Best Known (107−93, 107, s)-Nets in Base 32
(107−93, 107, 120)-Net over F32 — Constructive and digital
Digital (14, 107, 120)-net over F32, using
- t-expansion [i] based on digital (11, 107, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(107−93, 107, 146)-Net over F32 — Digital
Digital (14, 107, 146)-net over F32, using
- net from sequence [i] based on digital (14, 145)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
(107−93, 107, 1676)-Net over F32 — Upper bound on s (digital)
There is no digital (14, 107, 1677)-net over F32, because
- 1 times m-reduction [i] would yield digital (14, 106, 1677)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(32106, 1677, F32, 92) (dual of [1677, 1571, 93]-code), but
- the Johnson bound shows that N ≤ 3 856996 121762 089166 351152 403002 698024 575796 769132 708237 667562 008454 940814 705634 905811 027636 043235 009774 814012 230111 052479 364129 809328 457940 881842 091543 876958 033453 343227 009748 470242 814053 924275 982040 675859 228376 282807 207399 040675 188126 821266 993289 985981 149852 605365 606916 655326 788053 913638 304082 154433 893335 841934 182778 120991 813571 579358 036854 049558 875426 904542 393400 809878 962427 163541 750398 260996 878864 551571 268171 362142 509683 587616 644350 905329 919247 398445 540952 965857 341991 402685 640551 132927 685087 211841 519021 533495 077236 209220 710639 836724 030736 150341 203457 180810 471371 201275 022047 209641 633669 144741 975906 935570 048294 914563 869938 410107 053993 326744 840625 936970 420574 623786 899284 466391 668173 447429 014832 418121 715854 039264 365871 193346 711868 563418 293370 232470 613496 562349 835257 749205 853919 419012 463335 868986 694376 329705 777768 561518 338042 630924 629128 341787 787505 928572 094211 329164 129010 301457 241204 000152 187487 206145 959514 850280 377275 491352 429376 264527 786041 516406 955568 556627 075028 426812 877891 643462 740948 051469 230372 903866 674255 834219 451788 297989 536788 035763 471961 886992 453594 505378 086532 237370 697399 367713 639221 175571 097689 942431 003590 978233 319977 121636 521538 679935 865635 789174 681129 198787 198573 865431 955859 134340 097671 990332 202139 904351 968101 835011 306005 565314 869078 968172 744034 963240 651652 841911 607610 374066 852868 604449 705215 177915 771013 587649 427978 522238 476391 399612 037884 860525 121882 149313 218511 920142 929217 330003 547851 299931 722490 199967 814917 976497 400983 735952 577849 992224 516767 212855 719847 180947 020212 955785 152000 329684 681587 870485 547801 689716 212571 781355 554428 690322 007836 308638 669723 966772 593833 285783 065170 935399 417074 361997 191526 076469 903802 459946 895524 024670 160143 068842 254093 430315 618887 596166 812045 825492 725254 115951 524143 279803 117214 331327 996217 877132 237276 053150 041720 797621 201913 703911 021585 196683 882455 518315 104390 797825 733056 595451 303859 049077 822841 045506 077595 457501 146756 492837 837791 630252 520513 927399 593653 454599 101446 088613 561847 370223 100863 082276 340541 032305 793783 035713 523165 343068 880045 219992 856094 349109 865984 186154 489381 559071 373116 352359 843003 594612 089447 320976 249470 338835 211613 297191 010021 319128 497218 733844 062792 074770 502012 709625 694626 410686 074667 314324 471141 259174 475974 968056 558396 822653 024566 259514 284335 459773 605815 624960 194976 316524 183615 712322 694134 123768 667799 827795 684028 308069 831603 664913 839185 845329 643919 448285 060516 719060 < 321571 [i]
- extracting embedded orthogonal array [i] would yield linear OA(32106, 1677, F32, 92) (dual of [1677, 1571, 93]-code), but
(107−93, 107, 1683)-Net in Base 32 — Upper bound on s
There is no (14, 107, 1684)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 106, 1684)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3593 221482 641555 196596 197759 941976 909995 691068 925421 390004 501956 762826 614787 624714 518176 660385 324070 814729 844937 743397 252575 082142 627869 043872 627365 521850 566480 > 32106 [i]