Best Known (71, ∞, s)-Nets in Base 5
(71, ∞, 82)-Net over F5 — Constructive and digital
Digital (71, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (71, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(71, ∞, 132)-Net over F5 — Digital
Digital (71, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (71, 131)-sequence over F5, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
(71, ∞, 301)-Net in Base 5 — Upper bound on s
There is no (71, m, 302)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (71, 1203, 302)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51203, 302, S5, 4, 1132), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8602 676001 397176 590238 610311 003229 782179 145081 855933 811681 563601 402999 699611 621561 300734 585890 348483 043127 278624 259560 820586 988378 066466 110013 242291 708076 734298 587102 673225 535795 636322 621959 216779 400691 748651 682309 917534 677684 761196 014854 076472 440281 429912 840760 507109 906033 066903 364053 310896 231329 574656 732678 891981 970958 521870 944919 282299 920027 768669 940487 981101 485536 136257 076797 523925 396527 902804 900590 410537 042636 893587 312212 343359 516090 237805 849240 288614 056857 909071 994875 619949 332252 385551 671299 619054 363746 340254 034267 955139 491006 420814 130382 373709 764462 073395 572502 817173 128087 766047 265753 882105 270369 165373 135067 257510 835146 093488 400373 206865 687211 037303 597768 542192 346314 325580 224418 243739 459466 534294 922812 932700 632796 031639 228679 322872 156358 137166 932571 562229 090883 187474 903840 118356 493815 894581 178582 711800 117976 963520 050048 828125 / 1133 > 51203 [i]
- extracting embedded OOA [i] would yield OOA(51203, 302, S5, 4, 1132), but