Best Known (19, s)-Sequences in Base 2
(19, 19)-Sequence over F2 — Constructive and digital
Digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
(19, 25)-Sequence in Base 2 — Upper bound on s
There is no (19, 26)-sequence in base 2, because
- net from sequence [i] would yield (19, m, 27)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (19, 128, 27)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25180 895152 149446 296289 720949 950847 647744 / 55 > 2128 [i]
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), but
- m-reduction [i] would yield (19, 128, 27)-net in base 2, but