Best Known (57, ∞, s)-Nets in Base 5
(57, ∞, 82)-Net over F5 — Constructive and digital
Digital (57, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (57, 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
(57, ∞, 112)-Net over F5 — Digital
Digital (57, m, 112)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (57, 111)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 57 and N(F) ≥ 112, using
(57, ∞, 245)-Net in Base 5 — Upper bound on s
There is no (57, m, 246)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (57, 979, 246)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5979, 246, S5, 4, 922), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2456 280558 409434 410532 339457 465286 494245 512313 981356 885200 604226 270398 457104 770628 300985 043271 739314 717414 837164 560979 315162 741398 410227 939857 889756 375276 530589 626030 628217 686261 998698 600452 427185 245107 675333 063005 211130 763293 799287 274599 833167 244202 412451 226897 204345 684486 241610 827308 882737 846188 990974 263280 603451 086750 073797 617075 949294 109271 987798 969846 607034 635128 881928 790517 542855 716900 869905 687534 281378 350249 662537 839720 746315 648808 264119 532503 253561 122579 257156 236326 905242 127246 448718 542562 253078 880840 331683 182429 702817 992510 943941 233268 723724 311242 253188 943240 991420 546265 891386 044746 661999 414297 768091 507934 889395 780523 648641 363999 682585 284034 530559 438280 761241 912841 796875 / 923 > 5979 [i]
- extracting embedded OOA [i] would yield OOA(5979, 246, S5, 4, 922), but