docs/doc/dox/results.dox File Reference

Functions
page results Results f [\begin{array}{|l|l|c|} n &a &M_{8, 8, 8, 8} \ 2^4-3 &1, 5, 2, 3, 4, 6, 1, 1 &0.365013 \ 2^4 &1, 4, 7, 3, 5, 2, 6, 8 &0.465302 \ 2^5-1 &1, 12, 9, 14, 4, 5, 2, 3 &0.373740 \ 2^5 &1, 7, 5, 3, 4, 9, 11, 12 &0.465302 \ 2^6-3 &1, 8, 11, 5, 26, 14, 6, 21 &0.391994 \ 2^6 &1, 28, 19, 5, 11, 6, 9, 16 &0.385770 \ 2^7-1 &1, 12, 29, 19, 34, 14, 37, 50 &0.434146 \ 2^7 &1, 12, 19, 27, 22, 14, 17, 59 &0.433013 \ 2^8-5 &1, 74, 20, 48, 92, 35, 78, 51 &0.376115 \ 2^8 &1, 30, 39, 55, 82, 35, 42, 76 &0.353791 \ 2^9-3 &1, 133, 91, 216, 116, 12, 40, 198 &0.417497 \ 2^9 &1, 200, 35, 215, 26, 223, 119, 195 &0.385770 \ 2^{10}-3 &1, 96, 362, 398, 141, 271, 348, 83 &0.393582 \ 2^{10} &1, 271, 318, 499, 404, 359, 367, 168 &0.393293 \ 2^{11}-9 &1, 48, 423, 607, 178, 700, 223, 959 &0.395720 \ 2^{11} &1, 592, 605, 994, 709, 483, 33, 809 &0.420923 \ 2^{12}-3 &1, 1006, 726, 1499, 854, 1267, 1242, 1831 &0.393821 \ 2^{12} &1, 70, 923, 537, 552, 1799, 121, 1931 &0.407097 \ 2^{13}-1 &1, 352, 1140, 97, 504, 3600, 976, 3914 &0.409857 \ 2^{13} &1, 1530, 3993, 1459, 3735, 4017, 1677, 710 &0.402628 \ 2^{14}-3 &1, 2791, 4242, 1553, 646, 4268, 7810, 2490 &0.413170 \ 2^{14} &1, 1435, 3012, 5281, 4253, 2785, 5070, 521 &0.433878 \ 2^{15}-19 &1, 2930, 8238, 6188, 7401, 3830, 16145, 1970 &0.441163 \ 2^{15} &1, 15936, 2477, 8921, 10843, 5793, 14993, 3929 &0.425983 \ 2^{16}-15 &1, 15176, 5500, 11258, 21587, 11947, 11335, 13421 &0.426992 \ 2^{16} &1, 25962, 3951, 27605, 12867, 23469, 30465, 26877 &0.433013 \ 2^{17}-1 &1, 5728, 46083, 738, 57708, 25004, 44213, 15544 &0.437501 \ 2^{17} &1, 49531, 24184, 27343, 37315, 41751, 24099, 29195 &0.441607 \ 2^{18}-5 &1, 20607, 90986, 87159, 22139, 96431, 95971, 15285 &0.423601 \ 2^{18} &1, 1990, 6127, 95749, 6403, 50962, 90889, 16202 &0.436563 \ 2^{19}-19 &1, 86366, 257557, 123933, 69020, 130871, 104469, 138905 &0.430331 \ 2^{19} &1, 86592, 229449, 48883, 41139, 13183, 14653, 159370 &0.439726 \ 2^{20}-3 &1, 252568, 73563, 313721, 427298, 32383, 139705, 519946 &0.443624 \ 2^{20} &1, 195638, 294513, 74663, 28892, 80429, 92213, 143495 &0.433700 \\mbox{Nb. of projections} &&158\end{array}\f]< center > Best f $a f $’s with respect to f component by for general rank lattices of dimension</center > f [\begin{array}{|l|l|c|} n &a &M_{2, 2, 2, 2} \ 13 &2 &0.577137 \ 31 &12 &0.900085 \ 61 &17 &0.907433 \ 127 &12 &0.994369 \ 251 &78 &0.963395 \ 509 &155 &0.952292 \ 1021 &90 &0.958001 \ 2039 &977 &0.986867 \ 4093 &1153 &0.976319 \ 8191 &1466 &0.996338 \ 16381 &1543 &0.993605 \ 32749 &2059 &0.991324 \ 65521 &21748 &0.994778 \ 131071 &37302 &0.997013 \ 262139 &206676 &0.998712 \ 524269 &86366 &0.999171 \ 1048573 &395633 &0.999123 \\mbox{Nb. of projections} &&1\end{array}\f]< center > Best f $a f	$’s (primitive element) with respect to \f $M_

