	0.497741154684	Henry Cohn, 2024, needs more optimization.
13	721	0.497763938939	Henry Cohn, 2024, needs more optimization.
13	722	0.498051924748	Henry Cohn, 2024, needs more optimization.
13	723	0.498115252045	Henry Cohn, 2024, needs more optimization.
13	724	0.498307714357	Henry Cohn, 2024, needs more optimization.
13	726	0.498567214765	Henry Cohn, 2024, needs more optimization.
13	728	0.498855109405	Henry Cohn, 2024, needs more optimization.
13	730	0.499097504599	Henry Cohn, 2024, needs more optimization.
13	732	0.499176355011	Henry Cohn, 2024, needs more optimization.
13	734	0.499585297889	Henry Cohn, 2024, needs more optimization.
13	736	0.499922115594	Henry Cohn, 2024, needs more optimization.
13	758	0.499999999946	Orthogonal union of 756 points in 12 dimensions and 2 points in 1 dimension.
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	0.067586771091	H. Cohn, Small spherical and projective codes, data set, 2022, 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	0.071678820990	Henry Cohn, 2024, needs more optimization.
14	34	0.071707416489	Henry Cohn, 2024, needs more optimization.
14	36	0.080003299193	Henry Cohn, 2023. $2156 x^{2} + 140 x - 25$
14	37	0.087892856445	Henry Cohn, 2023.
14	38	0.092605785749	Henry Cohn, 2023, needs more optimization.
14	39	0.094407135777	Henry Cohn, 2023.
14	42	0.1	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $10 x - 1$
14	45	0.112912613537	Henry Cohn, 2023. $167 x^{2} - 10 x - 1$
14	46	0.114212424979	Henry Cohn, 2023, needs more optimization.
14	47	0.114784817594	Henry Cohn, 2023, needs more optimization.
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	0.125097652359	Henry Cohn, 2023.
14	50	0.126131765416	Henry Cohn, 2023, needs more optimization.
14	52	0.126131983623	Henry Cohn, 2023. $47 x^{2} + 2 x - 1$
14	53	0.127207031163	Henry Cohn, 2023, needs more optimization.
14	54	0.135105976113	Henry Cohn, 2023, needs more optimization.
14	55	0.136745922263	Henry Cohn, 2023.
14	56	0.139995758129	Henry Cohn, 2023, needs more optimization.
14	57	0.142195257215	Henry Cohn, 2023, needs more optimization.
14	64	0.142857142858	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 1$
14	65	0.165365119569	Henry Cohn, 2024, needs more optimization.
14	70	0.166666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $6 x - 1$
14	71	0.194909101909	Henry Cohn, 2024, needs more optimization.
14	72	0.196854757187	Henry Cohn, 2024, needs more optimization.
14	73	0.198009592305	Henry Cohn, 2024, needs more optimization.
14	74	0.200078890037	Henry Cohn, 2024, needs more optimization.
14	75	0.201703682352	Henry Cohn, 2024, needs more optimization.
14	76	0.202906926487	Henry Cohn, 2024, needs more optimization.
14	77	0.204948279565	Henry Cohn, 2024, needs more optimization.
14	78	0.205576944148	Henry Cohn, 2023, needs more optimization.
14	80	0.206046650060	Henry Cohn, 2023, needs more optimization.
14	81	0.207064760597	Henry Cohn, 2024, needs more optimization.
14	82	0.207114758498	Henry Cohn, 2024, needs more optimization.
14	85	0.208849195936	Henry Cohn, 2023. Minimal polynomial listed in plain text data
14	86	0.220167250836	Henry Cohn, 2024, needs more optimization.
14	87	0.221792907141	Henry Cohn, 2024, needs more optimization.
14	88	0.223549107865	Henry Cohn, 2024, needs more optimization.
14	89	0.225185817331	Henry Cohn, 2024, needs more optimization.
14	90	0.226748405021	Henry Cohn, 2024, needs more optimization.
14	91	0.228410971560	Henry Cohn, 2024, needs more optimization.
14	92	0.230317813049	Henry Cohn, 2024, needs more optimization.
14	93	0.231962896794	Henry Cohn, 2024, needs more optimization.
14	94	0.233528316408	Henry Cohn, 2024, needs more optimization.
14	98	0.233922658403	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $14 x^{2} + x - 1$
14	99	0.240668364607	Henry Cohn, 2024, needs more optimization.
14	100	0.242094686224	Henry Cohn, 2024, needs more optimization.
14	101	0.243314506450	Henry Cohn, 2024, needs more optimization.
14	102	0.244943906693	Henry Cohn, 2024, needs more optimization.
14	103	0.245706197803	Henry Cohn, 2024, needs more optimization.
14	104	0.247067400149	Henry Cohn, 2024, needs more optimization.
14	105	0.248136602794	Henry Cohn, 2024, needs more optimization.
14	106	0.249655037382	Henry Cohn, 2024, needs more optimization.
14	112	0.25	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4 x - 1$
14	113	0.257476881447	Henry Cohn, 2024, needs more optimization.
14	114	0.257993546061	Henry Cohn, 2024, needs more optimization.
14	115	0.259424094619	Henry Cohn, 2024, needs more optimization.
14	116	0.260322812709	Henry Cohn, 2024, needs more optimization.
14	117	0.261199699980	Henry Cohn, 2024, needs more optimization.
14	118	0.262837630267	Henry Cohn, 2024, needs more optimization.
14	119	0.263442594742	Henry Cohn, 2024, needs more optimization.
14	120	0.263830091064	Henry Cohn, 2024, needs more optimization.
14	121	0.265322322875	Henry Cohn, 2024, needs more optimization.
14	122	0.266934077755	Henry Cohn, 2024, needs more optimization.
14	123	0.267348315966	Henry Cohn, 2024, needs more optimization.
14	124	0.268482102462	Henry Cohn, 2024, needs more optimization.
14	125	0.269686334654	Henry Cohn, 2024, needs more optimization.
14	126	0.270275646233	Henry Cohn, 2024, needs more optimization.
14	127	0.271232692873	Henry Cohn, 2024, needs more optimization.
14	128	0.272034762575	Henry Cohn, 2024, needs more optimization.
14	136	0.272727272728	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $11 x - 3$
14	137	0.281505820782	Henry Cohn, 2024, needs more optimization.
14	138	0.282461524447	Henry Cohn, 2024, needs more optimization.
14	156	0.283473354757	Henry Cohn, 2024. $112 x^{2} - 9$
14	157	0.300835461198	Henry Cohn, 2024, needs more optimization.
14	158	0.302077993406	Henry Cohn, 2024, needs more optimization.
14	159	0.303042328761	Henry Cohn, 2024, needs more optimization.
14	160	0.303731941278	Henry Cohn, 2024, needs more optimization.
14	161	0.303919967431	Henry Cohn, 2024, needs more optimization.
14	162	0.305085794061	Henry Cohn, 2024, needs more optimization.
14	163	0.306023718487	Henry Cohn, 2024, needs more optimization.
14	164	0.306239710602	Henry Cohn, 2024, needs more optimization.
14	165	0.307047647609	Henry Cohn, 2024, needs more optimization.
14	166	0.307574205768	Henry Cohn, 2024, needs more optimization.
14	167	0.308748255041	Henry Cohn, 2024, needs more optimization.
14	168	0.309336020316	Henry Cohn, 2024, needs more optimization.
14	169	0.310081676521	Henry Cohn, 2024, needs more optimization.
14	171	0.310946311771	Henry Cohn, 2024, needs more optimization.
14	172	0.311587088871	Henry Cohn, 2024, needs more optimization.
14	173	0.312099492151	Henry Cohn, 2024, needs more optimization.
14	174	0.312627906099	Henry Cohn, 2024, needs more optimization.
14	175	0.313215586197	Henry Cohn, 2024, needs more optimization.
14	176	0.313897890950	Henry Cohn, 2024, needs more optimization.
14	177	0.314281429396	Henry Cohn, 2024, needs more optimization.
14	178	0.315095398589	Henry Cohn, 2024, needs more optimization.
14	179	0.315945235655	Henry Cohn, 2024, needs more optimization.
14	181	0.316273177661	Henry Cohn, 2024, needs more optimization.
14	182	0.316659552907	Henry Cohn, 2024, needs more optimization.
14	183	0.316826620465	Henry Cohn, 2024, needs more optimization.
14	184	0.317728029634	Henry Cohn, 2024, needs more optimization.
14	210	0.318181818182	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $22 x - 7$
14	212	0.329884871893	Henry Cohn, 2024, needs more optimization.
14	213	0.331286203375	Henry Cohn, 2024, needs more optimization.
14	214	0.331749113454	Henry Cohn, 2024, needs more optimization.
14	215	0.331803529154	Henry Cohn, 2024, needs more optimization.
14	217	0.332026083485	Henry Cohn, 2024, needs more optimization.
14	218	0.332969811760	Henry Cohn, 2024, needs more optimization.
14	220	0.333080971623	Henry Cohn, 2024, needs more optimization.
14	224	0.333213878014	Henry Cohn, 2024, needs more optimization.
14	240	0.333333333334	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $3 x - 1$
14	241	0.345135786580	Henry Cohn, 2024, needs more optimization.
14	242	0.346707411845	Henry Cohn, 2024, needs more optimization.
14	243	0.347324114268	Henry Cohn, 2024, needs more optimization.
14	244	0.347559184920	Henry Cohn, 2024, needs more optimization.
14	246	0.348143587809	Henry Cohn, 2024, needs more optimization.
14	248	0.350724237786	Henry Cohn, 2024, needs more optimization.
14	249	0.351365914032	Henry Cohn, 2024, needs more optimization.
14	251	0.352009319657	Henry Cohn, 2024, needs more optimization.
14	253	0.353955354750	Henry Cohn, 2024, needs more optimization.
14	254	0.355194631163	Henry Cohn, 2024, needs more optimization.
14	256	0.355280791172	Henry Cohn, 2024, needs more optimization.
14	258	0.358471592959	Henry Cohn, 2024, needs more optimization.
14	259	0.359935943148	Henry Cohn, 2024, needs more optimization.
14	265	0.360535450936	Henry Cohn, 2024, needs more optimization.
14	266	0.363564641675	Henry Cohn, 2024, needs more optimization.
14	267	0.364490637145	Henry Cohn, 2024, needs more optimization.
14	268	0.365154550828	Henry Cohn, 2024, needs more optimization.
14	269	0.365684515499	Henry Cohn, 2024, needs more optimization.
14	272	0.366238815166	Henry Cohn, 2024, needs more optimization.
14	273	0.367568848791	Henry Cohn, 2024, needs more optimization.
14	274	0.367664920037	Henry Cohn, 2024, needs more optimization.
14	275	0.368768118167	Henry Cohn, 2024, needs more optimization.
14	276	0.369050598383	Henry Cohn, 2024, needs more optimization.
14	277	0.369165312896	Henry Cohn, 2024, needs more optimization.
14	278	0.370384136217	Henry Cohn, 2024, needs more optimization.
14	279	0.370939628276	Henry Cohn, 2024, needs more optimization.
14	280	0.371128637686	Henry Cohn, 2024, needs more optimization.
14	281	0.371724532961	Henry Cohn, 2024, needs more optimization.
14	282	0.371951171452	Henry Cohn, 2024, needs more optimization.
14	283	0.372741537795	Henry Cohn, 2024, needs more optimization.
14	284	0.372980805592	Henry Cohn, 2024, needs more optimization.
14	286	0.373648891729	Henry Cohn, 2024, needs more optimization.
14	287	0.374391191036	Henry Cohn, 2024, needs more optimization.
14	288	0.375472146353	Henry Cohn, 2024, needs more optimization.
14	289	0.375739905873	Henry Cohn, 2024, needs more optimization.
14	290	0.375947826707	Henry Cohn, 2024, needs more optimization.
14	292	0.376361629712	Henry Cohn, 2024, needs more optimization.
14	294	0.377180729783	Henry Cohn, 2024, needs more optimization.
14	296	0.378249283988	Henry Cohn, 2024, needs more optimization.
14	297	0.379343991737	Henry Cohn, 2024, needs more optimization.
14	298	0.379700857489	Henry Cohn, 2024, needs more optimization.
14	300	0.380099636041	Henry Cohn, 2024, needs more optimization.
14	302	0.380698426354	Henry Cohn, 2024, needs more optimization.
14	364	0.380952380953	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $21 x - 8$
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	600	0.428571428572	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $7 x - 3$
14	601	0.453760527789	Henry Cohn, 2024, needs more optimization.
14	604	0.454121667254	Henry Cohn, 2024, needs more optimization.
14	605	0.454464378613	Henry Cohn, 2024, needs more optimization.
14	607	0.454530893440	Henry Cohn, 2024, needs more optimization.
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	0.490974033191	Henry Cohn, 2024, needs more optimization.
14	900	0.491315042274	Henry Cohn, 2024, needs more optimization.
14	902	0.491645994465	Henry Cohn, 2024, needs more optimization.
14	903	0.491772522257	Henry Cohn, 2024, needs more optimization.
14	904	0.492100040917	Henry Cohn, 2024, needs more optimization.
14	907	0.492415073976	Henry Cohn, 2024, needs more optimization.
14	909	0.492511974761	Henry Cohn, 2024, needs more optimization.
14	912	0.492707821799	Henry Cohn, 2024, needs more optimization.
14	913	0.492817910242	Henry Cohn, 2024, needs more optimization.
14	914	0.492888532143	Henry Cohn, 2024, needs more optimization.
14	915	0.493171022059	Henry Cohn, 2024, needs more optimization.
14	918	0.493187287588	Henry Cohn, 2024, needs more optimization.
14	919	0.493417907107	Henry Cohn, 2024, needs more optimization.
14	920	0.493441223239	Henry Cohn, 2024, needs more optimization.
14	921	0.493530324392	Henry Cohn, 2024, needs more optimization.
14	925	0.493771733330	Henry Cohn, 2024, needs more optimization.
14	928	0.494239247769	Henry Cohn, 2024, needs more optimization.
14	929	0.494477202272	Henry Cohn, 2024, needs more optimization.
14	930	0.494826087098	Henry Cohn, 2024, needs more optimization.
14	934	0.494873722823	Henry Cohn, 2024, needs more optimization.
14	937	0.494937770185	Henry Cohn, 2024, needs more optimization.
14	938	0.495241523164	Henry Cohn, 2024, needs more optimization.
14	941	0.495412186367	Henry Cohn, 2024, needs more optimization.
14	942	0.495737456175	Henry Cohn, 2024, needs more optimization.
14	945	0.495740000302	Henry Cohn, 2024, needs more optimization.
14	946	0.496124995171	Henry Cohn, 2024, needs more optimization.
14	947	0.496252467047	Henry Cohn, 2024, needs more optimization.
14	948	0.496300133605	Henry Cohn, 2024, needs more optimization.
14	949	0.496392372408	Henry Cohn, 2024, needs more optimization.
14	950	0.496624113781	Henry Cohn, 2024, needs more optimization.
14	951	0.496739808589	Henry Cohn, 2024, needs more optimization.
14	952	0.496893302458	Henry Cohn, 2024, needs more optimization.
14	954	0.496926240240	Henry Cohn, 2024, needs more optimization.
14	955	0.497017886845	Henry Cohn, 2024, needs more optimization.
14	960	0.497033902814	Henry Cohn, 2024, needs more optimization.
14	961	0.497399538124	Henry Cohn, 2024, needs more optimization.
14	962	0.497423397127	Henry Cohn, 2024, needs more optimization.
14	963	0.497581654079	Henry Cohn, 2024, needs more optimization.
14	964	0.497761839721	Henry Cohn, 2024, needs more optimization.
14	965	0.497952271248	Henry Cohn, 2024, needs more optimization.
14	967	0.498007114936	Henry Cohn, 2024, needs more optimization.
14	969	0.498217433763	Henry Cohn, 2024, needs more optimization.
14	971	0.498284021016	Henry Cohn, 2024, needs more optimization.
14	975	0.498544620586	Henry Cohn, 2024, needs more optimization.
14	976	0.498948598782	Henry Cohn, 2024, needs more optimization.
14	981	0.498978704663	Henry Cohn, 2024, needs more optimization.
14	982	0.499270701108	Henry Cohn, 2024, needs more optimization.
14	984	0.499548712288	Henry Cohn, 2024, needs more optimization.
14	986	0.499674169638	Henry Cohn, 2024, needs more optimization.
14	988	0.499742623240	Henry Cohn, 2024, needs more optimization.
14	989	0.499854605664	Henry Cohn, 2024, needs more optimization.
14	990	0.499918603174	Henry Cohn, 2024, needs more optimization.
14	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. $2 x - 1$
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 listed in plain text data
15	34	0.067169650200	Henry Cohn, 2023.
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	0.078799310669	Henry Cohn, 2023.
15	38	0.079986467575	Henry Cohn, 2023, needs more optimization.
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	0.086159367848	Henry Cohn, 2023.
15	41	0.093096832161	Henry Cohn, 2023, needs more optimization.
15	42	0.096809796022	Henry Cohn, 2023.
15	43	0.099946852944	Henry Cohn, 2023, needs more optimization.
15	44	0.099976638509	Henry Cohn, 2023, needs more optimization.
15	45	0.105767188891	Henry Cohn, 2023.
15	46	0.111769447569	Henry Cohn, 2024, needs more optimization.
15	47	0.111892127828	Henry Cohn, 2024, needs more optimization.
15	48	0.112711948602	Henry Cohn, 2024, needs more optimization.
15	50	0.112912613537	Henry Cohn, 2023. $167 x^{2} - 10 x - 1$
15	56	0.115470053838	Henry Cohn, 2023. $75 x^{2} - 1$
15	57	0.118881472778	Henry Cohn, 2023. Minimal polynomial listed in plain text data
15	58	0.119570206254	Henry Cohn, 2023, needs more optimization.
15	59	0.128965245004	Henry Cohn, 2023, needs more optimization.
15	60	0.129260671864	Henry Cohn, 2023, needs more optimization.
15	61	0.129429477010	Henry Cohn, 2023, needs more optimization.
15	62	0.129619231940	Henry Cohn, 2023, needs more optimization.
15	63	0.129676179739	Henry Cohn, 2023, needs more optimization.
15	64	0.129676246377	Henry Cohn, 2023, needs more optimization.
15	65	0.129676247112	Henry Cohn, 2024.
15	66	0.142857038845	Henry Cohn, 2024, needs more optimization.
15	67	0.144353409494	Henry Cohn, 2023.
15	68	0.147910866385	Henry Cohn, 2023, needs more optimization.
15	69	0.160033734974	Henry Cohn, 2023, needs more optimization.
15	70	0.165896154829	Henry Cohn, 2024, needs more optimization.
15	72	0.166659498241	Henry Cohn, 2024, needs more optimization.
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	128	0.2	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 1$
15	156	0.25	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $4 x - 1$
15	158	0.256564571531	Henry Cohn, 2024, needs more optimization.
15	159	0.280130356486	Henry Cohn, 2024, needs more optimization.
15	160	0.281059975646	Henry Cohn, 2024, needs more optimization.
15	161	0.282057112781	Henry Cohn, 2024, needs more optimization.
15	162	0.282678298991	Henry Cohn, 2024, needs more optimization.
15	163	0.283661509569	Henry Cohn, 2024, needs more optimization.
15	164	0.284237123105	Henry Cohn, 2024, needs more optimization.
15	165	0.285363473503	Henry Cohn, 2024, needs more optimization.
15	166	0.286375522970	Henry Cohn, 2024, needs more optimization.
15	167	0.287313194945	Henry Cohn, 2024, needs more optimization.
15	168	0.287768033516	Henry Cohn, 2024, needs more optimization.
15	169	0.288895182602	Henry Cohn, 2024, needs more optimization.
15	170	0.289702568949	Henry Cohn, 2024, needs more optimization.
15	171	0.290201101460	Henry Cohn, 2024, needs more optimization.
15	172	0.290805256504	Henry Cohn, 2024, needs more optimization.
15	173	0.291858658701	Henry Cohn, 2024, needs more optimization.
15	174	0.292811879031	Henry Cohn, 2024, needs more optimization.
15	175	0.293440262179	Henry Cohn, 2024, needs more optimization.
15	176	0.294255499703	Henry Cohn, 2024, needs more optimization.
15	177	0.294658898290	Henry Cohn, 2024, needs more optimization.
15	178	0.295689181025	Henry Cohn, 2024, needs more optimization.
15	179	0.295985066779	Henry Cohn, 2024, needs more optimization.
15	180	0.296793433274	Henry Cohn, 2024, needs more optimization.
15	181	0.297683682621	Henry Cohn, 2024, needs more optimization.
15	182	0.298449814451	Henry Cohn, 2024, needs more optimization.
15	183	0.299600647808	Henry Cohn, 2024, needs more optimization.
15	184	0.299629266163	Henry Cohn, 2024, needs more optimization.
15	185	0.300400493106	Henry Cohn, 2024, needs more optimization.
15	187	0.301216376819	Henry Cohn, 2024, needs more optimization.
15	188	0.302312803378	Henry Cohn, 2024, needs more optimization.
15	189	0.302652823645	Henry Cohn, 2024, needs more optimization.
15	190	0.303690296475	Henry Cohn, 2024, needs more optimization.
15	192	0.303954671461	Henry Cohn, 2024, needs more optimization.
15	256	0.304347826087	M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, preprint, 2024, arXiv:2403.04330. $23 x - 7$
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	322	0.364066327210	Henry Cohn, 2024, needs more optimization.
15	323	0.364661239075	Henry Cohn, 2024, needs more optimization.
15	324	0.365177519000	Henry Cohn, 2024, needs more optimization.
15	325	0.365279586273	Henry Cohn, 2024, needs more optimization.
15	326	0.365719358712	Henry Cohn, 2024, needs more optimization.
15	328	0.366211580822	Henry Cohn, 2024, needs more optimization.
