Best Known (3, s)-Sequences in Base 3
(3, 9)-Sequence over F3 — Constructive and digital
Digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
(3, 10)-Sequence in Base 3 — Upper bound on s
There is no (3, 11)-sequence in base 3, because
- net from sequence [i] would yield (3, m, 12)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (3, 22, 12)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(322, 12, S3, 3, 19), but
- the linear programming bound for OOAs shows that M ≥ 28 839193 780671 / 895 > 322 [i]
- extracting embedded OOA [i] would yield OOA(322, 12, S3, 3, 19), but
- m-reduction [i] would yield (3, 22, 12)-net in base 3, but