Best Known (56, s)-Sequences in Base 2
(56, 41)-Sequence over F2 — Constructive and digital
Digital (56, 41)-sequence over F2, using
- t-expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
(56, 64)-Sequence in Base 2 — Upper bound on s
There is no (56, 65)-sequence in base 2, because
- net from sequence [i] would yield (56, m, 66)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (56, 387, 66)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2387, 66, S2, 6, 331), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39086 790146 823323 378580 807779 342464 894639 101356 301723 094604 707057 011755 997325 232926 522952 124845 836315 680174 966384 361472 / 83 > 2387 [i]
- extracting embedded OOA [i] would yield OOA(2387, 66, S2, 6, 331), but
- m-reduction [i] would yield (56, 387, 66)-net in base 2, but