15	329	0.366749332176	Henry Cohn, 2024, needs more optimization.
15	330	0.367006324190	Henry Cohn, 2024, needs more optimization.
15	331	0.367562454063	Henry Cohn, 2024, needs more optimization.
15	332	0.368100542832	Henry Cohn, 2024, needs more optimization.
15	334	0.368868207318	Henry Cohn, 2024, needs more optimization.
15	335	0.368870101739	Henry Cohn, 2024, needs more optimization.
15	336	0.369365089162	Henry Cohn, 2024, needs more optimization.
15	337	0.369779224858	Henry Cohn, 2024, needs more optimization.
15	338	0.370279393711	Henry Cohn, 2024, needs more optimization.
15	339	0.370454498306	Henry Cohn, 2024, needs more optimization.
15	340	0.371339780226	Henry Cohn, 2024, needs more optimization.
15	341	0.371549583562	Henry Cohn, 2024, needs more optimization.
15	342	0.371779626725	Henry Cohn, 2024, needs more optimization.
15	344	0.372262377941	Henry Cohn, 2024, needs more optimization.
15	345	0.373259871552	Henry Cohn, 2024, needs more optimization.
15	346	0.373420367915	Henry Cohn, 2024, needs more optimization.
15	347	0.373470696872	Henry Cohn, 2024, needs more optimization.
15	348	0.373653854755	Henry Cohn, 2024, needs more optimization.
15	349	0.374034580267	Henry Cohn, 2024, needs more optimization.
15	351	0.374606248244	Henry Cohn, 2024, needs more optimization.
15	352	0.374783706513	Henry Cohn, 2024, needs more optimization.
15	353	0.375360068560	Henry Cohn, 2024, needs more optimization.
15	354	0.375958902948	Henry Cohn, 2024, needs more optimization.
15	355	0.376165895036	Henry Cohn, 2024, needs more optimization.
15	356	0.376663445061	Henry Cohn, 2024, needs more optimization.
15	358	0.376875240185	Henry Cohn, 2024, needs more optimization.
15	359	0.377536426291	Henry Cohn, 2024, needs more optimization.
15	360	0.377643215480	Henry Cohn, 2024, needs more optimization.
15	361	0.377921744658	Henry Cohn, 2024, needs more optimization.
15	362	0.378603878776	Henry Cohn, 2024, needs more optimization.
15	363	0.378695925362	Henry Cohn, 2024, needs more optimization.
15	365	0.379098768203	Henry Cohn, 2024, needs more optimization.
15	366	0.379214686472	Henry Cohn, 2024, needs more optimization.
15	367	0.380011962413	Henry Cohn, 2024, needs more optimization.
15	368	0.380204089678	Henry Cohn, 2024, needs more optimization.
15	369	0.380251272332	Henry Cohn, 2024, needs more optimization.
15	370	0.380584306699	Henry Cohn, 2024, needs more optimization.
15	371	0.381160691041	Henry Cohn, 2024, needs more optimization.
15	372	0.381458701024	Henry Cohn, 2024, needs more optimization.
15	373	0.381671931534	Henry Cohn, 2024, needs more optimization.
15	374	0.382001009876	Henry Cohn, 2024, needs more optimization.
15	375	0.382216711808	Henry Cohn, 2024, needs more optimization.
15	376	0.382724177193	Henry Cohn, 2024, needs more optimization.
15	377	0.383013572874	Henry Cohn, 2024, needs more optimization.
15	378	0.383121436289	Henry Cohn, 2024, needs more optimization.
15	379	0.383327848161	Henry Cohn, 2024, needs more optimization.
15	381	0.383521361620	Henry Cohn, 2024, needs more optimization.
15	382	0.383936650366	Henry Cohn, 2024, needs more optimization.
15	384	0.384426437317	Henry Cohn, 2024, needs more optimization.
15	385	0.384835093532	Henry Cohn, 2024, needs more optimization.
15	388	0.385424149333	Henry Cohn, 2024, needs more optimization.
15	390	0.386050309191	Henry Cohn, 2024, needs more optimization.
15	391	0.386653439861	Henry Cohn, 2024, needs more optimization.
15	392	0.387221206382	Henry Cohn, 2024, needs more optimization.
15	393	0.387271337739	Henry Cohn, 2024, needs more optimization.
15	394	0.387329460136	Henry Cohn, 2024, needs more optimization.
15	395	0.387705265114	Henry Cohn, 2024, needs more optimization.
15	396	0.388062447480	Henry Cohn, 2024, needs more optimization.
15	397	0.388172852162	Henry Cohn, 2024, needs more optimization.
15	398	0.388764204036	Henry Cohn, 2024, needs more optimization.
15	399	0.388772988900	Henry Cohn, 2024, needs more optimization.
15	400	0.389373704402	Henry Cohn, 2024, needs more optimization.
15	401	0.389514527224	Henry Cohn, 2024, needs more optimization.
15	402	0.389940138686	Henry Cohn, 2024, needs more optimization.
15	404	0.390235094646	Henry Cohn, 2024, needs more optimization.
15	405	0.390721411800	Henry Cohn, 2024, needs more optimization.
15	408	0.390974744914	Henry Cohn, 2024, needs more optimization.
15	409	0.391589951027	Henry Cohn, 2024, needs more optimization.
15	410	0.391885330096	Henry Cohn, 2024, needs more optimization.
15	412	0.392150775547	Henry Cohn, 2024, needs more optimization.
15	413	0.392473918736	Henry Cohn, 2024, needs more optimization.
15	414	0.392634002250	Henry Cohn, 2024, needs more optimization.
15	415	0.393227123449	Henry Cohn, 2024, needs more optimization.
15	416	0.393271903904	Henry Cohn, 2024, needs more optimization.
15	417	0.393798385071	Henry Cohn, 2024, needs more optimization.
15	418	0.393880848833	Henry Cohn, 2024, needs more optimization.
15	420	0.394173167432	Henry Cohn, 2024, needs more optimization.
15	423	0.394891507967	Henry Cohn, 2024, needs more optimization.
15	425	0.395203876879	Henry Cohn, 2024, needs more optimization.
15	426	0.395368178533	Henry Cohn, 2024, needs more optimization.
15	427	0.395800728402	Henry Cohn, 2024, needs more optimization.
15	428	0.396226463829	Henry Cohn, 2024, needs more optimization.
15	429	0.396304208313	Henry Cohn, 2024, needs more optimization.
15	430	0.396788819410	Henry Cohn, 2024, needs more optimization.
15	431	0.397003633445	Henry Cohn, 2024, needs more optimization.
15	432	0.397135139095	Henry Cohn, 2024, needs more optimization.
15	434	0.397432015881	Henry Cohn, 2024, needs more optimization.
15	435	0.398011849076	Henry Cohn, 2024, needs more optimization.
15	436	0.398276171924	Henry Cohn, 2024, needs more optimization.
15	438	0.398550692326	Henry Cohn, 2024, needs more optimization.
15	440	0.398960616606	Henry Cohn, 2024, needs more optimization.
15	441	0.399310652615	Henry Cohn, 2024, needs more optimization.
15	442	0.399360031775	Henry Cohn, 2024, needs more optimization.
15	443	0.399717194809	Henry Cohn, 2024, needs more optimization.
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	990	0.428571428572	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 3$
15	1024	0.459410961393	Henry Cohn, 2023, needs more optimization.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $18 x - 1$
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	0.074362231516	Henry Cohn, 2023.
16	40	0.077433436468	Henry Cohn, 2023, needs more optimization.
16	41	0.078328485376	Henry Cohn, 2023.
16	42	0.085144928730	Henry Cohn, 2023.
16	44	0.085376587737	Henry Cohn, 2023. $512 x^{2} - 32 x - 1$
16	45	0.090651346396	Henry Cohn, 2023. Minimal polynomial listed in plain text data
16	46	0.095441675774	Henry Cohn, 2023.
16	47	0.097487241491	Henry Cohn, 2023.
16	48	0.098771717854	Henry Cohn, 2023. $143 x^{2} - 4 x - 1$
16	49	0.108865229936	Henry Cohn, 2024, needs more optimization.
16	50	0.110920705754	Henry Cohn, 2023, needs more optimization.
16	51	0.111907199266	Henry Cohn, 2024.
16	52	0.112402936587	Henry Cohn, 2024, needs more optimization.
16	53	0.113355413340	Henry Cohn, 2023, needs more optimization.
16	54	0.115465335430	Henry Cohn, 2023, needs more optimization.
16	55	0.115467707901	Henry Cohn, 2023, needs more optimization.
16	56	0.115468483561	Henry Cohn, 2023, needs more optimization.
16	57	0.115468647073	Henry Cohn, 2023, needs more optimization.
16	58	0.115469159083	Henry Cohn, 2023, needs more optimization.
16	59	0.115469803431	Henry Cohn, 2023, needs more optimization.
16	60	0.115560598278	Henry Cohn, 2023. $6899200 x^{8} - 8279040 x^{7} - 1393024 x^{6} + 609792 x^{5} + 102576 x^{4} - 10560 x^{3} - 2560 x^{2} + 25$
16	61	0.120673431913	Henry Cohn, 2023, needs more optimization.
16	62	0.126589302315	Henry Cohn, 2024, needs more optimization.
16	74	0.127284656799	Henry Cohn, 2023. $156 x^{2} - 12 x - 1$
16	75	0.142525542301	Henry Cohn, 2024, needs more optimization.
16	76	0.157998142419	Henry Cohn, 2024, needs more optimization.
16	77	0.167184677105	Henry Cohn, 2024, needs more optimization.
16	94	0.168685175113	Code with 92 points in 15 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. $47 x^{2} - 2 x - 1$
16	95	0.198316307862	Henry Cohn, 2024, needs more optimization.
16	130	0.2	Code with 128 points in 15 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. $5 x - 1$
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	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	291	0.328885332565	Henry Cohn, 2024, needs more optimization.
16	294	0.329008178201	Henry Cohn, 2024, needs more optimization.
16	296	0.330316708584	Henry Cohn, 2024, needs more optimization.
16	298	0.330397905967	Henry Cohn, 2024, needs more optimization.
16	300	0.331871657845	Henry Cohn, 2024, needs more optimization.
16	512	0.333333333334	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
16	513	0.393443189459	Henry Cohn, 2024, needs more optimization.
16	514	0.393500503267	Henry Cohn, 2024, needs more optimization.
16	515	0.393814281393	Henry Cohn, 2024, needs more optimization.
16	516	0.393974089812	Henry Cohn, 2024, needs more optimization.
16	517	0.394006961285	Henry Cohn, 2024, needs more optimization.
16	518	0.394506602543	Henry Cohn, 2024, needs more optimization.
16	520	0.394738497756	Henry Cohn, 2024, needs more optimization.
16	521	0.394827518604	Henry Cohn, 2024, needs more optimization.
16	522	0.395482096230	Henry Cohn, 2024, needs more optimization.
16	523	0.395638001944	Henry Cohn, 2024, needs more optimization.
16	525	0.395745040495	Henry Cohn, 2024, needs more optimization.
16	528	0.396064608388	Henry Cohn, 2024, needs more optimization.
16	529	0.396469967636	Henry Cohn, 2024, needs more optimization.
16	530	0.396576932002	Henry Cohn, 2024, needs more optimization.
16	532	0.396818769177	Henry Cohn, 2024, needs more optimization.
16	533	0.397149843522	Henry Cohn, 2024, needs more optimization.
16	534	0.397408488565	Henry Cohn, 2024, needs more optimization.
16	535	0.397429031141	Henry Cohn, 2024, needs more optimization.
16	536	0.397687774658	Henry Cohn, 2024, needs more optimization.
16	538	0.397990773710	Henry Cohn, 2024, needs more optimization.
16	539	0.398385997032	Henry Cohn, 2024, needs more optimization.
16	541	0.398555132284	Henry Cohn, 2024, needs more optimization.
16	542	0.398765122447	Henry Cohn, 2024, needs more optimization.
16	543	0.398798812184	Henry Cohn, 2024, needs more optimization.
16	544	0.399100256750	Henry Cohn, 2024, needs more optimization.
16	545	0.399508928938	Henry Cohn, 2024, needs more optimization.
16	547	0.399738786490	Henry Cohn, 2024, needs more optimization.
16	548	0.399878896846	Henry Cohn, 2024, needs more optimization.
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	992	0.428571428572	Orthogonal union of 990 points in 15 dimensions and 2 points in 1 dimension. $7 x - 3$
16	993	0.454359120680	Henry Cohn, 2024, needs more optimization.
16	995	0.454412891126	Henry Cohn, 2024, needs more optimization.
16	996	0.454649411796	Henry Cohn, 2024, needs more optimization.
16	997	0.454892998764	Henry Cohn, 2024, needs more optimization.
16	998	0.454894115522	Henry Cohn, 2024, needs more optimization.
16	999	0.454921062467	Henry Cohn, 2024, needs more optimization.
16	1000	0.454928407368	Henry Cohn, 2024, needs more optimization.
16	1001	0.454962343308	Henry Cohn, 2024, needs more optimization.
16	1002	0.455244707787	Henry Cohn, 2024, needs more optimization.
16	1005	0.455380287216	Henry Cohn, 2024, needs more optimization.
16	1006	0.455517210464	Henry Cohn, 2024, needs more optimization.
16	1008	0.455542791687	Henry Cohn, 2024, needs more optimization.
16	1011	0.455685972460	Henry Cohn, 2024, needs more optimization.
16	1013	0.455843607042	Henry Cohn, 2024, needs more optimization.
16	1014	0.456133892602	Henry Cohn, 2024, needs more optimization.
16	1015	0.456257593979	Henry Cohn, 2024, needs more optimization.
16	1016	0.456365183210	Henry Cohn, 2024, needs more optimization.
16	1019	0.456455020559	Henry Cohn, 2024, needs more optimization.
16	1021	0.456588933387	Henry Cohn, 2024, needs more optimization.
16	1024	0.456714420511	Henry Cohn, 2024, needs more optimization.
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	0.052701900034	Henry Cohn, 2023.
17	37	0.055981544430	Henry Cohn, 2024, needs more optimization.
17	38	0.056002287699	Henry Cohn, 2024, needs more optimization.
17	39	0.062879658855	Henry Cohn, 2023.
17	40	0.064972486881	Henry Cohn, 2023, needs more optimization.
17	41	0.070153891671	Henry Cohn, 2023.
17	42	0.073342095231	Henry Cohn, 2023.
17	45	0.073591871415	Henry Cohn, 2023. $239 x^{2} - 4 x - 1$
17	52	0.084342587557	Henry Cohn, 2023. $188 x^{2} - 4 x - 1$
17	53	0.109398612694	Henry Cohn, 2023, needs more optimization.
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	76	0.127284656799	Orthogonal union of 74 points in 16 dimensions and 2 points in 1 dimension. $156 x^{2} - 12 x - 1$
17	77	0.129100425866	Henry Cohn, 2023, needs more optimization.
17	78	0.136013186656	Henry Cohn, 2024, needs more optimization.
17	79	0.151217244946	Henry Cohn, 2023, needs more optimization.
17	81	0.152829591661	Henry Cohn, 2024, needs more optimization.
17	82	0.158933006334	Henry Cohn, 2024, needs more optimization.
17	83	0.160501357004	Henry Cohn, 2024, needs more optimization.
17	84	0.166828528050	Henry Cohn, 2024, needs more optimization.
17	85	0.167822813901	Henry Cohn, 2024, needs more optimization.
17	96	0.168496723305	Henry Cohn, 2024, needs more optimization.
17	97	0.187581169621	Henry Cohn, 2024, needs more optimization.
17	98	0.188473550620	Henry Cohn, 2024, needs more optimization.
17	99	0.190236036405	Henry Cohn, 2024, needs more optimization.
17	100	0.191246908102	Henry Cohn, 2024, needs more optimization.
17	101	0.192344218530	Henry Cohn, 2024, needs more optimization.
17	102	0.193702524346	Henry Cohn, 2024, needs more optimization.
17	103	0.194559855113	Henry Cohn, 2024, needs more optimization.
17	104	0.195615208207	Henry Cohn, 2024, needs more optimization.
17	105	0.197387527149	Henry Cohn, 2024, needs more optimization.
17	106	0.197781706802	Henry Cohn, 2024, needs more optimization.
17	107	0.199326561219	Henry Cohn, 2024, needs more optimization.
17	108	0.199996931407	Henry Cohn, 2024, needs more optimization.
17	132	0.2	Code with 130 points in 16 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. $5 x - 1$
17	161	0.202913709779	Code with 159 points in 16 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. $44 x^{2} - 4 x - 1$
17	162	0.247738707955	Henry Cohn, 2024, needs more optimization.
17	163	0.248485495761	Henry Cohn, 2024, needs more optimization.
17	164	0.248856984641	Henry Cohn, 2024, needs more optimization.
17	165	0.249504870049	Henry Cohn, 2024, needs more optimization.
17	290	0.25	Code with 288 points in 16 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. $4 x - 1$
17	315	0.307692307693	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $13 x - 4$
17	320	0.322109427174	Henry Cohn, 2024, needs more optimization.
17	325	0.324038077469	Henry Cohn, 2024, needs more optimization.
17	326	0.324938822173	Henry Cohn, 2024, needs more optimization.
17	331	0.325065937041	Henry Cohn, 2024, needs more optimization.
17	335	0.325967643992	Henry Cohn, 2024, needs more optimization.
17	338	0.327635219930	Henry Cohn, 2024, needs more optimization.
17	339	0.328810491768	Henry Cohn, 2024, needs more optimization.
17	340	0.329230513928	Henry Cohn, 2024, needs more optimization.
17	343	0.329917553836	Henry Cohn, 2024, needs more optimization.
17	346	0.330121249666	Henry Cohn, 2024, needs more optimization.
17	348	0.331719987408	Henry Cohn, 2024, needs more optimization.
17	349	0.332507925522	Henry Cohn, 2024, needs more optimization.
17	350	0.332519049919	Henry Cohn, 2024, needs more optimization.
17	355	0.333086744253	Henry Cohn, 2024, needs more optimization.
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	553	0.347369928900	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $639 x^{2} - 150 x - 25$
17	554	0.381727073898	Henry Cohn, 2024, needs more optimization.
17	555	0.381861501497	Henry Cohn, 2024, needs more optimization.
17	557	0.382002686683	Henry Cohn, 2024, needs more optimization.
17	561	0.382644473446	Henry Cohn, 2024, needs more optimization.
17	562	0.383132503269	Henry Cohn, 2024, needs more optimization.
17	564	0.383162672435	Henry Cohn, 2024, needs more optimization.
17	566	0.383556319021	Henry Cohn, 2024, needs more optimization.
17	567	0.383592037395	Henry Cohn, 2024, needs more optimization.
17	568	0.383702281498	Henry Cohn, 2024, needs more optimization.
17	570	0.384236071913	Henry Cohn, 2024, needs more optimization.
17	571	0.384284966995	Henry Cohn, 2024, needs more optimization.
17	572	0.384918163374	Henry Cohn, 2024, needs more optimization.
17	576	0.385058753724	Henry Cohn, 2024, needs more optimization.
17	577	0.385558964620	Henry Cohn, 2024, needs more optimization.
17	579	0.385685623164	Henry Cohn, 2024, needs more optimization.
17	582	0.386167868652	Henry Cohn, 2024, needs more optimization.
17	583	0.386292432900	Henry Cohn, 2024, needs more optimization.
17	586	0.386711834374	Henry Cohn, 2024, needs more optimization.
17	587	0.387072182367	Henry Cohn, 2024, needs more optimization.
17	590	0.387347950724	Henry Cohn, 2024, needs more optimization.
17	591	0.387926400108	Henry Cohn, 2024, needs more optimization.
17	592	0.387986472300	Henry Cohn, 2024, needs more optimization.
17	594	0.388165959006	Henry Cohn, 2024, needs more optimization.
17	595	0.388271614376	Henry Cohn, 2024, needs more optimization.
17	597	0.388620722855	Henry Cohn, 2024, needs more optimization.
17	599	0.388880064728	Henry Cohn, 2024, needs more optimization.
17	600	0.388967003949	Henry Cohn, 2024, needs more optimization.
17	601	0.389412163346	Henry Cohn, 2024, needs more optimization.
17	603	0.389659133516	Henry Cohn, 2024, needs more optimization.
17	604	0.389926602927	Henry Cohn, 2024, needs more optimization.
17	607	0.390284318193	Henry Cohn, 2024, needs more optimization.
17	608	0.390428600491	Henry Cohn, 2024, needs more optimization.
17	609	0.390624418242	Henry Cohn, 2024, needs more optimization.
17	610	0.390641377010	Henry Cohn, 2024, needs more optimization.
17	611	0.390822633243	Henry Cohn, 2024, needs more optimization.
17	613	0.391060649978	Henry Cohn, 2024, needs more optimization.
17	614	0.391381850635	Henry Cohn, 2024, needs more optimization.
17	615	0.391439805897	Henry Cohn, 2024, needs more optimization.
17	616	0.391844928379	Henry Cohn, 2024, needs more optimization.
17	618	0.391959917357	Henry Cohn, 2024, needs more optimization.
17	621	0.392268584931	Henry Cohn, 2024, needs more optimization.
17	622	0.392318369775	Henry Cohn, 2024, needs more optimization.
17	624	0.392764714860	Henry Cohn, 2024, needs more optimization.
17	625	0.392894098373	Henry Cohn, 2024, needs more optimization.
17	627	0.393239445978	Henry Cohn, 2024, needs more optimization.
17	629	0.393474000133	Henry Cohn, 2024, needs more optimization.
17	630	0.393691823299	Henry Cohn, 2024, needs more optimization.
17	632	0.393883309237	Henry Cohn, 2024, needs more optimization.
17	633	0.394175218798	Henry Cohn, 2024, needs more optimization.
17	634	0.394298803689	Henry Cohn, 2024, needs more optimization.