Variables
page results Results f [\begin{array}{|l|l|c|} n &a &M_{8, 8, 8, 8} \ 2^4-3 &1, 5, 2, 3, 4, 6, 1, 1 &0.365013 \ 2^4 &1, 4, 7, 3, 5, 2, 6, 8 &0.465302 \ 2^5-1 &1, 12, 9, 14, 4, 5, 2, 3 &0.373740 \ 2^5 &1, 7, 5, 3, 4, 9, 11, 12 &0.465302 \ 2^6-3 &1, 8, 11, 5, 26, 14, 6, 21 &0.391994 \ 2^6 &1, 28, 19, 5, 11, 6, 9, 16 &0.385770 \ 2^7-1 &1, 12, 29, 19, 34, 14, 37, 50 &0.434146 \ 2^7 &1, 12, 19, 27, 22, 14, 17, 59 &0.433013 \ 2^8-5 &1, 74, 20, 48, 92, 35, 78, 51 &0.376115 \ 2^8 &1, 30, 39, 55, 82, 35, 42, 76 &0.353791 \ 2^9-3 &1, 133, 91, 216, 116, 12, 40, 198 &0.417497 \ 2^9 &1, 200, 35, 215, 26, 223, 119, 195 &0.385770 \ 2^{10}-3 &1, 96, 362, 398, 141, 271, 348, 83 &0.393582 \ 2^{10} &1, 271, 318, 499, 404, 359, 367, 168 &0.393293 \ 2^{11}-9 &1, 48, 423, 607, 178, 700, 223, 959 &0.395720 \ 2^{11} &1, 592, 605, 994, 709, 483, 33, 809 &0.420923 \ 2^{12}-3 &1, 1006, 726, 1499, 854, 1267, 1242, 1831 &0.393821 \ 2^{12} &1, 70, 923, 537, 552, 1799, 121, 1931 &0.407097 \ 2^{13}-1 &1, 352, 1140, 97, 504, 3600, 976, 3914 &0.409857 \ 2^{13} &1, 1530, 3993, 1459, 3735, 4017, 1677, 710 &0.402628 \ 2^{14}-3 &1, 2791, 4242, 1553, 646, 4268, 7810, 2490 &0.413170 \ 2^{14} &1, 1435, 3012, 5281, 4253, 2785, 5070, 521 &0.433878 \ 2^{15}-19 &1, 2930, 8238, 6188, 7401, 3830, 16145, 1970 &0.441163 \ 2^{15} &1, 15936, 2477, 8921, 10843, 5793, 14993, 3929 &0.425983 \ 2^{16}-15 &1, 15176, 5500, 11258, 21587, 11947, 11335, 13421 &0.426992 \ 2^{16} &1, 25962, 3951, 27605, 12867, 23469, 30465, 26877 &0.433013 \ 2^{17}-1 &1, 5728, 46083, 738, 57708, 25004, 44213, 15544 &0.437501 \ 2^{17} &1, 49531, 24184, 27343, 37315, 41751, 24099, 29195 &0.441607 \ 2^{18}-5 &1, 20607, 90986, 87159, 22139, 96431, 95971, 15285 &0.423601 \ 2^{18} &1, 1990, 6127, 95749, 6403, 50962, 90889, 16202 &0.436563 \ 2^{19}-19 &1, 86366, 257557, 123933, 69020, 130871, 104469, 138905 &0.430331 \ 2^{19} &1, 86592, 229449, 48883, 41139, 13183, 14653, 159370 &0.439726 \ 2^{20}-3 &1, 252568, 73563, 313721, 427298, 32383, 139705, 519946 &0.443624 \ 2^{20} &1, 195638, 294513, 74663, 28892, 80429, 92213, 143495 &0.433700 \\mbox{Nb. of projections} &&158\end{array}\f]< center > Best f $a f $’s with respect to f	$M_ {8,8,8,8}\f$ from a search
