Best Known (32, s)-Sequences in Base 2
(32, 20)-Sequence over F2 — Constructive and digital
Digital (32, 20)-sequence over F2, using
- t-expansion [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
(32, 26)-Sequence over F2 — Digital
Digital (32, 26)-sequence over F2, using
- t-expansion [i] based on digital (31, 26)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 31 and N(F) ≥ 27, using
(32, 39)-Sequence in Base 2 — Upper bound on s
There is no (32, 40)-sequence in base 2, because
- net from sequence [i] would yield (32, m, 41)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (32, 197, 41)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2197, 41, S2, 5, 165), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 479787 508978 388168 732564 061923 369929 005334 428502 117605 965824 / 83 > 2197 [i]
- extracting embedded OOA [i] would yield OOA(2197, 41, S2, 5, 165), but
- m-reduction [i] would yield (32, 197, 41)-net in base 2, but