17	637	0.394711856817	Henry Cohn, 2024, needs more optimization.
17	640	0.394947484369	Henry Cohn, 2024, needs more optimization.
17	642	0.395531636815	Henry Cohn, 2024, needs more optimization.
17	644	0.395579259925	Henry Cohn, 2024, needs more optimization.
17	646	0.395935135635	Henry Cohn, 2024, needs more optimization.
17	647	0.396054451855	Henry Cohn, 2024, needs more optimization.
17	649	0.396395441677	Henry Cohn, 2024, needs more optimization.
17	650	0.396658569624	Henry Cohn, 2024, needs more optimization.
17	651	0.396755111838	Henry Cohn, 2024, needs more optimization.
17	652	0.396867555241	Henry Cohn, 2024, needs more optimization.
17	653	0.396911934158	Henry Cohn, 2024, needs more optimization.
17	654	0.397330921979	Henry Cohn, 2024, needs more optimization.
17	658	0.397577064076	Henry Cohn, 2024, needs more optimization.
17	659	0.398038205274	Henry Cohn, 2024, needs more optimization.
17	660	0.398151001107	Henry Cohn, 2024, needs more optimization.
17	661	0.398196725294	Henry Cohn, 2024, needs more optimization.
17	662	0.398440147278	Henry Cohn, 2024, needs more optimization.
17	663	0.398552976601	Henry Cohn, 2024, needs more optimization.
17	664	0.398580521491	Henry Cohn, 2024, needs more optimization.
17	666	0.398780863832	Henry Cohn, 2024, needs more optimization.
17	668	0.399122450982	Henry Cohn, 2024, needs more optimization.
17	670	0.399475526431	Henry Cohn, 2024, needs more optimization.
17	672	0.399934995933	Henry Cohn, 2024, needs more optimization.
17	674	0.399939210113	Henry Cohn, 2024, needs more optimization.
17	770	0.4	Orthogonal union of 768 points in 16 dimensions and 2 points in 1 dimension. $5 x - 2$
17	771	0.412038230047	Henry Cohn, 2024, needs more optimization.
17	772	0.412201245094	Henry Cohn, 2024, needs more optimization.
17	773	0.412449486193	Henry Cohn, 2024, needs more optimization.
17	775	0.412563243620	Henry Cohn, 2024, needs more optimization.
17	776	0.412773329255	Henry Cohn, 2024, needs more optimization.
17	778	0.413148758448	Henry Cohn, 2024, needs more optimization.
17	781	0.413166278309	Henry Cohn, 2024, needs more optimization.
17	784	0.413652144766	Henry Cohn, 2024, needs more optimization.
17	786	0.413875685257	Henry Cohn, 2024, needs more optimization.
17	788	0.414025103590	Henry Cohn, 2024, needs more optimization.
17	790	0.414222362312	Henry Cohn, 2024, needs more optimization.
17	791	0.414599423590	Henry Cohn, 2024, needs more optimization.
17	793	0.414620332843	Henry Cohn, 2024, needs more optimization.
17	796	0.414821708020	Henry Cohn, 2024, needs more optimization.
17	797	0.415180289721	Henry Cohn, 2024, needs more optimization.
17	799	0.415413522892	Henry Cohn, 2024, needs more optimization.
17	800	0.415788794452	Henry Cohn, 2024, needs more optimization.
17	802	0.415807920272	Henry Cohn, 2024, needs more optimization.
17	804	0.415922372061	Henry Cohn, 2024, needs more optimization.
17	806	0.416001597464	Henry Cohn, 2024, needs more optimization.
17	807	0.416066402184	Henry Cohn, 2024, needs more optimization.
17	808	0.416194586493	Henry Cohn, 2024, needs more optimization.
17	812	0.416531942153	Henry Cohn, 2024, needs more optimization.
17	814	0.416889754319	Henry Cohn, 2024, needs more optimization.
17	816	0.417189039312	Henry Cohn, 2024, needs more optimization.
17	820	0.417453232457	Henry Cohn, 2024, needs more optimization.
17	823	0.417820359472	Henry Cohn, 2024, needs more optimization.
17	826	0.418340971011	Henry Cohn, 2024, needs more optimization.
17	827	0.418442058142	Henry Cohn, 2024, needs more optimization.
17	830	0.418610218535	Henry Cohn, 2024, needs more optimization.
17	831	0.418898165425	Henry Cohn, 2024, needs more optimization.
17	832	0.418900253527	Henry Cohn, 2024, needs more optimization.
17	835	0.419227933572	Henry Cohn, 2024, needs more optimization.
17	837	0.419416022360	Henry Cohn, 2024, needs more optimization.
17	839	0.419558230408	Henry Cohn, 2024, needs more optimization.
17	840	0.419834504503	Henry Cohn, 2024, needs more optimization.
17	842	0.420043780538	Henry Cohn, 2024, needs more optimization.
17	844	0.420377305439	Henry Cohn, 2024, needs more optimization.
17	846	0.420395968907	Henry Cohn, 2024, needs more optimization.
17	847	0.420593595552	Henry Cohn, 2024, needs more optimization.
17	848	0.420772296625	Henry Cohn, 2024, needs more optimization.
17	851	0.421105052272	Henry Cohn, 2024, needs more optimization.
17	852	0.421222776801	Henry Cohn, 2024, needs more optimization.
17	856	0.421391518726	Henry Cohn, 2024, needs more optimization.
17	858	0.421678872814	Henry Cohn, 2024, needs more optimization.
17	859	0.421864123271	Henry Cohn, 2024, needs more optimization.
17	860	0.422018334742	Henry Cohn, 2024, needs more optimization.
17	863	0.422047065076	Henry Cohn, 2024, needs more optimization.
17	866	0.422147126988	Henry Cohn, 2024, needs more optimization.
17	867	0.422789533342	Henry Cohn, 2024, needs more optimization.
17	868	0.422864176547	Henry Cohn, 2024, needs more optimization.
17	870	0.422992807258	Henry Cohn, 2024, needs more optimization.
17	874	0.423139038216	Henry Cohn, 2024, needs more optimization.
17	875	0.423352644065	Henry Cohn, 2024, needs more optimization.
17	876	0.423527630742	Henry Cohn, 2024, needs more optimization.
17	877	0.423649450255	Henry Cohn, 2024, needs more optimization.
17	878	0.423718602829	Henry Cohn, 2024, needs more optimization.
17	879	0.423848421122	Henry Cohn, 2024, needs more optimization.
17	881	0.423915066829	Henry Cohn, 2024, needs more optimization.
17	884	0.424179817042	Henry Cohn, 2024, needs more optimization.
17	885	0.424248093578	Henry Cohn, 2024, needs more optimization.
17	889	0.424554174299	Henry Cohn, 2024, needs more optimization.
17	892	0.424897098733	Henry Cohn, 2024, needs more optimization.
17	893	0.425271479382	Henry Cohn, 2024, needs more optimization.
17	896	0.425324698239	Henry Cohn, 2024, needs more optimization.
17	898	0.425798085271	Henry Cohn, 2024, needs more optimization.
17	901	0.425827645960	Henry Cohn, 2024, needs more optimization.
17	902	0.426193480786	Henry Cohn, 2024, needs more optimization.
17	903	0.426287626417	Henry Cohn, 2024, needs more optimization.
17	905	0.426407023999	Henry Cohn, 2024, needs more optimization.
17	908	0.426544393903	Henry Cohn, 2024, needs more optimization.
17	909	0.426762736147	Henry Cohn, 2024, needs more optimization.
17	911	0.426966398048	Henry Cohn, 2024, needs more optimization.
17	913	0.426990171392	Henry Cohn, 2024, needs more optimization.
17	916	0.427337510493	Henry Cohn, 2024, needs more optimization.
17	917	0.427341392678	Henry Cohn, 2024, needs more optimization.
17	920	0.427678474354	Henry Cohn, 2024, needs more optimization.
17	921	0.427943276536	Henry Cohn, 2024, needs more optimization.
17	922	0.428018687187	Henry Cohn, 2024, needs more optimization.
17	923	0.428170851510	Henry Cohn, 2024, needs more optimization.
17	925	0.428314865653	Henry Cohn, 2024, needs more optimization.
17	926	0.428366871739	Henry Cohn, 2024, needs more optimization.
17	927	0.428423217860	Henry Cohn, 2024, needs more optimization.
17	995	0.428571428572	Orthogonal union of 990 points in 15 dimensions and 5 points in 2 dimensions. $7 x - 3$
17	997	0.434709684307	Henry Cohn, 2024, needs more optimization.
17	998	0.434717902543	Henry Cohn, 2024, needs more optimization.
17	999	0.435126928540	Henry Cohn, 2024, needs more optimization.
17	1001	0.435140127073	Henry Cohn, 2024, needs more optimization.
17	1003	0.435304625189	Henry Cohn, 2024, needs more optimization.
17	1007	0.435319232478	Henry Cohn, 2024, needs more optimization.
17	1011	0.435678884176	Henry Cohn, 2024, needs more optimization.
17	1012	0.435804281607	Henry Cohn, 2024, needs more optimization.
17	1013	0.436127514640	Henry Cohn, 2024, needs more optimization.
17	1015	0.436156201525	Henry Cohn, 2024, needs more optimization.
17	1016	0.436475004943	Henry Cohn, 2024, needs more optimization.
17	1017	0.436566598203	Henry Cohn, 2024, needs more optimization.
17	1019	0.436601441586	Henry Cohn, 2024, needs more optimization.
17	1021	0.436609414377	Henry Cohn, 2024, needs more optimization.
17	1022	0.436889268531	Henry Cohn, 2024, needs more optimization.
17	1024	0.436902662142	Henry Cohn, 2024, needs more optimization.
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	0.050097355824	Henry Cohn, 2023.
18	39	0.055496642883	Henry Cohn, 2023.
18	40	0.055679405296	Henry Cohn, 2023.
18	41	0.060967744952	Henry Cohn, 2023.
18	42	0.063513513654	Henry Cohn, 2023.
18	43	0.066629786537	Henry Cohn, 2023, needs more optimization.
18	44	0.066804066179	Henry Cohn, 2023.
18	45	0.071480326622	Henry Cohn, 2023.
18	47	0.073591871415	Orthogonal union of 45 points in 17 dimensions and 2 points in 1 dimension. $239 x^{2} - 4 x - 1$
18	48	0.082747027414	Henry Cohn, 2023.
18	49	0.082860116302	Henry Cohn, 2024, needs more optimization.
18	50	0.084341943317	Henry Cohn, 2023, needs more optimization.
18	51	0.084342124103	Henry Cohn, 2023, needs more optimization.
18	52	0.084342528010	Henry Cohn, 2023, needs more optimization.
18	53	0.084342583739	Henry Cohn, 2023, needs more optimization.
18	54	0.084342585296	Henry Cohn, 2023, needs more optimization.
18	55	0.098432488663	Henry Cohn, 2023.
18	56	0.101019037261	Henry Cohn, 2024, needs more optimization.
18	68	0.101456854890	Henry Cohn, 2023. $176 x^{2} - 8 x - 1$
18	70	0.124437030169	Henry Cohn, 2024, needs more optimization.
18	71	0.126291553218	Henry Cohn, 2024, needs more optimization.
18	72	0.126735245261	Henry Cohn, 2023, needs more optimization.
18	78	0.127232218471	Henry Cohn, 2024, needs more optimization.
18	79	0.127505691760	Henry Cohn, 2023, needs more optimization.
18	80	0.132055656256	Henry Cohn, 2023, needs more optimization.
18	81	0.133243006269	Henry Cohn, 2023, needs more optimization.
18	85	0.134336803835	Henry Cohn, 2024, needs more optimization.
18	88	0.134690494495	Henry Cohn, 2023. $18 x^{2} + 5 x - 1$
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	98	0.166666666667	Kissing configuration of 192 points in 19 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $6 x - 1$
18	99	0.176657002223	Henry Cohn, 2024, needs more optimization.
18	100	0.178678611450	Henry Cohn, 2024, needs more optimization.
18	101	0.179747414903	Henry Cohn, 2024, needs more optimization.
18	102	0.180561912254	Henry Cohn, 2024, needs more optimization.
18	103	0.181782384802	Henry Cohn, 2024, needs more optimization.
18	104	0.183095085970	Henry Cohn, 2024, needs more optimization.
18	105	0.183761500612	Henry Cohn, 2024, needs more optimization.
18	106	0.185578417602	Henry Cohn, 2024, needs more optimization.
18	107	0.186064748882	Henry Cohn, 2024, needs more optimization.
18	108	0.186999015538	Henry Cohn, 2024, needs more optimization.
18	109	0.188289490261	Henry Cohn, 2024, needs more optimization.
18	110	0.189408874495	Henry Cohn, 2024, needs more optimization.
18	111	0.189985126187	Henry Cohn, 2024, needs more optimization.
18	112	0.191473371837	Henry Cohn, 2024, needs more optimization.
18	120	0.191489361703	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $47 x - 9$
18	144	0.2	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 1$
18	163	0.202913709779	Orthogonal union of 159 points in 16 dimensions and 4 points in 2 dimensions. $44 x^{2} - 4 x - 1$
18	168	0.224489795919	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $49 x - 11$
18	169	0.238537193027	Henry Cohn, 2024, needs more optimization.
18	170	0.238741233699	Henry Cohn, 2024, needs more optimization.
18	171	0.239406825990	Henry Cohn, 2024, needs more optimization.
18	172	0.239987408540	Henry Cohn, 2024, needs more optimization.
18	173	0.240647187594	Henry Cohn, 2024, needs more optimization.
18	174	0.241258168713	Henry Cohn, 2024, needs more optimization.
18	175	0.241774453833	Henry Cohn, 2024, needs more optimization.
18	176	0.242276463674	Henry Cohn, 2024, needs more optimization.
18	177	0.243060835307	Henry Cohn, 2024, needs more optimization.
18	178	0.243708413336	Henry Cohn, 2024, needs more optimization.
18	179	0.244142141634	Henry Cohn, 2024, needs more optimization.
18	180	0.244918953850	Henry Cohn, 2024, needs more optimization.
18	181	0.245468396533	Henry Cohn, 2024, needs more optimization.
18	182	0.246081490481	Henry Cohn, 2024, needs more optimization.
18	183	0.246568110530	Henry Cohn, 2024, needs more optimization.
18	184	0.246895134308	Henry Cohn, 2024, needs more optimization.
18	185	0.247681329941	Henry Cohn, 2024, needs more optimization.
18	186	0.248250249573	Henry Cohn, 2024, needs more optimization.
18	187	0.248478066067	Henry Cohn, 2024, needs more optimization.
18	188	0.249319196303	Henry Cohn, 2024, needs more optimization.
18	189	0.249967307862	Henry Cohn, 2024, needs more optimization.
18	292	0.25	Code with 290 points in 17 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. $4 x - 1$
18	364	0.296296296297	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $27 x - 8$
18	366	0.320742110346	Henry Cohn, 2024, needs more optimization.
18	367	0.320876584990	Henry Cohn, 2024, needs more optimization.
18	369	0.321696385799	Henry Cohn, 2024, needs more optimization.
18	370	0.321734041571	Henry Cohn, 2024, needs more optimization.
18	372	0.322222516098	Henry Cohn, 2024, needs more optimization.
18	373	0.322498387135	Henry Cohn, 2024, needs more optimization.
18	374	0.323721019077	Henry Cohn, 2024, needs more optimization.
18	379	0.323998004033	Henry Cohn, 2024, needs more optimization.
18	383	0.324848247303	Henry Cohn, 2024, needs more optimization.
18	384	0.325388805678	Henry Cohn, 2024, needs more optimization.
18	389	0.326469132049	Henry Cohn, 2024, needs more optimization.
18	393	0.327525178204	Henry Cohn, 2024, needs more optimization.
18	394	0.327996881788	Henry Cohn, 2024, needs more optimization.
18	395	0.328803172543	Henry Cohn, 2024, needs more optimization.
18	397	0.329156519201	Henry Cohn, 2024, needs more optimization.
18	400	0.329947517947	Henry Cohn, 2024, needs more optimization.
18	401	0.330302650242	Henry Cohn, 2024, needs more optimization.
18	405	0.330737891907	Henry Cohn, 2024, needs more optimization.
18	406	0.331400454905	Henry Cohn, 2024, needs more optimization.
18	408	0.331985187710	Henry Cohn, 2024, needs more optimization.
18	409	0.332467462827	Henry Cohn, 2024, needs more optimization.
18	412	0.332937370950	Henry Cohn, 2024, needs more optimization.
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	675	0.382142923873	Henry Cohn, 2024, needs more optimization.
18	676	0.382202149475	Henry Cohn, 2024, needs more optimization.
18	680	0.382715938698	Henry Cohn, 2024, needs more optimization.
18	681	0.383193806956	Henry Cohn, 2024, needs more optimization.
18	682	0.383230994509	Henry Cohn, 2024, needs more optimization.
18	684	0.383490345654	Henry Cohn, 2024, needs more optimization.
18	685	0.383579516271	Henry Cohn, 2024, needs more optimization.
18	686	0.383800508465	Henry Cohn, 2024, needs more optimization.
18	687	0.383886911322	Henry Cohn, 2024, needs more optimization.
18	688	0.384028417611	Henry Cohn, 2024, needs more optimization.
18	689	0.384281436595	Henry Cohn, 2024, needs more optimization.
18	691	0.384403904927	Henry Cohn, 2024, needs more optimization.
18	692	0.384532770226	Henry Cohn, 2024, needs more optimization.
18	693	0.384672278547	Henry Cohn, 2024, needs more optimization.
18	694	0.384692581058	Henry Cohn, 2024, needs more optimization.
18	695	0.384985783497	Henry Cohn, 2024, needs more optimization.
18	696	0.385038388725	Henry Cohn, 2024, needs more optimization.
18	698	0.385380469940	Henry Cohn, 2024, needs more optimization.
18	699	0.385797163101	Henry Cohn, 2024, needs more optimization.
18	701	0.385857129267	Henry Cohn, 2024, needs more optimization.
18	702	0.385868198579	Henry Cohn, 2024, needs more optimization.
18	704	0.385892784616	Henry Cohn, 2024, needs more optimization.
18	705	0.386361736598	Henry Cohn, 2024, needs more optimization.
18	706	0.386644829340	Henry Cohn, 2024, needs more optimization.
18	708	0.386730852249	Henry Cohn, 2024, needs more optimization.
18	709	0.386739365227	Henry Cohn, 2024, needs more optimization.
18	710	0.386963013400	Henry Cohn, 2024, needs more optimization.
18	711	0.387223730071	Henry Cohn, 2024, needs more optimization.
18	714	0.387228673982	Henry Cohn, 2024, needs more optimization.
18	715	0.387707597762	Henry Cohn, 2024, needs more optimization.
18	716	0.387735063235	Henry Cohn, 2024, needs more optimization.
18	718	0.387913804297	Henry Cohn, 2024, needs more optimization.
18	721	0.388079274832	Henry Cohn, 2024, needs more optimization.
18	722	0.388436549065	Henry Cohn, 2024, needs more optimization.
18	723	0.388616828770	Henry Cohn, 2024, needs more optimization.
18	724	0.388665435219	Henry Cohn, 2024, needs more optimization.
18	726	0.388873634544	Henry Cohn, 2024, needs more optimization.
18	727	0.389114978861	Henry Cohn, 2024, needs more optimization.
18	728	0.389170586020	Henry Cohn, 2024, needs more optimization.
18	730	0.389330356292	Henry Cohn, 2024, needs more optimization.
18	731	0.389554745895	Henry Cohn, 2024, needs more optimization.
18	733	0.389768020649	Henry Cohn, 2024, needs more optimization.
18	734	0.389942858978	Henry Cohn, 2024, needs more optimization.
18	735	0.390290031974	Henry Cohn, 2024, needs more optimization.
18	738	0.390313861573	Henry Cohn, 2024, needs more optimization.
18	739	0.390335790413	Henry Cohn, 2024, needs more optimization.
18	740	0.390359413753	Henry Cohn, 2024, needs more optimization.
18	741	0.390860650938	Henry Cohn, 2024, needs more optimization.
18	745	0.390943879933	Henry Cohn, 2024, needs more optimization.
18	746	0.391444638870	Henry Cohn, 2024, needs more optimization.
18	747	0.391491200463	Henry Cohn, 2024, needs more optimization.
18	748	0.391810120289	Henry Cohn, 2024, needs more optimization.
18	750	0.391829435671	Henry Cohn, 2024, needs more optimization.
18	752	0.392021063393	Henry Cohn, 2024, needs more optimization.
18	754	0.392188204511	Henry Cohn, 2024, needs more optimization.
18	757	0.392353130681	Henry Cohn, 2024, needs more optimization.
18	758	0.392755353780	Henry Cohn, 2024, needs more optimization.
18	761	0.392941975224	Henry Cohn, 2024, needs more optimization.
18	762	0.393302080048	Henry Cohn, 2024, needs more optimization.
18	763	0.393486151686	Henry Cohn, 2024, needs more optimization.
18	764	0.393516187306	Henry Cohn, 2024, needs more optimization.
18	765	0.393582290906	Henry Cohn, 2024, needs more optimization.
18	767	0.393744694391	Henry Cohn, 2024, needs more optimization.
18	768	0.393760324017	Henry Cohn, 2024, needs more optimization.
18	770	0.394097609975	Henry Cohn, 2024, needs more optimization.
18	771	0.394246091799	Henry Cohn, 2024, needs more optimization.
18	773	0.394330431277	Henry Cohn, 2024, needs more optimization.
18	775	0.394528536564	Henry Cohn, 2024, needs more optimization.
18	776	0.394849837055	Henry Cohn, 2024, needs more optimization.
18	779	0.394914404855	Henry Cohn, 2024, needs more optimization.
18	780	0.395066580522	Henry Cohn, 2024, needs more optimization.
18	781	0.395454116091	Henry Cohn, 2024, needs more optimization.
