Best Known (21, s)-Sequences in Base 2
(21, 20)-Sequence over F2 — Constructive and digital
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
(21, 27)-Sequence in Base 2 — Upper bound on s
There is no (21, 28)-sequence in base 2, because
- net from sequence [i] would yield (21, m, 29)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (21, 138, 29)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2138, 29, S2, 5, 117), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24 391440 060892 869061 054691 860709 145397 166080 / 59 > 2138 [i]
- extracting embedded OOA [i] would yield OOA(2138, 29, S2, 5, 117), but
- m-reduction [i] would yield (21, 138, 29)-net in base 2, but