page results Results f [\begin{array}{|l|l|c|} n &a &M_{8, 8, 8, 8} \ 2^4-3 &1, 5, 2, 3, 4, 6, 1, 1 &0.365013 \ 2^4 &1, 4, 7, 3, 5, 2, 6, 8 &0.465302 \ 2^5-1 &1, 12, 9, 14, 4, 5, 2, 3 &0.373740 \ 2^5 &1, 7, 5, 3, 4, 9, 11, 12 &0.465302 \ 2^6-3 &1, 8, 11, 5, 26, 14, 6, 21 &0.391994 \ 2^6 &1, 28, 19, 5, 11, 6, 9, 16 &0.385770 \ 2^7-1 &1, 12, 29, 19, 34, 14, 37, 50 &0.434146 \ 2^7 &1, 12, 19, 27, 22, 14, 17, 59 &0.433013 \ 2^8-5 &1, 74, 20, 48, 92, 35, 78, 51 &0.376115 \ 2^8 &1, 30, 39, 55, 82, 35, 42, 76 &0.353791 \ 2^9-3 &1, 133, 91, 216, 116, 12, 40, 198 &0.417497 \ 2^9 &1, 200, 35, 215, 26, 223, 119, 195 &0.385770 \ 2^{10}-3 &1, 96, 362, 398, 141, 271, 348, 83 &0.393582 \ 2^{10} &1, 271, 318, 499, 404, 359, 367, 168 &0.393293 \ 2^{11}-9 &1, 48, 423, 607, 178, 700, 223, 959 &0.395720 \ 2^{11} &1, 592, 605, 994, 709, 483, 33, 809 &0.420923 \ 2^{12}-3 &1, 1006, 726, 1499, 854, 1267, 1242, 1831 &0.393821 \ 2^{12} &1, 70, 923, 537, 552, 1799, 121, 1931 &0.407097 \ 2^{13}-1 &1, 352, 1140, 97, 504, 3600, 976, 3914 &0.409857 \ 2^{13} &1, 1530, 3993, 1459, 3735, 4017, 1677, 710 &0.402628 \ 2^{14}-3 &1, 2791, 4242, 1553, 646, 4268, 7810, 2490 &0.413170 \ 2^{14} &1, 1435, 3012, 5281, 4253, 2785, 5070, 521 &0.433878 \ 2^{15}-19 &1, 2930, 8238, 6188, 7401, 3830, 16145, 1970 &0.441163 \ 2^{15} &1, 15936, 2477, 8921, 10843, 5793, 14993, 3929 &0.425983 \ 2^{16}-15 &1, 15176, 5500, 11258, 21587, 11947, 11335, 13421 &0.426992 \ 2^{16} &1, 25962, 3951, 27605, 12867, 23469, 30465, 26877 &0.433013 \ 2^{17}-1 &1, 5728, 46083, 738, 57708, 25004, 44213, 15544 &0.437501 \ 2^{17} &1, 49531, 24184, 27343, 37315, 41751, 24099, 29195 &0.441607 \ 2^{18}-5 &1, 20607, 90986, 87159, 22139, 96431, 95971, 15285 &0.423601 \ 2^{18} &1, 1990, 6127, 95749, 6403, 50962, 90889, 16202 &0.436563 \ 2^{19}-19 &1, 86366, 257557, 123933, 69020, 130871, 104469, 138905 &0.430331 \ 2^{19} &1, 86592, 229449, 48883, 41139, 13183, 14653, 159370 &0.439726 \ 2^{20}-3 &1, 252568, 73563, 313721, 427298, 32383, 139705, 519946 &0.443624 \ 2^{20} &1, 195638, 294513, 74663, 28892, 80429, 92213, 143495 &0.433700 \\mbox{Nb. of projections} &&158\end{array}\f]< center > Best f $a f $’s with respect to f component by	component

