Best Known (58, s)-Sequences in Base 2
(58, 41)-Sequence over F2 — Constructive and digital
Digital (58, 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
(58, 66)-Sequence in Base 2 — Upper bound on s
There is no (58, 67)-sequence in base 2, because
- net from sequence [i] would yield (58, m, 68)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (58, 399, 68)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2399, 68, S2, 6, 341), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 103 289995 123476 343586 236766 880120 474973 188231 713168 940513 226374 261625 904880 673647 785185 814131 205513 257436 126878 909899 735040 / 57 > 2399 [i]
- extracting embedded OOA [i] would yield OOA(2399, 68, S2, 6, 341), but
- m-reduction [i] would yield (58, 399, 68)-net in base 2, but