Best Known (37, s)-Sequences in Base 7
(37, 37)-Sequence over F7 — Constructive and digital
Digital (37, 37)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 37)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
(37, 95)-Sequence over F7 — Digital
Digital (37, 95)-sequence over F7, using
- t-expansion [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
(37, 241)-Sequence in Base 7 — Upper bound on s
There is no (37, 242)-sequence in base 7, because
- net from sequence [i] would yield (37, m, 243)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (37, 725, 243)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7725, 243, S7, 3, 688), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4554 580118 084284 228494 919528 685281 675487 245418 089880 088370 375360 885366 808157 812912 442932 144092 889025 807666 576192 828307 496777 289666 189265 434461 150937 711705 316244 691453 204595 206416 427478 850591 332078 271850 374214 484825 299975 329608 937014 545859 688941 324773 853248 879020 506218 987992 704539 937896 365108 032843 696912 491357 648852 641537 406222 634408 175630 783080 765751 501189 440496 550138 441569 756029 429736 878605 804775 772727 584220 519465 503536 915058 687972 807818 302173 302317 661739 796509 673518 199952 997818 607781 051116 130694 541780 984946 127832 079472 393958 520262 462392 511940 514929 521215 867429 587550 909111 501905 650019 081182 197883 380446 020019 / 689 > 7725 [i]
- extracting embedded OOA [i] would yield OOA(7725, 243, S7, 3, 688), but
- m-reduction [i] would yield (37, 725, 243)-net in base 7, but