Best Known (41, s)-Sequences in Base 2
(41, 32)-Sequence over F2 — Constructive and digital
Digital (41, 32)-sequence over F2, using
- t-expansion [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
(41, 48)-Sequence in Base 2 — Upper bound on s
There is no (41, 49)-sequence in base 2, because
- net from sequence [i] would yield (41, m, 50)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (41, 292, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 206886 466346 471243 136639 015229 077469 481789 758731 696650 455233 014387 554350 757213 884221 751296 / 21 > 2292 [i]
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), but
- m-reduction [i] would yield (41, 292, 50)-net in base 2, but