18	784	0.395493176436	Henry Cohn, 2024, needs more optimization.
18	785	0.395536981061	Henry Cohn, 2024, needs more optimization.
18	787	0.395947021758	Henry Cohn, 2024, needs more optimization.
18	788	0.396163586513	Henry Cohn, 2024, needs more optimization.
18	790	0.396401032641	Henry Cohn, 2024, needs more optimization.
18	791	0.396582048273	Henry Cohn, 2024, needs more optimization.
18	792	0.396677515004	Henry Cohn, 2024, needs more optimization.
18	793	0.396774580429	Henry Cohn, 2024, needs more optimization.
18	796	0.396902458963	Henry Cohn, 2024, needs more optimization.
18	798	0.397164374182	Henry Cohn, 2024, needs more optimization.
18	799	0.397250865082	Henry Cohn, 2024, needs more optimization.
18	800	0.397344960638	Henry Cohn, 2024, needs more optimization.
18	801	0.397521126339	Henry Cohn, 2024, needs more optimization.
18	803	0.397660514969	Henry Cohn, 2024, needs more optimization.
18	804	0.398081402826	Henry Cohn, 2024, needs more optimization.
18	806	0.398363396762	Henry Cohn, 2024, needs more optimization.
18	807	0.398447249750	Henry Cohn, 2024, needs more optimization.
18	811	0.398587971656	Henry Cohn, 2024, needs more optimization.
18	813	0.398861905894	Henry Cohn, 2024, needs more optimization.
18	814	0.399090334485	Henry Cohn, 2024, needs more optimization.
18	816	0.399257989217	Henry Cohn, 2024, needs more optimization.
18	817	0.399399093150	Henry Cohn, 2024, needs more optimization.
18	819	0.399565047151	Henry Cohn, 2024, needs more optimization.
18	820	0.399782470090	Henry Cohn, 2024, needs more optimization.
18	823	0.400012743719	Henry Cohn, 2024, needs more optimization.
18	824	0.400130338043	Henry Cohn, 2024, needs more optimization.
18	826	0.400272052483	Henry Cohn, 2024, needs more optimization.
18	827	0.400349667976	Henry Cohn, 2024, needs more optimization.
18	828	0.400482734888	Henry Cohn, 2024, needs more optimization.
18	829	0.400743192574	Henry Cohn, 2024, needs more optimization.
18	832	0.400781138026	Henry Cohn, 2024, needs more optimization.
18	834	0.401159758420	Henry Cohn, 2024, needs more optimization.
18	835	0.401177713973	Henry Cohn, 2024, needs more optimization.
18	838	0.401478575234	Henry Cohn, 2024, needs more optimization.
18	839	0.401811430144	Henry Cohn, 2024, needs more optimization.
18	842	0.401905953249	Henry Cohn, 2024, needs more optimization.
18	844	0.402074410431	Henry Cohn, 2024, needs more optimization.
18	845	0.402291613993	Henry Cohn, 2024, needs more optimization.
18	846	0.402470643821	Henry Cohn, 2024, needs more optimization.
18	850	0.402544372853	Henry Cohn, 2024, needs more optimization.
18	851	0.402872999392	Henry Cohn, 2024, needs more optimization.
18	853	0.403026569874	Henry Cohn, 2024, needs more optimization.
18	855	0.403234563288	Henry Cohn, 2024, needs more optimization.
18	858	0.403633348837	Henry Cohn, 2024, needs more optimization.
18	859	0.403813599919	Henry Cohn, 2024, needs more optimization.
18	861	0.403934970638	Henry Cohn, 2024, needs more optimization.
18	864	0.404146154357	Henry Cohn, 2024, needs more optimization.
18	866	0.404243120326	Henry Cohn, 2024, needs more optimization.
18	868	0.404480979810	Henry Cohn, 2024, needs more optimization.
18	869	0.404814412013	Henry Cohn, 2024, needs more optimization.
18	871	0.404860131430	Henry Cohn, 2024, needs more optimization.
18	872	0.404934378238	Henry Cohn, 2024, needs more optimization.
18	874	0.404943335401	Henry Cohn, 2024, needs more optimization.
18	876	0.405323933396	Henry Cohn, 2024, needs more optimization.
18	879	0.405451059230	Henry Cohn, 2024, needs more optimization.
18	882	0.405861383599	Henry Cohn, 2024, needs more optimization.
18	884	0.406208919820	Henry Cohn, 2024, needs more optimization.
18	886	0.406411852575	Henry Cohn, 2024, needs more optimization.
18	887	0.406693455981	Henry Cohn, 2024, needs more optimization.
18	888	0.406731662579	Henry Cohn, 2024, needs more optimization.
18	893	0.406768715817	Henry Cohn, 2024, needs more optimization.
18	894	0.407072481723	Henry Cohn, 2024, needs more optimization.
18	896	0.407286205938	Henry Cohn, 2024, needs more optimization.
18	897	0.407520103794	Henry Cohn, 2024, needs more optimization.
18	898	0.407741652060	Henry Cohn, 2024, needs more optimization.
18	900	0.407805151558	Henry Cohn, 2024, needs more optimization.
18	901	0.407933974059	Henry Cohn, 2024, needs more optimization.
18	902	0.407997250882	Henry Cohn, 2024, needs more optimization.
18	905	0.408172545418	Henry Cohn, 2024, needs more optimization.
18	907	0.408494068582	Henry Cohn, 2024, needs more optimization.
18	909	0.408604614614	Henry Cohn, 2024, needs more optimization.
18	911	0.408735058921	Henry Cohn, 2024, needs more optimization.
18	912	0.408770728698	Henry Cohn, 2024, needs more optimization.
18	913	0.408955611870	Henry Cohn, 2024, needs more optimization.
18	914	0.409357075241	Henry Cohn, 2024, needs more optimization.
18	915	0.409436116205	Henry Cohn, 2024, needs more optimization.
18	917	0.409477036115	Henry Cohn, 2024, needs more optimization.
18	919	0.409635888772	Henry Cohn, 2024, needs more optimization.
18	921	0.409706986423	Henry Cohn, 2024, needs more optimization.
18	922	0.409870244927	Henry Cohn, 2024, needs more optimization.
18	923	0.410086104121	Henry Cohn, 2024, needs more optimization.
18	927	0.410093902076	Henry Cohn, 2024, needs more optimization.
18	928	0.410466394450	Henry Cohn, 2024, needs more optimization.
18	930	0.410534561249	Henry Cohn, 2024, needs more optimization.
18	932	0.410661096232	Henry Cohn, 2024, needs more optimization.
18	935	0.411039805353	Henry Cohn, 2024, needs more optimization.
18	937	0.411322234538	Henry Cohn, 2024, needs more optimization.
18	939	0.411424747145	Henry Cohn, 2024, needs more optimization.
18	940	0.411568451826	Henry Cohn, 2024, needs more optimization.
18	944	0.411741042548	Henry Cohn, 2024, needs more optimization.
18	946	0.411856730126	Henry Cohn, 2024, needs more optimization.
18	948	0.412258846512	Henry Cohn, 2024, needs more optimization.
18	951	0.412451953154	Henry Cohn, 2024, needs more optimization.
18	952	0.412588389152	Henry Cohn, 2024, needs more optimization.
18	953	0.412673392911	Henry Cohn, 2024, needs more optimization.
18	954	0.412900320334	Henry Cohn, 2024, needs more optimization.
18	959	0.412958817496	Henry Cohn, 2024, needs more optimization.
18	960	0.413049890437	Henry Cohn, 2024, needs more optimization.
18	961	0.413459084632	Henry Cohn, 2024, needs more optimization.
18	964	0.413486696118	Henry Cohn, 2024, needs more optimization.
18	965	0.413837544263	Henry Cohn, 2024, needs more optimization.
18	968	0.413891040548	Henry Cohn, 2024, needs more optimization.
18	969	0.414099856215	Henry Cohn, 2024, needs more optimization.
18	970	0.414170270898	Henry Cohn, 2024, needs more optimization.
18	972	0.414334037524	Henry Cohn, 2024, needs more optimization.
18	975	0.414508069057	Henry Cohn, 2024, needs more optimization.
18	977	0.414886137310	Henry Cohn, 2024, needs more optimization.
18	979	0.414932276509	Henry Cohn, 2024, needs more optimization.
18	980	0.415061715126	Henry Cohn, 2024, needs more optimization.
18	982	0.415125639043	Henry Cohn, 2024, needs more optimization.
18	984	0.415410232025	Henry Cohn, 2024, needs more optimization.
18	988	0.415550952501	Henry Cohn, 2024, needs more optimization.
18	989	0.415870828619	Henry Cohn, 2024, needs more optimization.
18	991	0.416021202407	Henry Cohn, 2024, needs more optimization.
18	992	0.416206763467	Henry Cohn, 2024, needs more optimization.
18	993	0.416365839646	Henry Cohn, 2024, needs more optimization.
18	994	0.416381065267	Henry Cohn, 2024, needs more optimization.
18	996	0.416414007226	Henry Cohn, 2024, needs more optimization.
18	1000	0.416535748430	Henry Cohn, 2024, needs more optimization.
18	1003	0.416783580293	Henry Cohn, 2024, needs more optimization.
18	1004	0.417195197794	Henry Cohn, 2024, needs more optimization.
18	1005	0.417214460864	Henry Cohn, 2024, needs more optimization.
18	1008	0.417385984771	Henry Cohn, 2024, needs more optimization.
18	1009	0.417774768291	Henry Cohn, 2024, needs more optimization.
18	1010	0.417796729656	Henry Cohn, 2024, needs more optimization.
18	1011	0.417886190979	Henry Cohn, 2024, needs more optimization.
18	1014	0.417918343771	Henry Cohn, 2024, needs more optimization.
18	1017	0.417924976976	Henry Cohn, 2024, needs more optimization.
18	1018	0.418152654104	Henry Cohn, 2024, needs more optimization.
18	1022	0.418468104840	Henry Cohn, 2024, needs more optimization.
18	1023	0.418536813051	Henry Cohn, 2024, needs more optimization.
18	1024	0.418647742045	Henry Cohn, 2024, needs more optimization.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $21 x - 1$
19	41	0.053165944699	Henry Cohn, 2023.
19	42	0.053978485862	Henry Cohn, 2023, needs more optimization.
19	43	0.058595441995	Henry Cohn, 2023, needs more optimization.
19	44	0.059131790994	Henry Cohn, 2023.
19	45	0.059418524383	Henry Cohn, 2023. Minimal polynomial listed in plain text data
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	0.077594348811	Henry Cohn, 2024, needs more optimization.
19	54	0.083013020962	Henry Cohn, 2023. $4106112 x^{6} + 374816 x^{5} - 59109 x^{4} + 1188 x^{3} - 6 x^{2} - 44 x + 3$
19	55	0.084302428993	Henry Cohn, 2024, needs more optimization.
19	56	0.084324397116	Henry Cohn, 2024, needs more optimization.
19	57	0.090617815907	Henry Cohn, 2024, needs more optimization.
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	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	70	0.101456854890	Orthogonal union of 68 points in 18 dimensions and 2 points in 1 dimension. $176 x^{2} - 8 x - 1$
19	72	0.111111111112	Kissing configuration of 105 points in 20 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $9 x - 1$
19	89	0.112912613537	Henry Cohn, 2023. $167 x^{2} - 10 x - 1$
19	90	0.121308037796	Henry Cohn, 2024.
19	102	0.142857142858	Henry Cohn, 2023. $7 x - 1$
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	140	0.191176470589	Kissing configuration of 378 points in 20 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $68 x - 13$
19	160	0.191919191920	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $99 x - 19$
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	240	0.230769230770	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $13 x - 3$
19	294	0.25	Code with 292 points in 18 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. $4 x - 1$
19	295	0.25	Orthogonal union of 288 points in 16 dimensions and 7 points in 3 dimensions. $4 x - 1$
19	296	0.261203874964	Orthogonal union of 288 points in 16 dimensions and 8 points in 3 dimensions. $7 x^{2} + 2 x - 1$
19	297	0.287145797248	Henry Cohn, 2024, needs more optimization.
19	299	0.287869795969	Henry Cohn, 2024, needs more optimization.
19	300	0.288491505356	Henry Cohn, 2024, needs more optimization.
19	301	0.288854777085	Henry Cohn, 2024, needs more optimization.
19	302	0.288996441769	Henry Cohn, 2024, needs more optimization.
19	303	0.289341634798	Henry Cohn, 2024, needs more optimization.
19	305	0.290021314680	Henry Cohn, 2024, needs more optimization.
19	306	0.290339955951	Henry Cohn, 2024, needs more optimization.
19	307	0.291055518549	Henry Cohn, 2024, needs more optimization.
19	309	0.291329090639	Henry Cohn, 2024, needs more optimization.
19	310	0.291881088607	Henry Cohn, 2024, needs more optimization.
19	312	0.292263444969	Henry Cohn, 2024, needs more optimization.
19	313	0.292747134075	Henry Cohn, 2024, needs more optimization.
19	314	0.292948789867	Henry Cohn, 2024, needs more optimization.
19	317	0.293800985760	Henry Cohn, 2024, needs more optimization.
19	318	0.294466632430	Henry Cohn, 2024, needs more optimization.
19	320	0.294554825180	Henry Cohn, 2024, needs more optimization.
19	322	0.295277376894	Henry Cohn, 2024, needs more optimization.
19	323	0.295825394341	Henry Cohn, 2024, needs more optimization.
19	366	0.296296296297	Orthogonal union of 364 points in 18 dimensions and 2 points in 1 dimension. $27 x - 8$
19	560	0.304347826087	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $23 x - 7$
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	0.390834643812	Henry Cohn, 2024, needs more optimization.
19	901	0.391030500965	Henry Cohn, 2024, needs more optimization.
19	902	0.391380459985	Henry Cohn, 2024, needs more optimization.
19	903	0.391382187600	Henry Cohn, 2024, needs more optimization.
19	904	0.391400799372	Henry Cohn, 2024, needs more optimization.
19	906	0.391559066154	Henry Cohn, 2024, needs more optimization.
19	907	0.391707435412	Henry Cohn, 2024, needs more optimization.
19	908	0.391921316849	Henry Cohn, 2024, needs more optimization.
19	911	0.392102584130	Henry Cohn, 2024, needs more optimization.
19	912	0.392301156900	Henry Cohn, 2024, needs more optimization.
19	914	0.392450788785	Henry Cohn, 2024, needs more optimization.
19	915	0.392642258346	Henry Cohn, 2024, needs more optimization.
19	917	0.392713050951	Henry Cohn, 2024, needs more optimization.
19	919	0.392954829683	Henry Cohn, 2024, needs more optimization.
19	922	0.393013851609	Henry Cohn, 2024, needs more optimization.
19	923	0.393387453959	Henry Cohn, 2024, needs more optimization.
19	925	0.393443142904	Henry Cohn, 2024, needs more optimization.
19	926	0.393605995930	Henry Cohn, 2024, needs more optimization.
19	927	0.393773585459	Henry Cohn, 2024, needs more optimization.
19	928	0.393816574004	Henry Cohn, 2024, needs more optimization.
19	929	0.393872777427	Henry Cohn, 2024, needs more optimization.
19	930	0.394002714050	Henry Cohn, 2024, needs more optimization.
19	931	0.394147354779	Henry Cohn, 2024, needs more optimization.
19	933	0.394288914011	Henry Cohn, 2024, needs more optimization.
19	935	0.394414717215	Henry Cohn, 2024, needs more optimization.
19	937	0.394666636155	Henry Cohn, 2024, needs more optimization.
19	940	0.394769435486	Henry Cohn, 2024, needs more optimization.
19	943	0.395046159683	Henry Cohn, 2024, needs more optimization.
19	945	0.395328274573	Henry Cohn, 2024, needs more optimization.
19	948	0.395500530653	Henry Cohn, 2024, needs more optimization.
19	950	0.395671720856	Henry Cohn, 2024, needs more optimization.
19	951	0.395710396579	Henry Cohn, 2024, needs more optimization.
19	952	0.395795312276	Henry Cohn, 2024, needs more optimization.
19	953	0.396062339948	Henry Cohn, 2024, needs more optimization.
19	955	0.396281302926	Henry Cohn, 2024, needs more optimization.
19	957	0.396300490649	Henry Cohn, 2024, needs more optimization.
19	960	0.396477079690	Henry Cohn, 2024, needs more optimization.
19	963	0.396867665930	Henry Cohn, 2024, needs more optimization.
19	965	0.397013816148	Henry Cohn, 2024, needs more optimization.
19	966	0.397191225997	Henry Cohn, 2024, needs more optimization.
19	967	0.397218266664	Henry Cohn, 2024, needs more optimization.
19	969	0.397431807941	Henry Cohn, 2024, needs more optimization.
19	971	0.397555405911	Henry Cohn, 2024, needs more optimization.
19	972	0.397779247360	Henry Cohn, 2024, needs more optimization.
19	974	0.397779552473	Henry Cohn, 2024, needs more optimization.
19	975	0.397911818010	Henry Cohn, 2024, needs more optimization.
19	976	0.397979801663	Henry Cohn, 2024, needs more optimization.
19	978	0.398210534166	Henry Cohn, 2024, needs more optimization.
19	979	0.398237622934	Henry Cohn, 2024, needs more optimization.
19	981	0.398461075292	Henry Cohn, 2024, needs more optimization.
19	982	0.398630724417	Henry Cohn, 2024, needs more optimization.
19	983	0.398733171399	Henry Cohn, 2024, needs more optimization.
19	984	0.398809830537	Henry Cohn, 2024, needs more optimization.
19	987	0.398932392475	Henry Cohn, 2024, needs more optimization.
19	989	0.399056393246	Henry Cohn, 2024, needs more optimization.
19	990	0.399291901661	Henry Cohn, 2024, needs more optimization.
19	994	0.399421456974	Henry Cohn, 2024, needs more optimization.
19	995	0.399581128586	Henry Cohn, 2024, needs more optimization.
19	998	0.399765495260	Henry Cohn, 2024, needs more optimization.
19	999	0.400013260014	Henry Cohn, 2024, needs more optimization.
19	1000	0.400027098738	Henry Cohn, 2024, needs more optimization.
19	1002	0.400279351183	Henry Cohn, 2024, needs more optimization.
19	1004	0.400384385796	Henry Cohn, 2024, needs more optimization.
19	1005	0.400424827962	Henry Cohn, 2024, needs more optimization.
19	1008	0.400634859202	Henry Cohn, 2024, needs more optimization.
19	1009	0.400933800860	Henry Cohn, 2024, needs more optimization.
19	1011	0.401062908249	Henry Cohn, 2024, needs more optimization.
19	1013	0.401084843939	Henry Cohn, 2024, needs more optimization.
19	1014	0.401275796358	Henry Cohn, 2024, needs more optimization.
19	1016	0.401346431047	Henry Cohn, 2024, needs more optimization.
19	1017	0.401563435972	Henry Cohn, 2024, needs more optimization.
19	1018	0.401676609780	Henry Cohn, 2024, needs more optimization.
19	1019	0.401679034998	Henry Cohn, 2024, needs more optimization.
19	1021	0.401681432165	Henry Cohn, 2024, needs more optimization.
19	1023	0.401879787697	Henry Cohn, 2024, needs more optimization.
19	1024	0.401890927906	Henry Cohn, 2024, needs more optimization.
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	0.051780672521	Henry Cohn, 2023, needs more optimization.
20	44	0.051781487230	Henry Cohn, 2023.
20	45	0.053400898990	Henry Cohn, 2023. Minimal polynomial listed in plain text data
20	46	0.053974615158	Henry Cohn, 2023, needs more optimization.
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 listed in plain text data
20	50	0.063705168064	Henry Cohn, 2024, needs more optimization.
20	56*	0.066666666667	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. $15 x - 1$
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	68	0.097744360903	Code with 66 points in 19 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. $133 x - 13$
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	91	0.112912613537	Orthogonal union of 89 points in 19 dimensions and 2 points in 1 dimension. $167 x^{2} - 10 x - 1$
20	92	0.121308037796	Orthogonal union of 90 points in 19 dimensions and 2 points in 1 dimension.
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	120	0.142857142858	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $7 x - 1$
20	141	0.157693167973	Henry Cohn, 2024, needs more optimization.
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	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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $5 x - 1$
20	294	0.220695461526	Henry Cohn, 2024, needs more optimization.
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	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	0.297501339774	Henry Cohn, 2024, needs more optimization.
20	381	0.297916518714	Henry Cohn, 2024, needs more optimization.
20	384	0.298317474183	Henry Cohn, 2024, needs more optimization.
20	385	0.299375942814	Henry Cohn, 2024, needs more optimization.
20	389	0.299897807252	Henry Cohn, 2024, needs more optimization.
20	391	0.300613148766	Henry Cohn, 2024, needs more optimization.
20	392	0.300853249456	Henry Cohn, 2024, needs more optimization.
20	394	0.301164917705	Henry Cohn, 2024, needs more optimization.
20	395	0.301491950219	Henry Cohn, 2024, needs more optimization.
20	396	0.301800064861	Henry Cohn, 2024, needs more optimization.
20	397	0.302060830552	Henry Cohn, 2024, needs more optimization.
20	398	0.302170969526	Henry Cohn, 2024, needs more optimization.
20	400	0.302251720875	Henry Cohn, 2024, needs more optimization.
20	403	0.302959191426	Henry Cohn, 2024, needs more optimization.
20	404	0.303441637813	Henry Cohn, 2024, needs more optimization.
20	405	0.303802401876	Henry Cohn, 2024, needs more optimization.
20	406	0.303982522923	Henry Cohn, 2024, needs more optimization.
20	562	0.304347826087	Orthogonal union of 560 points in 19 dimensions and 2 points in 1 dimension. $23 x - 7$
20	896	0.311475409837	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $61 x - 19$
20	1024	0.333333333334	Subcode of a code of size 1280 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $3 x - 1$
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	0.058803648698	Henry Cohn, 2023, needs more optimization.
