Best Known (7, s)-Sequences in Base 3
(7, 15)-Sequence over F3 — Constructive and digital
Digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
(7, 21)-Sequence in Base 3 — Upper bound on s
There is no (7, 22)-sequence in base 3, because
- net from sequence [i] would yield (7, m, 23)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (7, 35, 23)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(335, 23, S3, 2, 28), but
- the linear programming bound for OOAs shows that M ≥ 1 050995 602043 303294 963563 814764 130877 / 19 578586 921145 663665 > 335 [i]
- extracting embedded OOA [i] would yield OOA(335, 23, S3, 2, 28), but
- m-reduction [i] would yield (7, 35, 23)-net in base 3, but