Function Documentation

$’s()

page results Results f [\begin{array}{|l|l|c|} n & a & M_{8,8,8,8} \ 2^4-3 & 1,5,2,3,4,6,1,1 & 0.365013 \ 2^4 & 1,4,7,3,5,2,6,8 & 0.465302 \ 2^5-1 & 1,12,9,14,4,5,2,3 & 0.373740 \ 2^5 & 1,7,5,3,4,9,11,12 & 0.465302 \ 2^6-3 & 1,8,11,5,26,14,6,21 & 0.391994 \ 2^6 & 1,28,19,5,11,6,9,16 & 0.385770 \ 2^7-1 & 1,12,29,19,34,14,37,50 & 0.434146 \ 2^7 & 1,12,19,27,22,14,17,59 & 0.433013 \ 2^8-5 & 1,74,20,48,92,35,78,51 & 0.376115 \ 2^8 & 1,30,39,55,82,35,42,76 & 0.353791 \ 2^9-3 & 1,133,91,216,116,12,40,198 & 0.417497 \ 2^9 & 1,200,35,215,26,223,119,195 & 0.385770 \ 2^{10}-3 & 1,96,362,398,141,271,348,83 & 0.393582 \ 2^{10} & 1,271,318,499,404,359,367,168 & 0.393293 \ 2^{11}-9 & 1,48,423,607,178,700,223,959 & 0.395720 \ 2^{11} & 1,592,605,994,709,483,33,809 & 0.420923 \ 2^{12}-3 & 1,1006,726,1499,854,1267,1242,1831 & 0.393821 \ 2^{12} & 1,70,923,537,552,1799,121,1931 & 0.407097 \ 2^{13}-1 & 1,352,1140,97,504,3600,976,3914 & 0.409857 \ 2^{13} & 1,1530,3993,1459,3735,4017,1677,710 & 0.402628 \ 2^{14}-3 & 1,2791,4242,1553,646,4268,7810,2490 & 0.413170 \ 2^{14} & 1,1435,3012,5281,4253,2785,5070,521 & 0.433878 \ 2^{15}-19 & 1,2930,8238,6188,7401,3830,16145,1970 & 0.441163 \ 2^{15} & 1,15936,2477,8921,10843,5793,14993,3929 & 0.425983 \ 2^{16}-15 & 1,15176,5500,11258,21587,11947,11335,13421 & 0.426992 \ 2^{16} & 1,25962,3951,27605,12867,23469,30465,26877 & 0.433013 \ 2^{17}-1 & 1,5728,46083,738,57708,25004,44213,15544 & 0.437501 \ 2^{17} & 1,49531,24184,27343,37315,41751,24099,29195 & 0.441607 \ 2^{18}-5 & 1,20607,90986,87159,22139,96431,95971,15285 & 0.423601 \ 2^{18} & 1,1990,6127,95749,6403,50962,90889,16202 & 0.436563 \ 2^{19}-19 & 1,86366,257557,123933,69020,130871,104469,138905 & 0.430331 \ 2^{19} & 1,86592,229449,48883,41139,13183,14653,159370 & 0.439726 \ 2^{20}-3 & 1,252568,73563,313721,427298,32383,139705,519946 & 0.443624 \ 2^{20} & 1,195638,294513,74663,28892,80429,92213,143495 & 0.433700 \\mbox{Nb. of projections} & & 158\end{array}\f]<center> Best f $a f $’s with respect to f component by for general rank lattices of dimension</center> f [\begin{array}{|l|l|c|} n & a & M_{2,2,2,2} \ 13 & 2 & 0.577137 \ 31 & 12 & 0.900085 \ 61 & 17 & 0.907433 \ 127 & 12 & 0.994369 \ 251 & 78 & 0.963395 \ 509 & 155 & 0.952292 \ 1021 & 90 & 0.958001 \ 2039 & 977 & 0.986867 \ 4093 & 1153 & 0.976319 \ 8191 & 1466 & 0.996338 \ 16381 & 1543 & 0.993605 \ 32749 & 2059 & 0.991324 \ 65521 & 21748 & 0.994778 \ 131071 & 37302 & 0.997013 \ 262139 & 206676 & 0.998712 \ 524269 & 86366 & 0.999171 \ 1048573 & 395633 & 0.999123 \\mbox{Nb. of projections} & & 1\end{array}\f]<center> Best f $a f $’s