21	52	0.062643510087	Henry Cohn, 2023.
21	58	0.066666666667	Code with 56 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. $15 x - 1$
21	62	0.076923076924	Orthogonal union of 60 points in 20 dimensions and 2 points in 1 dimension. $13 x - 1$
21	65	0.081967213115	Code with 63 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. $61 x - 5$
21	77*	0.083333333334	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. $12 x - 1$
21	83	0.1	Orthogonal union of 81 points in 20 dimensions and 2 points in 1 dimension. $10 x - 1$
21	84	0.108710739022	Henry Cohn, 2024, needs more optimization.
21	87	0.108710836915	Henry Cohn, 2024, needs more optimization.
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	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	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	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	210	0.189189189190	Kissing configuration of 529 points in 22 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $37 x - 7$
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	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	380	0.236363636364	Orthogonal union of 378 points in 20 dimensions and 2 points in 1 dimension. $55 x - 13$
21	554	0.238095238096	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $21 x - 5$
21	660	0.266666666667	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $15 x - 4$
21	716	0.272727272728	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 3$
21	898	0.311475409837	Orthogonal union of 896 points in 20 dimensions and 2 points in 1 dimension. $61 x - 19$
21	1024	0.3125	Subcode of a code of size 1232 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $16 x - 5$
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	0.041709069258	Henry Cohn, 2023, needs more optimization.
22	47	0.047589364249	Henry Cohn, 2023, needs more optimization.
22	48	0.047607974313	Henry Cohn, 2023, needs more optimization.
22	52	0.047619047620	Code with 50 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. $21 x - 1$
22	53	0.057560345703	Henry Cohn, 2023, needs more optimization.
22	54	0.060109536348	Henry Cohn, 2023, needs more optimization.
22	55	0.064389502899	Henry Cohn, 2023, needs more optimization.
22	60	0.066665580263	Henry Cohn, 2024, needs more optimization.
22	61	0.076913768821	Henry Cohn, 2023, needs more optimization.
22	62	0.076920313946	Henry Cohn, 2023, needs more optimization.
22	63	0.076920526653	Henry Cohn, 2023, needs more optimization.
22	64	0.076921771593	Henry Cohn, 2023, needs more optimization.
22	67	0.081899690574	Henry Cohn, 2024, needs more optimization.
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	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	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	121	0.131782945737	Code with 119 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. $129 x - 17$
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	164	0.142857142858	Code with 162 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. $7 x - 1$
22	200	0.161904761905	Code with 198 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. $105 x - 17$
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	338	0.2	Code with 336 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. $5 x - 1$
22	506	0.232142857143	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $56 x - 13$
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	556	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 2 points in 1 dimension. $21 x - 5$
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	Subcode of a code of size 1068 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $11 x - 3$
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	0.040044426627	Henry Cohn, 2023, needs more optimization.
23	49	0.047348654464	Henry Cohn, 2024, needs more optimization.
23	50	0.047356448114	Henry Cohn, 2023, needs more optimization.
23	51	0.047573599199	Henry Cohn, 2024, needs more optimization.
23	52	0.047591731172	Henry Cohn, 2024, needs more optimization.
23	53	0.047609748885	Henry Cohn, 2023, needs more optimization.
23	54	0.047609798786	Henry Cohn, 2024, needs more optimization.
23	55	0.055674420072	Henry Cohn, 2023, needs more optimization.
23	56	0.058003088304	Henry Cohn, 2023, needs more optimization.
23	57	0.061724185409	Henry Cohn, 2024, needs more optimization.
23	58	0.064822227241	Henry Cohn, 2024, needs more optimization.
23	62	0.066599853197	Henry Cohn, 2024, needs more optimization.
23	63	0.076669180069	Henry Cohn, 2024, needs more optimization.
23	64	0.076843247781	Henry Cohn, 2023, needs more optimization.
23	65	0.076920526653	Orthogonal union of 63 points in 22 dimensions and 2 points in 1 dimension.
23	66	0.076921400374	Henry Cohn, 2023, needs more optimization.
23	69	0.081515452976	Henry Cohn, 2024, needs more optimization.
23	81	0.083333333334	Code with 79 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. $12 x - 1$
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	116	0.111111111112	Code with 114 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. $9 x - 1$
23	123	0.131782945737	Code with 121 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. $129 x - 17$
23	138	0.135135135136	Code with 136 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. $37 x - 5$
23	166	0.142857142858	Code with 164 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. $7 x - 1$
23	202	0.161904761905	Code with 200 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. $105 x - 17$
23	277	0.166666666667	Code with 275 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. $6 x - 1$
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	558	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 4 points in 2 dimensions. $21 x - 5$
23	893	0.25	Orthogonal union of 891 points in 22 dimensions and 2 points in 1 dimension. $4 x - 1$
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $26 x - 1$
24	51	0.046482394273	Henry Cohn, 2023, needs more optimization.
24	52	0.046700054105	Henry Cohn, 2023.
24	53	0.046732471047	Henry Cohn, 2024, needs more optimization.
24	54	0.047334654599	Henry Cohn, 2023, needs more optimization.
24	55	0.047381601961	Henry Cohn, 2023, needs more optimization.
24	56	0.047563043551	Henry Cohn, 2024, needs more optimization.
24	57	0.053585918418	Henry Cohn, 2023, needs more optimization.
24	58	0.057420015206	Henry Cohn, 2023, needs more optimization.
24	59	0.061115744272	Henry Cohn, 2023, needs more optimization.
24	60	0.062898409961	Henry Cohn, 2023, needs more optimization.
24	61	0.065020579751	Henry Cohn, 2024, needs more optimization.
24	64	0.066071114247	Henry Cohn, 2024, needs more optimization.
24	65	0.073784089833	Henry Cohn, 2024, needs more optimization.
24	66	0.075420585396	Henry Cohn, 2024, needs more optimization.
24	67	0.076920526653	Orthogonal union of 63 points in 22 dimensions and 4 points in 2 dimensions.
24	68	0.076921400374	Orthogonal union of 66 points in 23 dimensions and 2 points in 1 dimension.
24	71	0.079933016419	Henry Cohn, 2024, needs more optimization.
24	83	0.083320342518	Henry Cohn, 2024, needs more optimization.
24	104	0.090909090910	Code with 102 points in 23 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. $11 x - 1$
24	118	0.111111111112	Code with 116 points in 23 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. $9 x - 1$
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	140	0.135135135136	Code with 138 points in 23 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. $37 x - 5$
24	150	0.137931034483	T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001. $29 x - 4$
24	168	0.142857142858	Code with 166 points in 23 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. $7 x - 1$
24	204	0.161904761905	Code with 202 points in 23 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. $105 x - 17$
24	279	0.166666666667	Code with 277 points in 23 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. $6 x - 1$
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	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	554	0.2	Code with 552 points in 23 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. $5 x - 1$
24	561	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 7 points in 3 dimensions. $21 x - 5$
24	895	0.25	Orthogonal union of 891 points in 22 dimensions and 4 points in 2 dimensions. $4 x - 1$
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	0.037068470388	Henry Cohn, 2023, needs more optimization.
25	53	0.045305382277	Henry Cohn, 2023, needs more optimization.
25	54	0.045671055052	Henry Cohn, 2023, needs more optimization.
25	55	0.046293922088	Henry Cohn, 2023, needs more optimization.
25	56	0.046433748247	Henry Cohn, 2023, needs more optimization.
25	57	0.046863919881	Henry Cohn, 2023, needs more optimization.
25	58	0.046863921072	Henry Cohn, 2023, needs more optimization.
25	59	0.051394584233	Henry Cohn, 2023, needs more optimization.
25	60	0.054819961783	Henry Cohn, 2023, needs more optimization.
25	61	0.057834917581	Henry Cohn, 2023, needs more optimization.
25	62	0.060834801136	Henry Cohn, 2023, needs more optimization.
25	63	0.062881186461	Henry Cohn, 2023, needs more optimization.
25	64	0.064634103064	Henry Cohn, 2024, needs more optimization.
25	66	0.065382306343	Henry Cohn, 2024, needs more optimization.
25	67	0.071082118595	Henry Cohn, 2024, needs more optimization.
25	68	0.072565936652	Henry Cohn, 2024, needs more optimization.
25	69	0.074056638014	Henry Cohn, 2024, needs more optimization.
25	70	0.075898190866	Henry Cohn, 2024, needs more optimization.
25	71	0.077685481137	Henry Cohn, 2024, needs more optimization.
25	72	0.079413033226	Henry Cohn, 2024, needs more optimization.
25	73	0.079933016419	Orthogonal union of 71 points in 24 dimensions and 2 points in 1 dimension.
25	74	0.082540767501	Henry Cohn, 2024, needs more optimization.
25	85	0.083277848266	Henry Cohn, 2024, needs more optimization.
25	106	0.090909090910	Orthogonal union of 100 points in 22 dimensions and 6 points in 3 dimensions. $11 x - 1$
25	107	0.091199040524	Henry Cohn, 2024, needs more optimization.
25	120	0.111111111112	Orthogonal union of 112 points in 21 dimensions and 8 points in 4 dimensions. $9 x - 1$
25	127	0.122807017544	Orthogonal union of 125 points in 24 dimensions and 2 points in 1 dimension. $57 x - 7$
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	170	0.142857142858	Orthogonal union of 162 points in 21 dimensions and 8 points in 4 dimensions. $7 x - 1$
25	206	0.161898726407	Henry Cohn, 2024, needs more optimization.
25	207	0.162015199612	Orthogonal union of 198 points in 21 dimensions and 9 points in 4 dimensions. $16 x^{3} - 16 x^{2} - 4 x + 1$
25	281	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 6 points in 3 dimensions. $6 x - 1$
25	299	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 2 points in 1 dimension. $11 x - 2$
25	332	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension. $31 x - 6$
25	556	0.2	Orthogonal union of 552 points in 23 dimensions and 4 points in 2 dimensions. $5 x - 1$
25	565	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 11 points in 4 dimensions. $21 x - 5$
25	898	0.25	Orthogonal union of 891 points in 22 dimensions and 7 points in 3 dimensions. $4 x - 1$
25	899	0.261203874964	Orthogonal union of 891 points in 22 dimensions and 8 points in 3 dimensions. $7 x^{2} + 2 x - 1$
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	0.035747988474	Henry Cohn, 2023, needs more optimization.
26	55	0.044778405641	Henry Cohn, 2023, needs more optimization.
26	56	0.045390856520	Henry Cohn, 2023, needs more optimization.
26	57	0.045448993424	Henry Cohn, 2023, needs more optimization.
26	58	0.045550434603	Henry Cohn, 2023, needs more optimization.
26	59	0.046214515141	Henry Cohn, 2023, needs more optimization.
26	60	0.046618911314	Henry Cohn, 2023, needs more optimization.
26	61	0.049729286617	Henry Cohn, 2023, needs more optimization.
26	62	0.054364581244	Henry Cohn, 2023, needs more optimization.
26	63	0.056596146653	Henry Cohn, 2024, needs more optimization.
26	64	0.058813887790	Henry Cohn, 2023, needs more optimization.
26	65	0.060920899702	Henry Cohn, 2024, needs more optimization.
26	66	0.062422662196	Henry Cohn, 2024, needs more optimization.
26	67	0.064548769369	Henry Cohn, 2024, needs more optimization.
26	68	0.065382306343	Orthogonal union of 66 points in 25 dimensions and 2 points in 1 dimension.
26	69	0.068247403533	Henry Cohn, 2024, needs more optimization.
26	70	0.069730530564	Henry Cohn, 2024, needs more optimization.
26	71	0.071414067424	Henry Cohn, 2024, needs more optimization.
26	72	0.073305685130	Henry Cohn, 2023, needs more optimization.
26	73	0.074595574917	Henry Cohn, 2024, needs more optimization.
26	74	0.076296111677	Henry Cohn, 2024, needs more optimization.
26	75	0.077764094451	Henry Cohn, 2024, needs more optimization.
26	76	0.079245957789	Henry Cohn, 2024, needs more optimization.
26	77	0.080200439787	Henry Cohn, 2024, needs more optimization.
26	78	0.081895994030	Henry Cohn, 2024, needs more optimization.
26	87	0.083142657675	Henry Cohn, 2024, needs more optimization.
26	108	0.090909090910	Orthogonal union of 100 points in 22 dimensions and 8 points in 4 dimensions. $11 x - 1$
26	109	0.091199040524	Orthogonal union of 107 points in 25 dimensions and 2 points in 1 dimension.
26	122	0.111111111112	Orthogonal union of 112 points in 21 dimensions and 10 points in 5 dimensions. $9 x - 1$
26	123	0.122390273743	Henry Cohn, 2024, needs more optimization.
26	129	0.122807017544	Orthogonal union of 125 points in 24 dimensions and 4 points in 2 dimensions. $57 x - 7$
26	130	0.128585872356	Henry Cohn, 2024, needs more optimization.
26	131	0.129621228208	Henry Cohn, 2024, needs more optimization.
26	132	0.130372356879	Henry Cohn, 2024, needs more optimization.
26	133	0.131517845436	Henry Cohn, 2024, needs more optimization.
26	134	0.132673526822	Henry Cohn, 2024, needs more optimization.
26	158	0.133333333334	Orthogonal union of 156 points in 25 dimensions and 2 points in 1 dimension. $15 x - 2$
26	173	0.142857142858	Orthogonal union of 162 points in 21 dimensions and 11 points in 5 dimensions. $7 x - 1$
26	174	0.153931605034	Orthogonal union of 162 points in 21 dimensions and 12 points in 5 dimensions. $25 x^{4} + 30 x^{3} + 24 x^{2} + 2 x - 1$
26	208	0.161738087734	Henry Cohn, 2024, needs more optimization.
26	210	0.161904761905	Orthogonal union of 198 points in 21 dimensions and 12 points in 5 dimensions. $105 x - 17$
26	285	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions. $6 x - 1$
26	301	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 4 points in 2 dimensions. $11 x - 2$
26	334	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 4 points in 2 dimensions. $31 x - 6$
26	558	0.2	Orthogonal union of 552 points in 23 dimensions and 6 points in 3 dimensions. $5 x - 1$
26	559	0.210138312731	Orthogonal union of 552 points in 23 dimensions and 7 points in 3 dimensions. $3 x^{3} - 9 x^{2} - 3 x + 1$
26	570	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 16 points in 5 dimensions. $21 x - 5$
26	903	0.25	Orthogonal union of 891 points in 22 dimensions and 12 points in 4 dimensions. $4 x - 1$
26	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.034511432831	Henry Cohn, 2023, needs more optimization.
27	57	0.043679995743	Henry Cohn, 2023, needs more optimization.
27	58	0.045164834303	Henry Cohn, 2024, needs more optimization.
27	59	0.045448993424	Orthogonal union of 57 points in 26 dimensions and 2 points in 1 dimension.
27	60	0.045477974743	Henry Cohn, 2023, needs more optimization.
27	61	0.045484388255	Henry Cohn, 2023, needs more optimization.
27	62	0.046198056106	Henry Cohn, 2023, needs more optimization.
27	63	0.048347310405	Henry Cohn, 2023, needs more optimization.
27	64	0.053101886359	Henry Cohn, 2023, needs more optimization.
27	65	0.055852369229	Henry Cohn, 2023, needs more optimization.
27	66	0.057595215544	Henry Cohn, 2023, needs more optimization.
27	67	0.058925769437	Henry Cohn, 2023, needs more optimization.
27	68	0.060630286584	Henry Cohn, 2023, needs more optimization.
27	69	0.062222069538	Henry Cohn, 2024, needs more optimization.
27	70	0.063806979460	Henry Cohn, 2024, needs more optimization.
27	71	0.065781424194	Henry Cohn, 2024, needs more optimization.
27	72	0.067491561385	Henry Cohn, 2023, needs more optimization.
27	73	0.068966172955	Henry Cohn, 2024, needs more optimization.
27	74	0.070475291640	Henry Cohn, 2024, needs more optimization.
27	75	0.072026940592	Henry Cohn, 2024, needs more optimization.
27	76	0.073254869923	Henry Cohn, 2024, needs more optimization.
27	77	0.074854872053	Henry Cohn, 2024, needs more optimization.
27	78	0.076300143542	Henry Cohn, 2024, needs more optimization.
27	79	0.077841548811	Henry Cohn, 2024, needs more optimization.
27	80	0.079149061360	Henry Cohn, 2024, needs more optimization.
27	81	0.080338019801	Henry Cohn, 2024, needs more optimization.
27	82	0.081504696940	Henry Cohn, 2024, needs more optimization.
27	89	0.082076108368	Henry Cohn, 2024, needs more optimization.
27	90	0.090463535573	Henry Cohn, 2024, needs more optimization.
27	110	0.090870650464	Henry Cohn, 2024, needs more optimization.
27	111	0.091199040524	Orthogonal union of 107 points in 25 dimensions and 4 points in 2 dimensions.
27	112	0.108878495067	Henry Cohn, 2024, needs more optimization.
27	113	0.109720364549	Henry Cohn, 2024, needs more optimization.
27	114	0.110349808592	Henry Cohn, 2024, needs more optimization.
27	115	0.110518388996	Henry Cohn, 2024, needs more optimization.
27	124	0.111111111112	Orthogonal union of 112 points in 21 dimensions and 12 points in 6 dimensions. $9 x - 1$
27	125	0.113079752148	Orthogonal union of 112 points in 21 dimensions and 13 points in 6 dimensions. $96 x^{3} - 36 x^{2} - 6 x + 1$
27	126	0.118655983153	Henry Cohn, 2024, needs more optimization.
27	127	0.119338328577	Henry Cohn, 2024, needs more optimization.
27	128	0.120387403434	Henry Cohn, 2024, needs more optimization.
27	129	0.121086516893	Henry Cohn, 2024, needs more optimization.
27	130	0.121763812095	Henry Cohn, 2024, needs more optimization.
27	131	0.122558272629	Henry Cohn, 2024, needs more optimization.
27	132	0.123356416124	Henry Cohn, 2024, needs more optimization.
27	133	0.124223661681	Henry Cohn, 2024, needs more optimization.
27	134	0.125185178765	Henry Cohn, 2024, needs more optimization.
27	135	0.126000657289	Henry Cohn, 2024, needs more optimization.
27	136	0.126756977493	Henry Cohn, 2024, needs more optimization.
27	137	0.127656378947	Henry Cohn, 2024, needs more optimization.
27	138	0.128386615966	Henry Cohn, 2024, needs more optimization.
27	139	0.129412457879	Henry Cohn, 2024, needs more optimization.
27	140	0.130033331998	Henry Cohn, 2024, needs more optimization.
27	141	0.131239729329	Henry Cohn, 2024, needs more optimization.
27	142	0.132161392127	Henry Cohn, 2024, needs more optimization.
27	143	0.132730104926	Henry Cohn, 2024, needs more optimization.
27	160	0.133282008372	Henry Cohn, 2024, needs more optimization.
27	176	0.142857142858	Orthogonal union of 162 points in 21 dimensions and 14 points in 6 dimensions. $7 x - 1$
27	177	0.144948974279	Orthogonal union of 162 points in 21 dimensions and 15 points in 6 dimensions. $20 x^{2} + 4 x - 1$
27	178	0.156242051865	Henry Cohn, 2024, needs more optimization.
27	179	0.156835129928	Henry Cohn, 2024, needs more optimization.
27	180	0.157441600379	Henry Cohn, 2024, needs more optimization.
27	181	0.157913122664	Henry Cohn, 2024, needs more optimization.
27	182	0.158503365264	Henry Cohn, 2024, needs more optimization.
27	183	0.158944962985	Henry Cohn, 2024, needs more optimization.
27	184	0.159541261888	Henry Cohn, 2024, needs more optimization.
27	185	0.160048523360	Henry Cohn, 2024, needs more optimization.
27	186	0.160518518303	Henry Cohn, 2024, needs more optimization.
27	187	0.160932133558	Henry Cohn, 2024, needs more optimization.
27	210	0.161180412496	Henry Cohn, 2024, needs more optimization.
27	213	0.161904761905	Orthogonal union of 198 points in 21 dimensions and 15 points in 6 dimensions. $105 x - 17$
27	287	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 12 points in 5 dimensions. $6 x - 1$
27	303	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 6 points in 3 dimensions. $11 x - 2$
27	336	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 6 points in 3 dimensions. $31 x - 6$
27	562	0.2	Orthogonal union of 552 points in 23 dimensions and 10 points in 4 dimensions. $5 x - 1$
27	563	0.230405563595	Orthogonal union of 552 points in 23 dimensions and 11 points in 4 dimensions. $8 x^{3} - 12 x^{2} - 2 x + 1$
27	574	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 20 points in 6 dimensions. $21 x - 5$
27	575	0.242852848014	Orthogonal union of 554 points in 21 dimensions and 21 points in 6 dimensions.
27	576	0.248865699460	Orthogonal union of 554 points in 21 dimensions and 22 points in 6 dimensions.
27	907	0.25	Orthogonal union of 891 points in 22 dimensions and 16 points in 5 dimensions. $4 x - 1$
27	908	0.270475835269	Orthogonal union of 891 points in 22 dimensions and 17 points in 5 dimensions. $9 x^{4} - 16 x^{3} - 10 x^{2} + 1$
27	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.033360604975	Henry Cohn, 2023, needs more optimization.
28	59	0.042130667237	Henry Cohn, 2023, needs more optimization.
28	60	0.044335084232	Henry Cohn, 2023, needs more optimization.
28	61	0.044427836227	Henry Cohn, 2024, needs more optimization.
28	62	0.044625903117	Henry Cohn, 2023, needs more optimization.
28	63	0.045182177671	Henry Cohn, 2023, needs more optimization.
28	64	0.045901905542	Henry Cohn, 2023, needs more optimization.
