Best Known (15, s)-Sequences in Base 2
(15, 16)-Sequence over F2 — Constructive and digital
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
(15, 21)-Sequence in Base 2 — Upper bound on s
There is no (15, 22)-sequence in base 2, because
- net from sequence [i] would yield (15, m, 23)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (15, 85, 23)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(285, 23, S2, 4, 70), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2785 365088 392105 618523 029504 / 71 > 285 [i]
- extracting embedded OOA [i] would yield OOA(285, 23, S2, 4, 70), but
- m-reduction [i] would yield (15, 85, 23)-net in base 2, but