Best Known (24, s)-Sequences in Base 2
(24, 20)-Sequence over F2 — Constructive and digital
Digital (24, 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
(24, 21)-Sequence over F2 — Digital
Digital (24, 21)-sequence over F2, using
- t-expansion [i] based on digital (23, 21)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 23 and N(F) ≥ 22, using
(24, 30)-Sequence in Base 2 — Upper bound on s
There is no (24, 31)-sequence in base 2, because
- net from sequence [i] would yield (24, m, 32)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (24, 185, 32)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2185, 32, S2, 6, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1569 275433 846670 190958 947355 801916 604025 588861 116008 628224 / 27 > 2185 [i]
- extracting embedded OOA [i] would yield OOA(2185, 32, S2, 6, 161), but
- m-reduction [i] would yield (24, 185, 32)-net in base 2, but