Best Known (5, s)-Sequences in Base 2
(5, 8)-Sequence over F2 — Constructive and digital
Digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
(5, 9)-Sequence in Base 2 — Upper bound on s
There is no (5, 10)-sequence in base 2, because
- net from sequence [i] would yield (5, m, 11)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (5, 23, 11)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), but
- the linear programming bound for OOAs shows that M ≥ 1644 167168 / 183 > 223 [i]
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), but
- m-reduction [i] would yield (5, 23, 11)-net in base 2, but