28	65	0.047212523446	Henry Cohn, 2023, needs more optimization.
28	66	0.051595262681	Henry Cohn, 2023, needs more optimization.
28	67	0.053749042625	Henry Cohn, 2024, needs more optimization.
28	68	0.055392825408	Henry Cohn, 2024, needs more optimization.
28	69	0.057319096103	Henry Cohn, 2023, needs more optimization.
28	70	0.058669391383	Henry Cohn, 2023, needs more optimization.
28	71	0.060441119465	Henry Cohn, 2023, needs more optimization.
28	72	0.061761644674	Henry Cohn, 2024, needs more optimization.
28	73	0.063380387760	Henry Cohn, 2024, needs more optimization.
28	74	0.065116248445	Henry Cohn, 2024, needs more optimization.
28	75	0.066604546574	Henry Cohn, 2024, needs more optimization.
28	76	0.067888853246	Henry Cohn, 2024, needs more optimization.
28	77	0.069519151043	Henry Cohn, 2024, needs more optimization.
28	78	0.070830568035	Henry Cohn, 2024, needs more optimization.
28	79	0.071934783866	Henry Cohn, 2024, needs more optimization.
28	80	0.073517665577	Henry Cohn, 2024, needs more optimization.
28	81	0.074859889735	Henry Cohn, 2024, needs more optimization.
28	82	0.076390495198	Henry Cohn, 2024, needs more optimization.
28	83	0.077489333789	Henry Cohn, 2024, needs more optimization.
28	84	0.078544120499	Henry Cohn, 2024, needs more optimization.
28	85	0.079929574248	Henry Cohn, 2024, needs more optimization.
28	91	0.081004855691	Henry Cohn, 2024, needs more optimization.
28	92	0.087350622282	Henry Cohn, 2024, needs more optimization.
28	93	0.088144820100	Henry Cohn, 2024, needs more optimization.
28	94	0.089040710790	Henry Cohn, 2024, needs more optimization.
28	95	0.089998402630	Henry Cohn, 2024, needs more optimization.
28	97	0.090730194756	Henry Cohn, 2024, needs more optimization.
28	112	0.090730194772	Henry Cohn, 2024, needs more optimization.
28	113	0.091199040524	Orthogonal union of 107 points in 25 dimensions and 6 points in 3 dimensions.
28	114	0.105494009421	Henry Cohn, 2024, needs more optimization.
28	115	0.106095088387	Henry Cohn, 2024, needs more optimization.
28	116	0.106849515191	Henry Cohn, 2024, needs more optimization.
28	117	0.107496092108	Henry Cohn, 2024, needs more optimization.
28	118	0.108333682855	Henry Cohn, 2024, needs more optimization.
28	119	0.108549404733	Henry Cohn, 2024, needs more optimization.
28	120	0.109326786849	Henry Cohn, 2024, needs more optimization.
28	121	0.110031676651	Henry Cohn, 2024, needs more optimization.
28	122	0.110559254690	Henry Cohn, 2024, needs more optimization.
28	127	0.111111111112	Orthogonal union of 112 points in 21 dimensions and 15 points in 7 dimensions. $9 x - 1$
28	128	0.113320879601	Orthogonal union of 112 points in 21 dimensions and 16 points in 7 dimensions.
28	129	0.115197945860	Henry Cohn, 2024, needs more optimization.
28	130	0.115732829570	Henry Cohn, 2024, needs more optimization.
28	131	0.116714489119	Henry Cohn, 2024, needs more optimization.
28	132	0.117251267020	Henry Cohn, 2024, needs more optimization.
28	133	0.118049833583	Henry Cohn, 2024, needs more optimization.
28	134	0.118993511351	Henry Cohn, 2024, needs more optimization.
28	135	0.119272591118	Henry Cohn, 2024, needs more optimization.
28	136	0.120401740699	Henry Cohn, 2024, needs more optimization.
28	137	0.121360085779	Henry Cohn, 2024, needs more optimization.
28	138	0.121623408642	Henry Cohn, 2024, needs more optimization.
28	139	0.122401429520	Henry Cohn, 2024, needs more optimization.
28	140	0.123301772544	Henry Cohn, 2024, needs more optimization.
28	141	0.124079629912	Henry Cohn, 2024, needs more optimization.
28	142	0.124830548631	Henry Cohn, 2024, needs more optimization.
28	143	0.125605034265	Henry Cohn, 2024, needs more optimization.
28	144	0.126322902923	Henry Cohn, 2024, needs more optimization.
28	145	0.127396342170	Henry Cohn, 2024, needs more optimization.
28	146	0.127964953350	Henry Cohn, 2024, needs more optimization.
28	147	0.128717364273	Henry Cohn, 2024, needs more optimization.
28	148	0.129665907714	Henry Cohn, 2024, needs more optimization.
28	149	0.130599687500	Henry Cohn, 2024, needs more optimization.
28	150	0.131252205362	Henry Cohn, 2024, needs more optimization.
28	151	0.132190822901	Henry Cohn, 2024, needs more optimization.
28	152	0.132750318628	Henry Cohn, 2024, needs more optimization.
28	162	0.132782322631	Henry Cohn, 2024, needs more optimization.
28	163	0.140583007111	Henry Cohn, 2024, needs more optimization.
28	164	0.141184020484	Henry Cohn, 2024, needs more optimization.
28	165	0.141929463968	Henry Cohn, 2024, needs more optimization.
28	176	0.142046694745	Henry Cohn, 2024, needs more optimization.
28	180	0.142857142858	Orthogonal union of 162 points in 21 dimensions and 18 points in 7 dimensions. $7 x - 1$
28	181	0.151217267618	Henry Cohn, 2024, needs more optimization.
28	182	0.151670323738	Henry Cohn, 2024, needs more optimization.
28	183	0.152268509291	Henry Cohn, 2024, needs more optimization.
28	184	0.152956733161	Henry Cohn, 2024, needs more optimization.
28	185	0.153265485213	Henry Cohn, 2024, needs more optimization.
28	186	0.153798240522	Henry Cohn, 2024, needs more optimization.
28	187	0.154314513905	Henry Cohn, 2024, needs more optimization.
28	188	0.154607956655	Henry Cohn, 2024, needs more optimization.
28	190	0.155893915776	Henry Cohn, 2024, needs more optimization.
28	192	0.156716702404	Henry Cohn, 2024, needs more optimization.
28	194	0.158339236851	Henry Cohn, 2024, needs more optimization.
28	196	0.158518600229	Henry Cohn, 2024, needs more optimization.
28	212	0.159252251498	Henry Cohn, 2024, needs more optimization.
28	217	0.161904761905	Orthogonal union of 198 points in 21 dimensions and 19 points in 7 dimensions. $105 x - 17$
28	290	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 15 points in 6 dimensions. $6 x - 1$
28	291	0.171147649430	Orthogonal union of 275 points in 22 dimensions and 16 points in 6 dimensions. Minimal polynomial listed in plain text data
28	307	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 10 points in 4 dimensions. $11 x - 2$
28	340	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 10 points in 4 dimensions. $31 x - 6$
28	568	0.2	Orthogonal union of 552 points in 23 dimensions and 16 points in 5 dimensions. $5 x - 1$
28	580	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 26 points in 7 dimensions. $21 x - 5$
28	581	0.240549382010	Orthogonal union of 554 points in 21 dimensions and 27 points in 7 dimensions.
28	582	0.247356651208	Orthogonal union of 554 points in 21 dimensions and 28 points in 7 dimensions.
28	583	0.248933144681	Orthogonal union of 554 points in 21 dimensions and 29 points in 7 dimensions.
28	584	0.249468286876	Orthogonal union of 554 points in 21 dimensions and 30 points in 7 dimensions.
28	918	0.25	Orthogonal union of 891 points in 22 dimensions and 27 points in 6 dimensions. $4 x - 1$
28	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.032283994156	Henry Cohn, 2023, needs more optimization.
29	61	0.040959828457	Henry Cohn, 2023, needs more optimization.
29	62	0.043374727077	Henry Cohn, 2023, needs more optimization.
29	63	0.044418616792	Henry Cohn, 2024, needs more optimization.
29	64	0.044625900541	Henry Cohn, 2023, needs more optimization.
29	65	0.045182177671	Orthogonal union of 63 points in 28 dimensions and 2 points in 1 dimension.
29	66	0.045713348408	Henry Cohn, 2023, needs more optimization.
29	67	0.046459826565	Henry Cohn, 2023, needs more optimization.
29	68	0.047753062874	Henry Cohn, 2023, needs more optimization.
29	69	0.051946733825	Henry Cohn, 2023, needs more optimization.
29	70	0.054244405080	Henry Cohn, 2023, needs more optimization.
29	71	0.055456441566	Henry Cohn, 2023, needs more optimization.
29	72	0.057063992459	Henry Cohn, 2023, needs more optimization.
29	73	0.058462733400	Henry Cohn, 2024, needs more optimization.
29	74	0.059904078009	Henry Cohn, 2024, needs more optimization.
29	75	0.061555930019	Henry Cohn, 2024, needs more optimization.
29	76	0.063041941617	Henry Cohn, 2024, needs more optimization.
29	77	0.064584397314	Henry Cohn, 2024, needs more optimization.
29	78	0.065753468702	Henry Cohn, 2024, needs more optimization.
29	79	0.067221671764	Henry Cohn, 2024, needs more optimization.
29	80	0.068531634516	Henry Cohn, 2024, needs more optimization.
29	81	0.069804039115	Henry Cohn, 2024, needs more optimization.
29	82	0.071286612027	Henry Cohn, 2024, needs more optimization.
29	83	0.072386227129	Henry Cohn, 2024, needs more optimization.
29	84	0.073480048914	Henry Cohn, 2024, needs more optimization.
29	85	0.074845390393	Henry Cohn, 2024, needs more optimization.
29	86	0.076027835791	Henry Cohn, 2024, needs more optimization.
29	87	0.077202464758	Henry Cohn, 2024, needs more optimization.
29	88	0.078217072529	Henry Cohn, 2024, needs more optimization.
29	89	0.079384604582	Henry Cohn, 2024, needs more optimization.
29	93	0.079450934739	Henry Cohn, 2024, needs more optimization.
29	94	0.084217881018	Henry Cohn, 2024, needs more optimization.
29	95	0.085195861065	Henry Cohn, 2024, needs more optimization.
29	96	0.086236729721	Henry Cohn, 2024, needs more optimization.
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	114	0.090597286827	Henry Cohn, 2024, needs more optimization.
29	115	0.091199040524	Orthogonal union of 107 points in 25 dimensions and 8 points in 4 dimensions.
29	116	0.101962562668	Henry Cohn, 2024, needs more optimization.
29	117	0.102748745798	Henry Cohn, 2024, needs more optimization.
29	118	0.103445016065	Henry Cohn, 2024, needs more optimization.
29	119	0.103906667845	Henry Cohn, 2024, needs more optimization.
29	120	0.104680594866	Henry Cohn, 2024, needs more optimization.
29	121	0.105224173440	Henry Cohn, 2024, needs more optimization.
29	122	0.105974322505	Henry Cohn, 2024, needs more optimization.
29	123	0.106641229002	Henry Cohn, 2024, needs more optimization.
29	124	0.107068103287	Henry Cohn, 2024, needs more optimization.
29	125	0.107767906014	Henry Cohn, 2024, needs more optimization.
29	126	0.108518823581	Henry Cohn, 2024, needs more optimization.
29	127	0.109061270466	Henry Cohn, 2024, needs more optimization.
29	128	0.109419532848	Henry Cohn, 2024, needs more optimization.
29	129	0.110176692161	Henry Cohn, 2024, needs more optimization.
29	130	0.110762018930	Henry Cohn, 2024, needs more optimization.
29	131	0.111349700901	Henry Cohn, 2024, needs more optimization.
29	132	0.112111376416	Henry Cohn, 2024, needs more optimization.
29	133	0.112931524032	Henry Cohn, 2024, needs more optimization.
29	134	0.113409671728	Henry Cohn, 2024, needs more optimization.
29	135	0.113782308842	Henry Cohn, 2024, needs more optimization.
29	136	0.114541415969	Henry Cohn, 2024, needs more optimization.
29	137	0.115378135086	Henry Cohn, 2024, needs more optimization.
29	138	0.115958745236	Henry Cohn, 2024, needs more optimization.
29	139	0.116704343430	Henry Cohn, 2024, needs more optimization.
29	140	0.117102540529	Henry Cohn, 2024, needs more optimization.
29	141	0.117944401699	Henry Cohn, 2024, needs more optimization.
29	142	0.118746592958	Henry Cohn, 2024, needs more optimization.
29	143	0.119189091219	Henry Cohn, 2024, needs more optimization.
29	144	0.120034199854	Henry Cohn, 2024, needs more optimization.
29	145	0.120728715866	Henry Cohn, 2024, needs more optimization.
29	146	0.121756773929	Henry Cohn, 2024, needs more optimization.
29	147	0.122197602172	Henry Cohn, 2024, needs more optimization.
29	148	0.123140752142	Henry Cohn, 2024, needs more optimization.
29	149	0.123716670186	Henry Cohn, 2024, needs more optimization.
29	150	0.124097919399	Henry Cohn, 2024, needs more optimization.
29	151	0.125172624884	Henry Cohn, 2024, needs more optimization.
29	152	0.125808429277	Henry Cohn, 2024, needs more optimization.
29	153	0.126429728848	Henry Cohn, 2024, needs more optimization.
29	154	0.127520817384	Henry Cohn, 2024, needs more optimization.
29	155	0.128517917994	Henry Cohn, 2024, needs more optimization.
29	156	0.128902505274	Henry Cohn, 2024, needs more optimization.
29	157	0.129735041974	Henry Cohn, 2024, needs more optimization.
29	164	0.130358843703	Henry Cohn, 2024, needs more optimization.
29	165	0.135349806141	Henry Cohn, 2024, needs more optimization.
29	166	0.135858208338	Henry Cohn, 2024, needs more optimization.
29	167	0.136437725315	Henry Cohn, 2024, needs more optimization.
29	168	0.137329755304	Henry Cohn, 2024, needs more optimization.
29	169	0.137678525764	Henry Cohn, 2024, needs more optimization.
29	170	0.138219591070	Henry Cohn, 2024, needs more optimization.
29	171	0.138945691316	Henry Cohn, 2024, needs more optimization.
29	172	0.139541921445	Henry Cohn, 2024, needs more optimization.
29	173	0.140204807997	Henry Cohn, 2024, needs more optimization.
29	174	0.140762693659	Henry Cohn, 2024, needs more optimization.
29	175	0.141415003435	Henry Cohn, 2024, needs more optimization.
29	176	0.141859287879	Henry Cohn, 2024, needs more optimization.
29	178	0.142046694745	Orthogonal union of 176 points in 28 dimensions and 2 points in 1 dimension.
29	182	0.142854813225	Henry Cohn, 2024, needs more optimization.
29	184	0.142857142858	Orthogonal union of 162 points in 21 dimensions and 22 points in 8 dimensions. $7 x - 1$
29	185	0.146789812392	Henry Cohn, 2024, needs more optimization.
29	186	0.147490841194	Henry Cohn, 2024, needs more optimization.
29	187	0.147805420991	Henry Cohn, 2024, needs more optimization.
29	188	0.148352058193	Henry Cohn, 2024, needs more optimization.
29	189	0.148829383747	Henry Cohn, 2024, needs more optimization.
29	190	0.149294597690	Henry Cohn, 2024, needs more optimization.
29	191	0.149895090566	Henry Cohn, 2024, needs more optimization.
29	192	0.151156183352	Henry Cohn, 2024, needs more optimization.
29	193	0.151993211835	Henry Cohn, 2024, needs more optimization.
29	194	0.152366106115	Henry Cohn, 2024, needs more optimization.
29	195	0.152871221880	Henry Cohn, 2024, needs more optimization.
29	196	0.153488397348	Henry Cohn, 2024, needs more optimization.
29	197	0.154007024850	Henry Cohn, 2024, needs more optimization.
29	198	0.154200756954	Henry Cohn, 2024, needs more optimization.
29	199	0.154888845124	Henry Cohn, 2024, needs more optimization.
29	200	0.155215493220	Henry Cohn, 2024, needs more optimization.
29	201	0.155651294466	Henry Cohn, 2024, needs more optimization.
29	202	0.156215766800	Henry Cohn, 2024, needs more optimization.
29	218	0.156597700436	Henry Cohn, 2024, needs more optimization.
29	222	0.161904761905	Orthogonal union of 198 points in 21 dimensions and 24 points in 8 dimensions. $105 x - 17$
29	223	0.164334174126	Orthogonal union of 198 points in 21 dimensions and 25 points in 8 dimensions.
29	224	0.165592704441	Henry Cohn, 2024, needs more optimization.
29	225	0.165974436145	Henry Cohn, 2024, needs more optimization.
29	226	0.166227283737	Henry Cohn, 2024, needs more optimization.
29	227	0.166610018759	Henry Cohn, 2024, needs more optimization.
29	294	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 19 points in 7 dimensions. $6 x - 1$
29	295	0.169520847199	Orthogonal union of 275 points in 22 dimensions and 20 points in 7 dimensions. $23 x^{2} + 2 x - 1$
29	296	0.181523960801	Orthogonal union of 275 points in 22 dimensions and 21 points in 7 dimensions.
29	309	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 12 points in 5 dimensions. $11 x - 2$
29	310	0.187259851883	Orthogonal union of 297 points in 24 dimensions and 13 points in 5 dimensions. $17 x^{3} - 5 x^{2} - 5 x + 1$
29	343	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 13 points in 5 dimensions. $31 x - 6$
29	570	0.2	Orthogonal union of 552 points in 23 dimensions and 18 points in 6 dimensions. $5 x - 1$
29	571	0.200226025892	Orthogonal union of 552 points in 23 dimensions and 19 points in 6 dimensions.
29	572	0.214285714286	Orthogonal union of 552 points in 23 dimensions and 20 points in 6 dimensions. $14 x - 3$
29	589	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 35 points in 8 dimensions. $21 x - 5$
29	592	0.239920745566	Orthogonal union of 554 points in 21 dimensions and 38 points in 8 dimensions. $1088 x^{4} - 80 x^{2} + 1$
29	593	0.243600150512	Orthogonal union of 554 points in 21 dimensions and 39 points in 8 dimensions. $1183744 x^{8} + 122880 x^{7} - 575488 x^{6} - 138240 x^{5} + 53632 x^{4} + 14976 x^{3} - 1568 x^{2} - 720 x + 81$
29	921	0.25	Orthogonal union of 891 points in 22 dimensions and 30 points in 7 dimensions. $4 x - 1$
29	922	0.254502767515	Orthogonal union of 891 points in 22 dimensions and 31 points in 7 dimensions.
29	923	0.265595699432	Orthogonal union of 891 points in 22 dimensions and 32 points in 7 dimensions.
29	924	0.270027345615	Orthogonal union of 891 points in 22 dimensions and 33 points in 7 dimensions.
29	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.031275273372	Henry Cohn, 2023, needs more optimization.
30	63	0.039882314205	Henry Cohn, 2023, needs more optimization.
30	64	0.042243230806	Henry Cohn, 2023, needs more optimization.
30	65	0.043893814249	Henry Cohn, 2023, needs more optimization.
30	66	0.044324786357	Henry Cohn, 2023, needs more optimization.
30	67	0.044636487473	Henry Cohn, 2023, needs more optimization.
30	68	0.045103518422	Henry Cohn, 2023, needs more optimization.
30	69	0.045918527826	Henry Cohn, 2023, needs more optimization.
30	70	0.047749153443	Henry Cohn, 2023, needs more optimization.
30	71	0.051112405172	Henry Cohn, 2023, needs more optimization.
30	72	0.052929388727	Henry Cohn, 2023, needs more optimization.
30	73	0.054096683182	Henry Cohn, 2023, needs more optimization.
30	74	0.055381164313	Henry Cohn, 2024, needs more optimization.
30	75	0.056870005048	Henry Cohn, 2023, needs more optimization.
30	76	0.058130911652	Henry Cohn, 2024, needs more optimization.
30	77	0.059591586837	Henry Cohn, 2024, needs more optimization.
30	78	0.060902563500	Henry Cohn, 2024, needs more optimization.
30	79	0.062369588478	Henry Cohn, 2024, needs more optimization.
30	80	0.063768089182	Henry Cohn, 2024, needs more optimization.
30	81	0.064703915626	Henry Cohn, 2024, needs more optimization.
30	82	0.066404815020	Henry Cohn, 2024, needs more optimization.
30	83	0.067601737582	Henry Cohn, 2024, needs more optimization.
30	84	0.068731723125	Henry Cohn, 2024, needs more optimization.
30	85	0.069764372769	Henry Cohn, 2024, needs more optimization.
30	86	0.071141339435	Henry Cohn, 2024, needs more optimization.
30	87	0.072220278590	Henry Cohn, 2024, needs more optimization.
30	88	0.073463269375	Henry Cohn, 2024, needs more optimization.
30	89	0.074345210692	Henry Cohn, 2024, needs more optimization.
30	90	0.075622561574	Henry Cohn, 2024, needs more optimization.
30	91	0.076752143901	Henry Cohn, 2024, needs more optimization.
30	92	0.077877092402	Henry Cohn, 2024, needs more optimization.
30	93	0.078697394369	Henry Cohn, 2024, needs more optimization.
30	95	0.079450934739	Orthogonal union of 93 points in 29 dimensions and 2 points in 1 dimension.
30	96	0.081537983732	Henry Cohn, 2024, needs more optimization.
30	97	0.082390240561	Henry Cohn, 2024, needs more optimization.
30	98	0.083303761176	Henry Cohn, 2024, needs more optimization.
30	99	0.084433747675	Henry Cohn, 2024, needs more optimization.
30	100	0.085230562162	Henry Cohn, 2024, needs more optimization.
