Best Known (70, 70+∞, s)-Nets in Base 5
(70, 70+∞, 82)-Net over F5 — Constructive and digital
Digital (70, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (70, 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
(70, 70+∞, 132)-Net over F5 — Digital
Digital (70, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (70, 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
(70, 70+∞, 297)-Net in Base 5 — Upper bound on s
There is no (70, m, 298)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (70, 1187, 298)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51187, 298, S5, 4, 1117), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28308 190699 105602 716087 523323 074688 765224 557720 699049 331477 295911 225355 109424 439006 889108 893117 415824 464562 164767 264757 288869 483363 312534 529668 149271 179865 614438 849079 719117 526141 112161 469609 109059 798162 193382 599819 269160 659819 861881 561817 609252 339117 202996 364522 190160 599751 977061 976846 049014 579980 331459 802661 780559 798902 862882 183671 468393 290934 110488 959138 657893 066571 920195 574014 894864 556808 212636 461538 432172 877436 254649 127883 809280 464275 227492 173907 837552 189366 477444 779951 083059 465477 041519 917850 096323 741398 792587 222946 995888 008535 450861 817299 565388 072460 163124 141985 574061 061840 008626 649538 026877 834966 548947 409195 091476 532052 317113 856968 843769 118806 093817 173594 828081 432640 768483 478864 729360 082977 323288 900976 681239 988117 960679 962192 676939 327869 763041 046020 328424 995069 345294 633109 642867 818678 269031 806848 943233 489990 234375 / 559 > 51187 [i]
- extracting embedded OOA [i] would yield OOA(51187, 298, S5, 4, 1117), but