Best Known (4, s)-Sequences in Base 3
(4, 11)-Sequence over F3 — Constructive and digital
Digital (4, 11)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
(4, 13)-Sequence in Base 3 — Upper bound on s
There is no (4, 14)-sequence in base 3, because
- net from sequence [i] would yield (4, m, 15)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (4, 22, 15)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(322, 15, S3, 3, 18), but
- the linear programming bound for OOAs shows that M ≥ 84237 806413 134527 140642 081122 / 2 548701 622307 460229 > 322 [i]
- extracting embedded OOA [i] would yield OOA(322, 15, S3, 3, 18), but
- m-reduction [i] would yield (4, 22, 15)-net in base 3, but