Best Known (56, s)-Sequences in Base 5
(56, 81)-Sequence over F5 — Constructive and digital
Digital (56, 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
(56, 107)-Sequence over F5 — Digital
Digital (56, 107)-sequence over F5, using
- t-expansion [i] based on digital (55, 107)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 55 and N(F) ≥ 108, using
(56, 240)-Sequence in Base 5 — Upper bound on s
There is no (56, 241)-sequence in base 5, because
- net from sequence [i] would yield (56, m, 242)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (56, 963, 242)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5963, 242, S5, 4, 907), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4040 403413 778089 120440 153831 521926 688555 002145 646286 416014 314067 764932 468901 812596 601195 782923 893460 935136 024864 641476 272950 534453 398964 139757 442140 896429 374760 744656 264862 581702 223044 949479 189993 932299 891023 721066 892250 971833 869759 251862 551388 946817 173725 668196 779518 694440 195539 064640 016399 909057 381628 217950 808983 879099 174778 183210 929488 103964 416940 548659 615949 472674 025332 019349 615291 359584 609895 922593 442174 473467 569202 004553 046344 290318 246626 403973 861832 290418 053549 975915 125060 847500 822941 338461 222517 922187 001817 892332 238742 803706 543822 453306 948969 632302 412436 018648 295484 233452 243763 417209 795286 851701 739987 107184 588613 879665 762451 676158 661939 552985 131740 570068 359375 / 227 > 5963 [i]
- extracting embedded OOA [i] would yield OOA(5963, 242, S5, 4, 907), but
- m-reduction [i] would yield (56, 963, 242)-net in base 5, but