(

primitive

element

)

Variable Documentation

$M_

page results Results f [\begin{array}{|l|l|c|} n & a & M_{8,8,8,8} \ 2^4-3 & 1,5,2,3,4,6,1,1 & 0.365013 \ 2^4 & 1,4,7,3,5,2,6,8 & 0.465302 \ 2^5-1 & 1,12,9,14,4,5,2,3 & 0.373740 \ 2^5 & 1,7,5,3,4,9,11,12 & 0.465302 \ 2^6-3 & 1,8,11,5,26,14,6,21 & 0.391994 \ 2^6 & 1,28,19,5,11,6,9,16 & 0.385770 \ 2^7-1 & 1,12,29,19,34,14,37,50 & 0.434146 \ 2^7 & 1,12,19,27,22,14,17,59 & 0.433013 \ 2^8-5 & 1,74,20,48,92,35,78,51 & 0.376115 \ 2^8 & 1,30,39,55,82,35,42,76 & 0.353791 \ 2^9-3 & 1,133,91,216,116,12,40,198 & 0.417497 \ 2^9 & 1,200,35,215,26,223,119,195 & 0.385770 \ 2^{10}-3 & 1,96,362,398,141,271,348,83 & 0.393582 \ 2^{10} & 1,271,318,499,404,359,367,168 & 0.393293 \ 2^{11}-9 & 1,48,423,607,178,700,223,959 & 0.395720 \ 2^{11} & 1,592,605,994,709,483,33,809 & 0.420923 \ 2^{12}-3 & 1,1006,726,1499,854,1267,1242,1831 & 0.393821 \ 2^{12} & 1,70,923,537,552,1799,121,1931 & 0.407097 \ 2^{13}-1 & 1,352,1140,97,504,3600,976,3914 & 0.409857 \ 2^{13} & 1,1530,3993,1459,3735,4017,1677,710 & 0.402628 \ 2^{14}-3 & 1,2791,4242,1553,646,4268,7810,2490 & 0.413170 \ 2^{14} & 1,1435,3012,5281,4253,2785,5070,521 & 0.433878 \ 2^{15}-19 & 1,2930,8238,6188,7401,3830,16145,1970 & 0.441163 \ 2^{15} & 1,15936,2477,8921,10843,5793,14993,3929 & 0.425983 \ 2^{16}-15 & 1,15176,5500,11258,21587,11947,11335,13421 & 0.426992 \ 2^{16} & 1,25962,3951,27605,12867,23469,30465,26877 & 0.433013 \ 2^{17}-1 & 1,5728,46083,738,57708,25004,44213,15544 & 0.437501 \ 2^{17} & 1,49531,24184,27343,37315,41751,24099,29195 & 0.441607 \ 2^{18}-5 & 1,20607,90986,87159,22139,96431,95971,15285 & 0.423601 \ 2^{18} & 1,1990,6127,95749,6403,50962,90889,16202 & 0.436563 \ 2^{19}-19 & 1,86366,257557,123933,69020,130871,104469,138905 & 0.430331 \ 2^{19} & 1,86592,229449,48883,41139,13183,14653,159370 & 0.439726 \ 2^{20}-3 & 1,252568,73563,313721,427298,32383,139705,519946 & 0.443624 \ 2^{20} & 1,195638,294513,74663,28892,80429,92213,143495 & 0.433700 \\mbox{Nb. of projections} & & 158\end{array}\f]<center> Best f $a f $’s with respect to f $M_ {8,8,8,8}\f$ from a search

