Best Known (3, s)-Sequences in Base 2
(3, 6)-Sequence over F2 — Constructive and digital
Digital (3, 6)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
(3, 6)-Sequence in Base 2 — Upper bound on s
There is no (3, 7)-sequence in base 2, because
- net from sequence [i] would yield (3, m, 8)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (3, 16, 8)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(216, 8, S2, 4, 13), but
- the linear programming bound for OOAs shows that M ≥ 33 246619 995147 141120 / 498 007000 776397 > 216 [i]
- extracting embedded OOA [i] would yield OOA(216, 8, S2, 4, 13), but
- m-reduction [i] would yield (3, 16, 8)-net in base 2, but