Best Known (4, s)-Sequences in Base 2
(4, 7)-Sequence over F2 — Constructive and digital
Digital (4, 7)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
(4, 8)-Sequence in Base 2 — Upper bound on s
There is no (4, 9)-sequence in base 2, because
- net from sequence [i] would yield (4, m, 10)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (4, 16, 10)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(216, 10, S2, 3, 12), but
- the linear programming bound for OOAs shows that M ≥ 83807 961088 / 1 262099 > 216 [i]
- extracting embedded OOA [i] would yield OOA(216, 10, S2, 3, 12), but
- m-reduction [i] would yield (4, 16, 10)-net in base 2, but