30	101	0.086007423110	Henry Cohn, 2024, needs more optimization.
30	114	0.086333380579	Orthogonal union of 112 points in 29 dimensions and 2 points in 1 dimension. $111 x^{2} + 2 x - 1$
30	116	0.088982380301	Henry Cohn, 2024, needs more optimization.
30	117	0.090909090910	Orthogonal union of 100 points in 22 dimensions and 17 points in 8 dimensions. $11 x - 1$
30	118	0.098909285097	Henry Cohn, 2024, needs more optimization.
30	119	0.099391332684	Henry Cohn, 2024, needs more optimization.
30	120	0.100112965796	Henry Cohn, 2024, needs more optimization.
30	121	0.100689336306	Henry Cohn, 2024, needs more optimization.
30	122	0.101468860958	Henry Cohn, 2024, needs more optimization.
30	123	0.102014577002	Henry Cohn, 2024, needs more optimization.
30	124	0.102756514176	Henry Cohn, 2024, needs more optimization.
30	125	0.103406033654	Henry Cohn, 2024, needs more optimization.
30	126	0.103909210938	Henry Cohn, 2024, needs more optimization.
30	127	0.104468040958	Henry Cohn, 2024, needs more optimization.
30	128	0.105084976994	Henry Cohn, 2024, needs more optimization.
30	129	0.105837217295	Henry Cohn, 2024, needs more optimization.
30	130	0.106298847219	Henry Cohn, 2024, needs more optimization.
30	131	0.106867937200	Henry Cohn, 2024, needs more optimization.
30	132	0.107404606542	Henry Cohn, 2024, needs more optimization.
30	133	0.107767852094	Henry Cohn, 2024, needs more optimization.
30	134	0.108748360403	Henry Cohn, 2024, needs more optimization.
30	135	0.109049767442	Henry Cohn, 2024, needs more optimization.
30	136	0.109716858669	Henry Cohn, 2024, needs more optimization.
30	137	0.110581758627	Henry Cohn, 2024, needs more optimization.
30	138	0.110945899043	Henry Cohn, 2024, needs more optimization.
30	139	0.111629876667	Henry Cohn, 2024, needs more optimization.
30	140	0.112155130945	Henry Cohn, 2024, needs more optimization.
30	141	0.112886822191	Henry Cohn, 2024, needs more optimization.
30	142	0.113583917241	Henry Cohn, 2024, needs more optimization.
30	143	0.113939473978	Henry Cohn, 2024, needs more optimization.
30	144	0.114625000338	Henry Cohn, 2024, needs more optimization.
30	145	0.115319401945	Henry Cohn, 2024, needs more optimization.
30	146	0.116052452160	Henry Cohn, 2024, needs more optimization.
30	147	0.116673276200	Henry Cohn, 2024, needs more optimization.
30	148	0.117108506624	Henry Cohn, 2024, needs more optimization.
30	149	0.117746260016	Henry Cohn, 2024, needs more optimization.
30	150	0.118863953641	Henry Cohn, 2024, needs more optimization.
30	151	0.119158283312	Henry Cohn, 2024, needs more optimization.
30	152	0.119732873041	Henry Cohn, 2024, needs more optimization.
30	153	0.120482343104	Henry Cohn, 2024, needs more optimization.
30	154	0.121202220351	Henry Cohn, 2024, needs more optimization.
30	155	0.121776864450	Henry Cohn, 2024, needs more optimization.
30	156	0.122581307637	Henry Cohn, 2024, needs more optimization.
30	157	0.123528887976	Henry Cohn, 2024, needs more optimization.
30	158	0.124059723596	Henry Cohn, 2024, needs more optimization.
30	159	0.124630970236	Henry Cohn, 2024, needs more optimization.
30	160	0.125270438079	Henry Cohn, 2024, needs more optimization.
30	161	0.126084250726	Henry Cohn, 2024, needs more optimization.
30	162	0.126721230741	Henry Cohn, 2024, needs more optimization.
30	163	0.127434469004	Henry Cohn, 2024, needs more optimization.
30	164	0.127858876268	Henry Cohn, 2024, needs more optimization.
30	165	0.128847680906	Henry Cohn, 2024, needs more optimization.
30	166	0.129314855514	Henry Cohn, 2024, needs more optimization.
30	167	0.129900870161	Henry Cohn, 2024, needs more optimization.
30	168	0.130802530426	Henry Cohn, 2024, needs more optimization.
30	169	0.131498617579	Henry Cohn, 2024, needs more optimization.
30	170	0.132096757734	Henry Cohn, 2024, needs more optimization.
30	171	0.132681923189	Henry Cohn, 2024, needs more optimization.
30	172	0.133240235902	Henry Cohn, 2024, needs more optimization.
30	173	0.133799255754	Henry Cohn, 2024, needs more optimization.
30	174	0.134447182790	Henry Cohn, 2024, needs more optimization.
30	175	0.135197963272	Henry Cohn, 2024, needs more optimization.
30	176	0.135646042909	Henry Cohn, 2024, needs more optimization.
30	177	0.136158868559	Henry Cohn, 2024, needs more optimization.
30	178	0.136717840681	Henry Cohn, 2024, needs more optimization.
30	179	0.137309051759	Henry Cohn, 2024, needs more optimization.
30	180	0.137955802293	Henry Cohn, 2024, needs more optimization.
30	181	0.138535792029	Henry Cohn, 2024, needs more optimization.
30	182	0.139136119913	Henry Cohn, 2024, needs more optimization.
30	183	0.139492713685	Henry Cohn, 2024, needs more optimization.
30	184	0.140166409854	Henry Cohn, 2024, needs more optimization.
30	185	0.140672803960	Henry Cohn, 2024, needs more optimization.
30	186	0.141231989140	Henry Cohn, 2024, needs more optimization.
30	187	0.141850733883	Henry Cohn, 2024, needs more optimization.
30	189	0.142803726104	Henry Cohn, 2024, needs more optimization.
30	190	0.143389113002	Henry Cohn, 2024, needs more optimization.
30	192	0.144101915842	Henry Cohn, 2024, needs more optimization.
30	193	0.144967842395	Henry Cohn, 2024, needs more optimization.
30	195	0.145484696048	Henry Cohn, 2024, needs more optimization.
30	196	0.146164619785	Henry Cohn, 2024, needs more optimization.
30	197	0.147795998133	Henry Cohn, 2024, needs more optimization.
30	198	0.148211252770	Henry Cohn, 2024, needs more optimization.
30	199	0.148723747343	Henry Cohn, 2024, needs more optimization.
30	200	0.149284960566	Henry Cohn, 2024, needs more optimization.
30	201	0.149594498252	Henry Cohn, 2024, needs more optimization.
30	202	0.150191919407	Henry Cohn, 2024, needs more optimization.
30	203	0.150590282774	Henry Cohn, 2024, needs more optimization.
30	204	0.151066166122	Henry Cohn, 2024, needs more optimization.
30	205	0.151411684959	Henry Cohn, 2024, needs more optimization.
30	206	0.151937988677	Henry Cohn, 2024, needs more optimization.
30	207	0.152348247412	Henry Cohn, 2024, needs more optimization.
30	208	0.152634403925	Henry Cohn, 2024, needs more optimization.
30	209	0.153170714276	Henry Cohn, 2024, needs more optimization.
30	210	0.153484251907	Henry Cohn, 2024, needs more optimization.
30	211	0.154089464411	Henry Cohn, 2024, needs more optimization.
30	212	0.154301618212	Henry Cohn, 2024, needs more optimization.
30	213	0.154928384627	Henry Cohn, 2024, needs more optimization.
30	214	0.155323112604	Henry Cohn, 2024, needs more optimization.
30	215	0.155738746464	Henry Cohn, 2024, needs more optimization.
30	216	0.156204176986	Henry Cohn, 2024, needs more optimization.
30	228	0.156393959963	Henry Cohn, 2024, needs more optimization.
30	229	0.161291363805	Henry Cohn, 2024, needs more optimization.
30	230	0.161605839846	Henry Cohn, 2024, needs more optimization.
30	231	0.162162356079	Henry Cohn, 2024, needs more optimization.
30	232	0.162456775625	Henry Cohn, 2024, needs more optimization.
30	233	0.162904839468	Henry Cohn, 2024, needs more optimization.
30	234	0.163196071217	Henry Cohn, 2024, needs more optimization.
30	235	0.163555132934	Henry Cohn, 2024, needs more optimization.
30	236	0.163967546813	Henry Cohn, 2024, needs more optimization.
30	237	0.164382075348	Henry Cohn, 2024, needs more optimization.
30	238	0.164731093288	Henry Cohn, 2024, needs more optimization.
30	239	0.164983220602	Henry Cohn, 2024, needs more optimization.
30	240	0.165460960691	Henry Cohn, 2024, needs more optimization.
30	241	0.165713087214	Henry Cohn, 2024, needs more optimization.
30	242	0.166281978303	Henry Cohn, 2024, needs more optimization.
30	243	0.166547231186	Henry Cohn, 2024, needs more optimization.
30	300	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 25 points in 8 dimensions. $6 x - 1$
30	301	0.172652095036	Orthogonal union of 275 points in 22 dimensions and 26 points in 8 dimensions. Minimal polynomial listed in plain text data
30	302	0.179856457059	Orthogonal union of 275 points in 22 dimensions and 27 points in 8 dimensions. Minimal polynomial listed in plain text data
30	303	0.181158420022	Orthogonal union of 275 points in 22 dimensions and 28 points in 8 dimensions. $36 x^{4} + 24 x^{3} - 36 x^{2} + 1$
30	313	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 16 points in 6 dimensions. $11 x - 2$
30	314	0.183274337024	Orthogonal union of 297 points in 24 dimensions and 17 points in 6 dimensions. $400 x^{4} + 240 x^{3} + 16 x^{2} - 8 x - 1$
30	320	0.190036335836	Henry Cohn, 2024, needs more optimization.
30	347	0.193548387097	Orthogonal union of 330 points in 24 dimensions and 17 points in 6 dimensions. $31 x - 6$
30	348	0.196921795460	Henry Cohn, 2024, needs more optimization.
30	576	0.2	Orthogonal union of 552 points in 23 dimensions and 24 points in 7 dimensions. $5 x - 1$
30	577	0.214737233855	Orthogonal union of 552 points in 23 dimensions and 25 points in 7 dimensions. $31 x^{2} - 2 x - 1$
30	578	0.231331430372	Orthogonal union of 552 points in 23 dimensions and 26 points in 7 dimensions.
30	598	0.238095238096	Orthogonal union of 554 points in 21 dimensions and 44 points in 9 dimensions. $21 x - 5$
30	601	0.238172399483	Orthogonal union of 554 points in 21 dimensions and 47 points in 9 dimensions. $335 x^{2} - 42 x - 9$
30	640	0.245448779707	Henry Cohn, 2024, needs more optimization.
30	930	0.25	Orthogonal union of 891 points in 22 dimensions and 39 points in 8 dimensions. $4 x - 1$
30	931	0.265123725370	Orthogonal union of 891 points in 22 dimensions and 40 points in 8 dimensions.
30	932	0.269595854246	Orthogonal union of 891 points in 22 dimensions and 41 points in 8 dimensions.
30	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.030326003112	Henry Cohn, 2023, needs more optimization.
31	65	0.038669360507	Henry Cohn, 2023, needs more optimization.
31	66	0.040845052935	Henry Cohn, 2023, needs more optimization.
31	67	0.043555597695	Henry Cohn, 2024, needs more optimization.
31	68	0.043775218948	Henry Cohn, 2023, needs more optimization.
31	69	0.044046194499	Henry Cohn, 2023, needs more optimization.
31	70	0.044247209698	Henry Cohn, 2023, needs more optimization.
31	71	0.045132360093	Henry Cohn, 2023, needs more optimization.
31	72	0.047749153443	Orthogonal union of 70 points in 30 dimensions and 2 points in 1 dimension.
31	73	0.050148901897	Henry Cohn, 2023, needs more optimization.
31	74	0.051391812133	Henry Cohn, 2023, needs more optimization.
31	75	0.052425487468	Henry Cohn, 2023, needs more optimization.
31	76	0.054087652338	Henry Cohn, 2023, needs more optimization.
31	77	0.055297966114	Henry Cohn, 2023, needs more optimization.
31	78	0.056749474614	Henry Cohn, 2023, needs more optimization.
31	79	0.057922667385	Henry Cohn, 2023, needs more optimization.
31	80	0.059105989542	Henry Cohn, 2024, needs more optimization.
31	81	0.060343674781	Henry Cohn, 2024, needs more optimization.
31	82	0.061808064806	Henry Cohn, 2024, needs more optimization.
31	83	0.063149282539	Henry Cohn, 2024, needs more optimization.
31	84	0.064053939832	Henry Cohn, 2024, needs more optimization.
31	85	0.065443966217	Henry Cohn, 2024, needs more optimization.
31	86	0.066364775531	Henry Cohn, 2024, needs more optimization.
31	87	0.067878865183	Henry Cohn, 2024, needs more optimization.
31	88	0.068617247004	Henry Cohn, 2024, needs more optimization.
31	89	0.069615915532	Henry Cohn, 2024, needs more optimization.
31	90	0.071164908509	Henry Cohn, 2024, needs more optimization.
31	91	0.072141905276	Henry Cohn, 2024, needs more optimization.
31	92	0.073190852410	Henry Cohn, 2024, needs more optimization.
31	93	0.074319174147	Henry Cohn, 2024, needs more optimization.
31	94	0.074978233367	Henry Cohn, 2024, needs more optimization.
31	95	0.076072257857	Henry Cohn, 2024, needs more optimization.
31	96	0.077001725629	Henry Cohn, 2024, needs more optimization.
31	97	0.078032319277	Henry Cohn, 2024, needs more optimization.
31	98	0.079071763950	Henry Cohn, 2024, needs more optimization.
31	99	0.079905709509	Henry Cohn, 2024, needs more optimization.
31	100	0.080592766903	Henry Cohn, 2024, needs more optimization.
31	101	0.081567389469	Henry Cohn, 2024, needs more optimization.
31	102	0.082485134972	Henry Cohn, 2024, needs more optimization.
31	103	0.083366339350	Henry Cohn, 2024, needs more optimization.
31	104	0.084293438310	Henry Cohn, 2024, needs more optimization.
31	105	0.084943811017	Henry Cohn, 2024, needs more optimization.
31	106	0.085957563295	Henry Cohn, 2024, needs more optimization.
31	116	0.086333305850	Henry Cohn, 2024, needs more optimization.
31	119	0.088384604201	Henry Cohn, 2024, needs more optimization.
31	121	0.090909090910	Orthogonal union of 100 points in 22 dimensions and 21 points in 9 dimensions. $11 x - 1$
31	122	0.097075019140	Henry Cohn, 2024, needs more optimization.
31	123	0.097719944481	Henry Cohn, 2024, needs more optimization.
31	124	0.098246224233	Henry Cohn, 2024, needs more optimization.
31	125	0.098808971229	Henry Cohn, 2024, needs more optimization.
31	126	0.099578231743	Henry Cohn, 2024, needs more optimization.
31	127	0.100293341787	Henry Cohn, 2024, needs more optimization.
31	128	0.100771919550	Henry Cohn, 2024, needs more optimization.
31	129	0.101280472100	Henry Cohn, 2024, needs more optimization.
31	130	0.101888661101	Henry Cohn, 2024, needs more optimization.
31	131	0.102404682165	Henry Cohn, 2024, needs more optimization.
31	132	0.103128258506	Henry Cohn, 2024, needs more optimization.
31	133	0.103691560609	Henry Cohn, 2024, needs more optimization.
31	134	0.104159695240	Henry Cohn, 2024, needs more optimization.
31	135	0.104686167563	Henry Cohn, 2024, needs more optimization.
31	136	0.105357288574	Henry Cohn, 2024, needs more optimization.
31	137	0.105714227034	Henry Cohn, 2024, needs more optimization.
31	138	0.106290145479	Henry Cohn, 2024, needs more optimization.
31	139	0.107089609510	Henry Cohn, 2024, needs more optimization.
31	140	0.107606620308	Henry Cohn, 2024, needs more optimization.
31	141	0.108080608008	Henry Cohn, 2024, needs more optimization.
31	142	0.108654540648	Henry Cohn, 2024, needs more optimization.
31	143	0.109370683000	Henry Cohn, 2024, needs more optimization.
31	144	0.109697861349	Henry Cohn, 2024, needs more optimization.
31	145	0.110397023389	Henry Cohn, 2024, needs more optimization.
31	146	0.110805420329	Henry Cohn, 2024, needs more optimization.
31	147	0.111552213817	Henry Cohn, 2024, needs more optimization.
31	148	0.112152438495	Henry Cohn, 2024, needs more optimization.
31	149	0.112977234084	Henry Cohn, 2024, needs more optimization.
31	150	0.113482238343	Henry Cohn, 2024, needs more optimization.
31	151	0.114126591977	Henry Cohn, 2024, needs more optimization.
31	152	0.114377592776	Henry Cohn, 2024, needs more optimization.
31	153	0.115029108950	Henry Cohn, 2024, needs more optimization.
31	154	0.115831577419	Henry Cohn, 2024, needs more optimization.
31	155	0.116222191649	Henry Cohn, 2024, needs more optimization.
31	156	0.117139993281	Henry Cohn, 2024, needs more optimization.
31	157	0.117597806524	Henry Cohn, 2024, needs more optimization.
31	158	0.118116098225	Henry Cohn, 2024, needs more optimization.
31	159	0.118845328001	Henry Cohn, 2024, needs more optimization.
31	160	0.119481156688	Henry Cohn, 2024, needs more optimization.
31	161	0.120313792397	Henry Cohn, 2024, needs more optimization.
31	162	0.120662393999	Henry Cohn, 2024, needs more optimization.
31	163	0.121451145415	Henry Cohn, 2024, needs more optimization.
31	164	0.122040188717	Henry Cohn, 2024, needs more optimization.
31	165	0.122618688933	Henry Cohn, 2024, needs more optimization.
31	166	0.123448505215	Henry Cohn, 2024, needs more optimization.
31	167	0.123905695105	Henry Cohn, 2024, needs more optimization.
31	168	0.124687469129	Henry Cohn, 2024, needs more optimization.
31	169	0.125288921229	Henry Cohn, 2024, needs more optimization.
31	170	0.125847524493	Henry Cohn, 2024, needs more optimization.
31	171	0.126383179192	Henry Cohn, 2024, needs more optimization.
31	172	0.127186509311	Henry Cohn, 2024, needs more optimization.
31	173	0.127812369839	Henry Cohn, 2024, needs more optimization.
31	174	0.128446474676	Henry Cohn, 2024, needs more optimization.
31	175	0.128919345703	Henry Cohn, 2024, needs more optimization.
31	176	0.129487896380	Henry Cohn, 2024, needs more optimization.
31	177	0.130232363346	Henry Cohn, 2024, needs more optimization.
31	178	0.130767653339	Henry Cohn, 2024, needs more optimization.
31	179	0.131421943519	Henry Cohn, 2024, needs more optimization.
31	180	0.132109727595	Henry Cohn, 2024, needs more optimization.
31	181	0.132704266308	Henry Cohn, 2024, needs more optimization.
31	182	0.133165647800	Henry Cohn, 2024, needs more optimization.
31	183	0.133592906924	Henry Cohn, 2024, needs more optimization.
31	184	0.134020981501	Henry Cohn, 2024, needs more optimization.
31	185	0.134819608867	Henry Cohn, 2024, needs more optimization.
31	186	0.135253824767	Henry Cohn, 2024, needs more optimization.
31	187	0.135928069478	Henry Cohn, 2024, needs more optimization.
31	188	0.136205963392	Henry Cohn, 2024, needs more optimization.
31	189	0.136962974548	Henry Cohn, 2024, needs more optimization.
31	190	0.137448448528	Henry Cohn, 2024, needs more optimization.
31	191	0.137837860167	Henry Cohn, 2024, needs more optimization.
31	193	0.138785604708	Henry Cohn, 2024, needs more optimization.
31	194	0.140626287602	Henry Cohn, 2024, needs more optimization.
31	195	0.140935909114	Henry Cohn, 2024, needs more optimization.
31	196	0.141634059830	Henry Cohn, 2024, needs more optimization.
31	197	0.142052633451	Henry Cohn, 2024, needs more optimization.
31	198	0.142279490316	Henry Cohn, 2024, needs more optimization.
31	199	0.142915834948	Henry Cohn, 2024, needs more optimization.
31	200	0.143269451825	Henry Cohn, 2024, needs more optimization.
31	201	0.143781778452	Henry Cohn, 2024, needs more optimization.
31	202	0.144363732482	Henry Cohn, 2024, needs more optimization.
31	203	0.144766911561	Henry Cohn, 2024, needs more optimization.
31	204	0.145231211899	Henry Cohn, 2024, needs more optimization.
31	206	0.145575641944	Henry Cohn, 2024, needs more optimization.
31	207	0.146329758147	Henry Cohn, 2024, needs more optimization.
31	208	0.146893758352	Henry Cohn, 2024, needs more optimization.
31	209	0.147401991637	Henry Cohn, 2024, needs more optimization.
31	210	0.147662297683	Henry Cohn, 2024, needs more optimization.
31	211	0.148099035183	Henry Cohn, 2024, needs more optimization.
31	212	0.148680608437	Henry Cohn, 2024, needs more optimization.
31	213	0.149033350354	Henry Cohn, 2024, needs more optimization.
31	214	0.149383896743	Henry Cohn, 2024, needs more optimization.
31	215	0.149818840342	Henry Cohn, 2024, needs more optimization.
31	216	0.150141225449	Henry Cohn, 2024, needs more optimization.
31	217	0.150783335686	Henry Cohn, 2024, needs more optimization.
31	218	0.151139144976	Henry Cohn, 2024, needs more optimization.
31	219	0.151588988391	Henry Cohn, 2024, needs more optimization.
