Best Known (40, s)-Sequences in Base 3
(40, 41)-Sequence over F3 — Constructive and digital
Digital (40, 41)-sequence over F3, using
- t-expansion [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
(40, 55)-Sequence over F3 — Digital
Digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
(40, 90)-Sequence in Base 3 — Upper bound on s
There is no (40, 91)-sequence in base 3, because
- net from sequence [i] would yield (40, m, 92)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (40, 363, 92)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3363, 92, S3, 4, 323), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 168286 662303 730863 643615 296801 545555 681715 967451 921423 155000 514749 907683 286978 494846 457366 460224 244406 583604 225224 434212 599631 542753 099233 585309 765906 718871 299729 525745 776829 > 3363 [i]
- extracting embedded OOA [i] would yield OOA(3363, 92, S3, 4, 323), but
- m-reduction [i] would yield (40, 363, 92)-net in base 3, but