component

page results Results f [\begin{array}{|l|l|c|} n & a & M_{8,8,8,8} \ 2^4-3 & 1,5,2,3,4,6,1,1 & 0.365013 \ 2^4 & 1,4,7,3,5,2,6,8 & 0.465302 \ 2^5-1 & 1,12,9,14,4,5,2,3 & 0.373740 \ 2^5 & 1,7,5,3,4,9,11,12 & 0.465302 \ 2^6-3 & 1,8,11,5,26,14,6,21 & 0.391994 \ 2^6 & 1,28,19,5,11,6,9,16 & 0.385770 \ 2^7-1 & 1,12,29,19,34,14,37,50 & 0.434146 \ 2^7 & 1,12,19,27,22,14,17,59 & 0.433013 \ 2^8-5 & 1,74,20,48,92,35,78,51 & 0.376115 \ 2^8 & 1,30,39,55,82,35,42,76 & 0.353791 \ 2^9-3 & 1,133,91,216,116,12,40,198 & 0.417497 \ 2^9 & 1,200,35,215,26,223,119,195 & 0.385770 \ 2^{10}-3 & 1,96,362,398,141,271,348,83 & 0.393582 \ 2^{10} & 1,271,318,499,404,359,367,168 & 0.393293 \ 2^{11}-9 & 1,48,423,607,178,700,223,959 & 0.395720 \ 2^{11} & 1,592,605,994,709,483,33,809 & 0.420923 \ 2^{12}-3 & 1,1006,726,1499,854,1267,1242,1831 & 0.393821 \ 2^{12} & 1,70,923,537,552,1799,121,1931 & 0.407097 \ 2^{13}-1 & 1,352,1140,97,504,3600,976,3914 & 0.409857 \ 2^{13} & 1,1530,3993,1459,3735,4017,1677,710 & 0.402628 \ 2^{14}-3 & 1,2791,4242,1553,646,4268,7810,2490 & 0.413170 \ 2^{14} & 1,1435,3012,5281,4253,2785,5070,521 & 0.433878 \ 2^{15}-19 & 1,2930,8238,6188,7401,3830,16145,1970 & 0.441163 \ 2^{15} & 1,15936,2477,8921,10843,5793,14993,3929 & 0.425983 \ 2^{16}-15 & 1,15176,5500,11258,21587,11947,11335,13421 & 0.426992 \ 2^{16} & 1,25962,3951,27605,12867,23469,30465,26877 & 0.433013 \ 2^{17}-1 & 1,5728,46083,738,57708,25004,44213,15544 & 0.437501 \ 2^{17} & 1,49531,24184,27343,37315,41751,24099,29195 & 0.441607 \ 2^{18}-5 & 1,20607,90986,87159,22139,96431,95971,15285 & 0.423601 \ 2^{18} & 1,1990,6127,95749,6403,50962,90889,16202 & 0.436563 \ 2^{19}-19 & 1,86366,257557,123933,69020,130871,104469,138905 & 0.430331 \ 2^{19} & 1,86592,229449,48883,41139,13183,14653,159370 & 0.439726 \ 2^{20}-3 & 1,252568,73563,313721,427298,32383,139705,519946 & 0.443624 \ 2^{20} & 1,195638,294513,74663,28892,80429,92213,143495 & 0.433700 \\mbox{Nb. of projections} & & 158\end{array}\f]<center> Best f $a f $’s with respect to f component by component