Best Known (22, s)-Sequences in Base 2
(22, 20)-Sequence over F2 — Constructive and digital
Digital (22, 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
(22, 28)-Sequence in Base 2 — Upper bound on s
There is no (22, 29)-sequence in base 2, because
- net from sequence [i] would yield (22, m, 30)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (22, 143, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2143, 30, S2, 5, 121), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 758 225336 750041 186812 214421 270044 291203 334144 / 61 > 2143 [i]
- extracting embedded OOA [i] would yield OOA(2143, 30, S2, 5, 121), but
- m-reduction [i] would yield (22, 143, 30)-net in base 2, but