Best Known (103, ∞, s)-Nets in Base 4
(103, ∞, 104)-Net over F4 — Constructive and digital
Digital (103, m, 104)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (103, 103)-sequence over F4, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
(103, ∞, 144)-Net over F4 — Digital
Digital (103, m, 144)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (103, 143)-sequence over F4, using
- t-expansion [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- t-expansion [i] based on digital (91, 143)-sequence over F4, using
(103, ∞, 325)-Net in Base 4 — Upper bound on s
There is no (103, m, 326)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (103, 1299, 326)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41299, 326, S4, 4, 1196), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 50500 373668 597189 300403 768125 697557 433396 856764 854890 003749 395300 771308 764154 874362 902079 402364 089437 227922 749954 940519 594093 176068 864560 014133 462948 660388 387868 545839 155893 587160 786760 551604 909165 144302 338072 027690 583642 665841 233301 059259 294609 050161 962555 486173 221121 302537 858544 163929 629305 527276 672994 170359 931941 463535 724182 389737 509857 717265 629858 465166 275473 101367 033722 242513 394467 525069 755514 340547 128468 327353 901322 084809 841009 391872 520990 444345 779034 793689 514809 220216 791194 834015 552653 579577 474390 301508 810987 384618 182987 719445 143929 489532 354686 866667 941504 317029 924079 156079 219291 849242 745781 725400 811862 389845 951594 637490 369094 993657 654828 989152 684854 667065 538648 987187 522315 851968 498141 980755 146635 716467 077369 660709 841600 648395 283546 123365 208699 107065 436457 669394 169856 / 399 > 41299 [i]
- extracting embedded OOA [i] would yield OOA(41299, 326, S4, 4, 1196), but