Best Known (16, s)-Sequences in Base 2
(16, 16)-Sequence over F2 — Constructive and digital
Digital (16, 16)-sequence over F2, using
- t-expansion [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
(16, 22)-Sequence in Base 2 — Upper bound on s
There is no (16, 23)-sequence in base 2, because
- net from sequence [i] would yield (16, m, 24)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (16, 90, 24)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(290, 24, S2, 4, 74), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39614 081257 132168 796771 975168 / 25 > 290 [i]
- extracting embedded OOA [i] would yield OOA(290, 24, S2, 4, 74), but
- m-reduction [i] would yield (16, 90, 24)-net in base 2, but