31	220	0.152017567705	Henry Cohn, 2024, needs more optimization.
31	221	0.152317541079	Henry Cohn, 2024, needs more optimization.
31	222	0.152708151337	Henry Cohn, 2024, needs more optimization.
31	223	0.153141112930	Henry Cohn, 2024, needs more optimization.
31	224	0.153569349926	Henry Cohn, 2024, needs more optimization.
31	225	0.154004956773	Henry Cohn, 2024, needs more optimization.
31	226	0.154364467108	Henry Cohn, 2024, needs more optimization.
31	227	0.154660664650	Henry Cohn, 2024, needs more optimization.
31	228	0.155079306475	Henry Cohn, 2024, needs more optimization.
31	229	0.155584409685	Henry Cohn, 2024, needs more optimization.
31	230	0.155817747733	Henry Cohn, 2024, needs more optimization.
31	231	0.156287716116	Henry Cohn, 2024, needs more optimization.
31	232	0.156457034734	Henry Cohn, 2024, needs more optimization.
31	233	0.157021734225	Henry Cohn, 2024, needs more optimization.
31	234	0.157310611332	Henry Cohn, 2024, needs more optimization.
31	235	0.157581277503	Henry Cohn, 2024, needs more optimization.
31	236	0.158082352287	Henry Cohn, 2024, needs more optimization.
31	237	0.158436941690	Henry Cohn, 2024, needs more optimization.
31	238	0.158922811900	Henry Cohn, 2024, needs more optimization.
31	239	0.159145541711	Henry Cohn, 2024, needs more optimization.
31	240	0.159592418999	Henry Cohn, 2024, needs more optimization.
31	241	0.159880676011	Henry Cohn, 2024, needs more optimization.
31	242	0.160293419696	Henry Cohn, 2024, needs more optimization.
31	243	0.160637118065	Henry Cohn, 2024, needs more optimization.
31	244	0.161075140904	Henry Cohn, 2024, needs more optimization.
31	245	0.161227402549	Henry Cohn, 2024, needs more optimization.
31	246	0.161675769279	Henry Cohn, 2024, needs more optimization.
31	247	0.162042821463	Henry Cohn, 2024, needs more optimization.
31	248	0.162169362083	Henry Cohn, 2024, needs more optimization.
31	249	0.162839798575	Henry Cohn, 2024, needs more optimization.
31	250	0.163018815759	Henry Cohn, 2024, needs more optimization.
31	251	0.163383781125	Henry Cohn, 2024, needs more optimization.
31	252	0.163830044300	Henry Cohn, 2024, needs more optimization.
31	253	0.164233580233	Henry Cohn, 2024, needs more optimization.
31	254	0.164489105779	Henry Cohn, 2024, needs more optimization.
31	255	0.164827942935	Henry Cohn, 2024, needs more optimization.
31	256	0.165213322974	Henry Cohn, 2024, needs more optimization.
31	307	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 32 points in 9 dimensions. $6 x - 1$
31	308	0.180525091271	Orthogonal union of 275 points in 22 dimensions and 33 points in 9 dimensions.
31	318	0.181818181819	Orthogonal union of 297 points in 24 dimensions and 21 points in 7 dimensions. $11 x - 2$
31	321	0.182743997632	Orthogonal union of 297 points in 24 dimensions and 24 points in 7 dimensions. $19 x^{2} + 2 x - 1$
31	322	0.184421713382	Henry Cohn, 2024, needs more optimization.
31	354	0.192103883717	Henry Cohn, 2024, needs more optimization.
31	384	0.198471420781	Henry Cohn, 2024, needs more optimization.
31	581	0.2	Orthogonal union of 552 points in 23 dimensions and 29 points in 8 dimensions. $5 x - 1$
31	582	0.203916279404	Orthogonal union of 552 points in 23 dimensions and 30 points in 8 dimensions.
31	583	0.219706574300	Orthogonal union of 552 points in 23 dimensions and 31 points in 8 dimensions.
31	585	0.227325452024	Orthogonal union of 552 points in 23 dimensions and 33 points in 8 dimensions. $95 x^{2} - 4 x - 4$
31	586	0.231571616436	Henry Cohn, 2024, needs more optimization.
31	587	0.231696388312	Henry Cohn, 2024, needs more optimization.
31	611	0.234739212583	Henry Cohn, 2024, needs more optimization.
31	640	0.238330124758	Henry Cohn, 2024, needs more optimization.
31	642	0.238613911178	Henry Cohn, 2024, needs more optimization.
31	704	0.245697980685	Henry Cohn, 2024, needs more optimization.
31	938	0.25	Orthogonal union of 891 points in 22 dimensions and 47 points in 9 dimensions. $4 x - 1$
31	939	0.254741941811	Orthogonal union of 891 points in 22 dimensions and 48 points in 9 dimensions.
31	940	0.261827927697	Orthogonal union of 891 points in 22 dimensions and 49 points in 9 dimensions.
31	943	0.267191024627	Orthogonal union of 891 points in 22 dimensions and 52 points in 9 dimensions. $71 x^{2} - 4 x - 4$
31	944	0.267727681714	Henry Cohn, 2024, needs more optimization.
31	945	0.267850355681	Henry Cohn, 2024, needs more optimization.
31	960	0.268864067760	Henry Cohn, 2024, needs more optimization.
31	1024	0.272727272728	Code with 1024 points in 22 dimensions. $11 x - 3$
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	0.029445340348	Henry Cohn, 2023, needs more optimization.
32	67	0.037581892467	Henry Cohn, 2023, needs more optimization.
32	68	0.040226652445	Henry Cohn, 2024, needs more optimization.
32	69	0.042823334368	Henry Cohn, 2023, needs more optimization.
32	70	0.043196851307	Henry Cohn, 2023, needs more optimization.
32	71	0.043563460215	Henry Cohn, 2023, needs more optimization.
32	72	0.043962434247	Henry Cohn, 2023, needs more optimization.
32	73	0.044667272203	Henry Cohn, 2023, needs more optimization.
32	74	0.047181179664	Henry Cohn, 2023, needs more optimization.
32	75	0.049145686426	Henry Cohn, 2023, needs more optimization.
32	76	0.050189771888	Henry Cohn, 2024, needs more optimization.
32	77	0.051597414931	Henry Cohn, 2023, needs more optimization.
32	78	0.052487445963	Henry Cohn, 2023, needs more optimization.
32	79	0.053816998591	Henry Cohn, 2023, needs more optimization.
32	80	0.055209750842	Henry Cohn, 2023, needs more optimization.
32	81	0.056315367776	Henry Cohn, 2023, needs more optimization.
32	82	0.057605436780	Henry Cohn, 2024, needs more optimization.
32	83	0.058664452660	Henry Cohn, 2024, needs more optimization.
32	84	0.059950435979	Henry Cohn, 2024, needs more optimization.
32	85	0.060949039535	Henry Cohn, 2024, needs more optimization.
32	86	0.062285819891	Henry Cohn, 2024, needs more optimization.
32	87	0.063499574511	Henry Cohn, 2024, needs more optimization.
32	88	0.064415218950	Henry Cohn, 2024, needs more optimization.
32	89	0.065608268875	Henry Cohn, 2024, needs more optimization.
32	90	0.066461669541	Henry Cohn, 2024, needs more optimization.
32	91	0.067833287386	Henry Cohn, 2024, needs more optimization.
32	92	0.068784683903	Henry Cohn, 2024, needs more optimization.
32	93	0.069874817250	Henry Cohn, 2024, needs more optimization.
32	94	0.070694338373	Henry Cohn, 2024, needs more optimization.
32	95	0.071771482909	Henry Cohn, 2024, needs more optimization.
32	96	0.073138173194	Henry Cohn, 2024, needs more optimization.
32	97	0.073959329801	Henry Cohn, 2024, needs more optimization.
32	98	0.074790878611	Henry Cohn, 2024, needs more optimization.
32	99	0.075692955783	Henry Cohn, 2024, needs more optimization.
32	100	0.076418937245	Henry Cohn, 2024, needs more optimization.
32	101	0.077434800052	Henry Cohn, 2024, needs more optimization.
32	102	0.078291671934	Henry Cohn, 2024, needs more optimization.
32	103	0.079142788349	Henry Cohn, 2024, needs more optimization.
32	104	0.080102471268	Henry Cohn, 2024, needs more optimization.
32	105	0.081099277422	Henry Cohn, 2024, needs more optimization.
32	106	0.081695409363	Henry Cohn, 2024, needs more optimization.
32	107	0.082188092332	Henry Cohn, 2024, needs more optimization.
32	108	0.083160548753	Henry Cohn, 2024, needs more optimization.
32	109	0.083806345170	Henry Cohn, 2024, needs more optimization.
32	110	0.084697338620	Henry Cohn, 2024, needs more optimization.
32	111	0.085505482267	Henry Cohn, 2024, needs more optimization.
32	112	0.086022845124	Henry Cohn, 2024, needs more optimization.
32	118	0.086322451079	Henry Cohn, 2024, needs more optimization.
32	121	0.087115245525	Henry Cohn, 2024, needs more optimization.
32	123	0.090909090910	Orthogonal union of 100 points in 22 dimensions and 23 points in 10 dimensions. $11 x - 1$
32	124	0.094247880572	Henry Cohn, 2024, needs more optimization.
32	125	0.094921797910	Henry Cohn, 2024, needs more optimization.
32	126	0.095236820600	Henry Cohn, 2024, needs more optimization.
32	127	0.095959875042	Henry Cohn, 2024, needs more optimization.
32	128	0.096665133236	Henry Cohn, 2024, needs more optimization.
32	129	0.097207373205	Henry Cohn, 2024, needs more optimization.
32	130	0.097753212820	Henry Cohn, 2024, needs more optimization.
32	131	0.098399111068	Henry Cohn, 2024, needs more optimization.
32	132	0.098917249661	Henry Cohn, 2024, needs more optimization.
32	133	0.099580461460	Henry Cohn, 2024, needs more optimization.
32	134	0.100174414427	Henry Cohn, 2024, needs more optimization.
32	135	0.100846028147	Henry Cohn, 2024, needs more optimization.
32	136	0.100973164693	Henry Cohn, 2024, needs more optimization.
32	137	0.101677931946	Henry Cohn, 2024, needs more optimization.
32	138	0.102174312781	Henry Cohn, 2024, needs more optimization.
32	139	0.102635526755	Henry Cohn, 2024, needs more optimization.
32	140	0.103260536468	Henry Cohn, 2024, needs more optimization.
32	141	0.103792451631	Henry Cohn, 2024, needs more optimization.
32	142	0.104263655246	Henry Cohn, 2024, needs more optimization.
32	143	0.105090699344	Henry Cohn, 2024, needs more optimization.
32	144	0.105487786149	Henry Cohn, 2024, needs more optimization.
32	145	0.106023935628	Henry Cohn, 2024, needs more optimization.
32	146	0.106451586146	Henry Cohn, 2024, needs more optimization.
32	147	0.106855065256	Henry Cohn, 2024, needs more optimization.
32	148	0.107630510421	Henry Cohn, 2024, needs more optimization.
32	149	0.108142113287	Henry Cohn, 2024, needs more optimization.
32	150	0.108781514535	Henry Cohn, 2024, needs more optimization.
32	151	0.109157616876	Henry Cohn, 2024, needs more optimization.
32	152	0.109732207821	Henry Cohn, 2024, needs more optimization.
32	153	0.110301066396	Henry Cohn, 2024, needs more optimization.
32	154	0.110697436038	Henry Cohn, 2024, needs more optimization.
32	155	0.111393501673	Henry Cohn, 2024, needs more optimization.
32	156	0.112249864991	Henry Cohn, 2024, needs more optimization.
32	157	0.112712035944	Henry Cohn, 2024, needs more optimization.
32	158	0.113343333855	Henry Cohn, 2024, needs more optimization.
32	159	0.113911844059	Henry Cohn, 2024, needs more optimization.
32	160	0.114306405210	Henry Cohn, 2024, needs more optimization.
32	161	0.114922705925	Henry Cohn, 2024, needs more optimization.
32	162	0.115511600197	Henry Cohn, 2024, needs more optimization.
32	163	0.116024300457	Henry Cohn, 2024, needs more optimization.
32	164	0.116788199149	Henry Cohn, 2024, needs more optimization.
32	165	0.117075026109	Henry Cohn, 2024, needs more optimization.
32	166	0.117783678450	Henry Cohn, 2024, needs more optimization.
32	167	0.118516318213	Henry Cohn, 2024, needs more optimization.
32	168	0.119104852945	Henry Cohn, 2024, needs more optimization.
32	169	0.119608492518	Henry Cohn, 2024, needs more optimization.
32	170	0.120232877287	Henry Cohn, 2024, needs more optimization.
32	171	0.121023216114	Henry Cohn, 2024, needs more optimization.
32	172	0.121611033286	Henry Cohn, 2024, needs more optimization.
32	173	0.121956368117	Henry Cohn, 2024, needs more optimization.
32	174	0.122547527589	Henry Cohn, 2024, needs more optimization.
32	175	0.123463526284	Henry Cohn, 2024, needs more optimization.
32	176	0.123940542063	Henry Cohn, 2024, needs more optimization.
32	177	0.124475117668	Henry Cohn, 2024, needs more optimization.
32	178	0.125047188332	Henry Cohn, 2024, needs more optimization.
32	179	0.125586736264	Henry Cohn, 2024, needs more optimization.
32	180	0.126109622396	Henry Cohn, 2024, needs more optimization.
32	181	0.126636017575	Henry Cohn, 2024, needs more optimization.
32	182	0.127292733138	Henry Cohn, 2024, needs more optimization.
32	183	0.127945851948	Henry Cohn, 2024, needs more optimization.
32	184	0.128637668533	Henry Cohn, 2024, needs more optimization.
32	185	0.128862548357	Henry Cohn, 2024, needs more optimization.
32	186	0.129570358424	Henry Cohn, 2024, needs more optimization.
32	187	0.130181855496	Henry Cohn, 2024, needs more optimization.
32	188	0.130556308761	Henry Cohn, 2024, needs more optimization.
32	189	0.131219899361	Henry Cohn, 2024, needs more optimization.
32	190	0.131765273811	Henry Cohn, 2024, needs more optimization.
32	191	0.132284294857	Henry Cohn, 2024, needs more optimization.
32	192	0.133539596390	Henry Cohn, 2024, needs more optimization.
32	193	0.134262654550	Henry Cohn, 2024, needs more optimization.
32	194	0.134929835447	Henry Cohn, 2024, needs more optimization.
32	195	0.135434727410	Henry Cohn, 2024, needs more optimization.
32	198	0.135660128288	Henry Cohn, 2024, needs more optimization.
32	199	0.136147798396	Henry Cohn, 2024, needs more optimization.
32	200	0.137776910845	Henry Cohn, 2024, needs more optimization.
32	201	0.138145244190	Henry Cohn, 2024, needs more optimization.
32	202	0.138747194053	Henry Cohn, 2024, needs more optimization.
32	203	0.139165889514	Henry Cohn, 2024, needs more optimization.
32	204	0.139619184497	Henry Cohn, 2024, needs more optimization.
32	205	0.139962970787	Henry Cohn, 2024, needs more optimization.
32	206	0.140532455872	Henry Cohn, 2024, needs more optimization.
32	207	0.141114916562	Henry Cohn, 2024, needs more optimization.
32	208	0.141447765166	Henry Cohn, 2024, needs more optimization.
32	209	0.141920604185	Henry Cohn, 2024, needs more optimization.
32	210	0.142397148679	Henry Cohn, 2024, needs more optimization.
32	211	0.142547029999	Henry Cohn, 2024, needs more optimization.
32	212	0.143292784673	Henry Cohn, 2024, needs more optimization.
32	213	0.143496652271	Henry Cohn, 2024, needs more optimization.
32	214	0.143970521276	Henry Cohn, 2024, needs more optimization.
32	215	0.144448160892	Henry Cohn, 2024, needs more optimization.
32	216	0.144822522128	Henry Cohn, 2024, needs more optimization.
32	217	0.145154703196	Henry Cohn, 2024, needs more optimization.
32	218	0.145535448958	Henry Cohn, 2024, needs more optimization.
32	219	0.146063229319	Henry Cohn, 2024, needs more optimization.
32	220	0.146268599081	Henry Cohn, 2024, needs more optimization.
32	221	0.146669538127	Henry Cohn, 2024, needs more optimization.
32	222	0.147239059189	Henry Cohn, 2024, needs more optimization.
32	223	0.147575978269	Henry Cohn, 2024, needs more optimization.
32	224	0.148028373804	Henry Cohn, 2024, needs more optimization.
32	225	0.148554925284	Henry Cohn, 2024, needs more optimization.
32	226	0.148789642076	Henry Cohn, 2024, needs more optimization.
32	227	0.149151968983	Henry Cohn, 2024, needs more optimization.
32	228	0.149519171910	Henry Cohn, 2024, needs more optimization.
32	229	0.149915839019	Henry Cohn, 2024, needs more optimization.
32	230	0.150195661057	Henry Cohn, 2024, needs more optimization.
32	231	0.150746241841	Henry Cohn, 2024, needs more optimization.
32	232	0.150992436237	Henry Cohn, 2024, needs more optimization.
32	233	0.151315512910	Henry Cohn, 2024, needs more optimization.
32	234	0.151849179718	Henry Cohn, 2024, needs more optimization.
32	235	0.152191294806	Henry Cohn, 2024, needs more optimization.
32	236	0.152493936910	Henry Cohn, 2024, needs more optimization.
32	237	0.152846462273	Henry Cohn, 2024, needs more optimization.
32	238	0.153313327689	Henry Cohn, 2024, needs more optimization.
32	239	0.153679441926	Henry Cohn, 2024, needs more optimization.
32	240	0.153983448378	Henry Cohn, 2024, needs more optimization.
32	241	0.154403415712	Henry Cohn, 2024, needs more optimization.
32	242	0.154623333874	Henry Cohn, 2024, needs more optimization.
32	243	0.155057772420	Henry Cohn, 2024, needs more optimization.
32	244	0.155440481924	Henry Cohn, 2024, needs more optimization.
32	245	0.155784522588	Henry Cohn, 2024, needs more optimization.
32	246	0.156087902833	Henry Cohn, 2024, needs more optimization.
32	247	0.156449174614	Henry Cohn, 2024, needs more optimization.
32	248	0.156836637705	Henry Cohn, 2024, needs more optimization.
32	249	0.157100779642	Henry Cohn, 2024, needs more optimization.
32	250	0.157471888930	Henry Cohn, 2024, needs more optimization.
32	251	0.157820261960	Henry Cohn, 2024, needs more optimization.
32	252	0.157901053151	Henry Cohn, 2024, needs more optimization.
32	253	0.158528698811	Henry Cohn, 2024, needs more optimization.
32	254	0.158789357358	Henry Cohn, 2024, needs more optimization.
32	255	0.159047752240	Henry Cohn, 2024, needs more optimization.
32	256	0.159527957521	Henry Cohn, 2024, needs more optimization.
32	257	0.159777420384	Henry Cohn, 2024, needs more optimization.
32	258	0.160237382944	Henry Cohn, 2024, needs more optimization.
32	315	0.166666666667	Orthogonal union of 275 points in 22 dimensions and 40 points in 10 dimensions. $6 x - 1$
32	316	0.176776695297	Orthogonal union of 275 points in 22 dimensions and 41 points in 10 dimensions. $32 x^{2} - 1$
32	320	0.178057661503	Henry Cohn, 2024, needs more optimization.
32	325	0.179336524553	Henry Cohn, 2024, needs more optimization.
32	326	0.179585504443	Henry Cohn, 2024, needs more optimization.
32	359	0.187269281447	Henry Cohn, 2024, needs more optimization.
32	384	0.192717660678	Henry Cohn, 2024, needs more optimization.
32	386	0.193139872996	Henry Cohn, 2024, needs more optimization.
32	588	0.2	Orthogonal union of 552 points in 23 dimensions and 36 points in 9 dimensions. $5 x - 1$
32	589	0.213783378445	Orthogonal union of 552 points in 23 dimensions and 37 points in 9 dimensions.
32	590	0.217711380183	Orthogonal union of 552 points in 23 dimensions and 38 points in 9 dimensions.
32	591	0.222837046412	Orthogonal union of 552 points in 23 dimensions and 39 points in 9 dimensions.
32	592	0.225704407232	Orthogonal union of 552 points in 23 dimensions and 40 points in 9 dimensions.
32	593	0.226047015984	Henry Cohn, 2024, needs more optimization.
32	594	0.226137634576	Henry Cohn, 2024, needs more optimization.
32	595	0.226367289457	Henry Cohn, 2024, needs more optimization.
32	640	0.231725087010	Henry Cohn, 2024, needs more optimization.
32	642	0.232123880077	Henry Cohn, 2024, needs more optimization.
32	644	0.232220466778	Henry Cohn, 2024, needs more optimization.
32	704	0.239034485380	Henry Cohn, 2024, needs more optimization.
32	768	0.245528148444	Henry Cohn, 2024, needs more optimization.
32	948	0.25	Orthogonal union of 891 points in 22 dimensions and 57 points in 10 dimensions. $4 x - 1$
32	949	0.253642861547	Orthogonal union of 891 points in 22 dimensions and 58 points in 10 dimensions.
32	950	0.253695768487	Orthogonal union of 891 points in 22 dimensions and 59 points in 10 dimensions.
32	951	0.256704396577	Orthogonal union of 891 points in 22 dimensions and 60 points in 10 dimensions.
32	952	0.260972170006	Orthogonal union of 891 points in 22 dimensions and 61 points in 10 dimensions.
32	957	0.261722453430	Henry Cohn, 2024, needs more optimization.
32	960	0.261983297388	Henry Cohn, 2024, needs more optimization.
32	1024	0.266505957750	Henry Cohn, 2024, needs more optimization.
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. $8 x - 1$