Best Known (46, 46+∞, s)-Nets in Base 16
(46, 46+∞, 225)-Net over F16 — Constructive and digital
Digital (46, m, 225)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 224)-sequence over F16, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- t-expansion [i] based on digital (40, 224)-sequence over F16, using
(46, 46+∞, 243)-Net over F16 — Digital
Digital (46, m, 243)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 46 and N(F) ≥ 243, using
(46, 46+∞, 728)-Net in Base 16 — Upper bound on s
There is no (46, m, 729)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (46, 1455, 729)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161455, 729, S16, 2, 1409), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 55 304795 576207 334187 430675 405279 009952 581695 776977 089224 920464 957225 848506 217367 207309 413982 347416 632001 346358 977279 730875 092204 825672 014259 027920 819210 046123 417346 246760 221047 948428 144863 432270 778865 307843 460215 262510 153471 965642 133250 513583 594054 889054 595226 966901 382140 477114 778549 359550 013669 354020 281889 314621 132653 011890 450683 771473 296367 773366 142909 127880 376808 301787 236378 557029 233600 317781 596911 575357 542252 614334 284697 360060 752743 784669 825989 834258 341677 792643 837919 703930 605192 339718 442053 509929 845005 956046 042406 834987 868929 680615 828155 207741 879227 015990 085920 775454 746756 940309 883790 976245 347370 053789 154075 132676 094185 888042 783433 571332 379344 694508 880530 988528 673869 099492 724695 110632 678553 088616 518192 076979 865288 266797 126158 050278 732283 094278 154727 791383 695890 522719 408619 624168 474043 017109 973162 650100 014905 837577 724867 006302 441439 662511 075144 901154 377270 156259 174132 169791 897406 822155 711719 563878 468856 851026 597556 421141 524716 196769 037982 189996 235088 165366 641266 410054 577317 341269 723746 338133 299611 846485 244727 686247 294480 594603 122435 890027 950944 783351 450576 031174 064535 032669 055164 853769 797261 237483 830950 078222 451123 833469 400808 780789 618069 722695 225911 488654 074687 320296 859802 187288 951517 955369 954850 266549 384106 837989 252484 757162 182050 108565 164379 644774 351699 945596 961464 439748 696544 717757 647097 524155 111152 450243 795936 436175 170855 839261 718698 242709 679575 993880 091243 180609 516812 263575 384303 950726 190157 717666 842056 409793 550328 977865 736828 193999 023339 135817 751675 384928 619081 568465 664772 684495 283715 500100 650225 182871 698622 523382 008571 181101 340566 191972 820075 030445 194531 889883 522318 599105 309942 481646 558764 590564 719643 643623 577243 086577 812835 674004 556590 479601 581127 574099 044219 223490 501584 346629 426735 261595 827686 632320 855500 128256 / 47 > 161455 [i]
- extracting embedded OOA [i] would yield OOA(161455, 729, S16, 2, 1409), but