Best Known (12, s)-Sequences in Base 2
(12, 13)-Sequence over F2 — Constructive and digital
Digital (12, 13)-sequence over F2, using
- t-expansion [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
(12, 17)-Sequence in Base 2 — Upper bound on s
There is no (12, 18)-sequence in base 2, because
- net from sequence [i] would yield (12, m, 19)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (12, 89, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9284 550294 640352 061743 431680 / 13 > 289 [i]
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- m-reduction [i] would yield (12, 89, 19)-net in base 2, but