Best Known (3, s)-Sequences in Base 4
(3, 13)-Sequence over F4 — Constructive and digital
Digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
(3, 15)-Sequence in Base 4 — Upper bound on s
There is no (3, 16)-sequence in base 4, because
- net from sequence [i] would yield (3, m, 17)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (3, 20, 17)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(420, 17, S4, 2, 17), but
- the linear programming bound for OOAs shows that M ≥ 3 573412 790272 / 3 > 420 [i]
- extracting embedded OOA [i] would yield OOA(420, 17, S4, 2, 17), but
- m-reduction [i] would yield (3, 20, 17)-net in base 4, but