Best Known (55, s)-Sequences in Base 2
(55, 41)-Sequence over F2 — Constructive and digital
Digital (55, 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
(55, 63)-Sequence in Base 2 — Upper bound on s
There is no (55, 64)-sequence in base 2, because
- net from sequence [i] would yield (55, m, 65)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (55, 381, 65)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2381, 65, S2, 6, 326), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 827 442130 124284 063457 859842 103015 889906 674524 679774 380026 914161 489160 157201 441422 839699 591352 583228 456939 187796 443136 / 109 > 2381 [i]
- extracting embedded OOA [i] would yield OOA(2381, 65, S2, 6, 326), but
- m-reduction [i] would yield (55, 381, 65)-net in base 2, but