Best Known (65−54, 65, s)-Nets in Base 2
(65−54, 65, 14)-Net over F2 — Constructive and digital
Digital (11, 65, 14)-net over F2, using
- net from sequence [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
(65−54, 65, 18)-Net in Base 2 — Upper bound on s
There is no (11, 65, 19)-net in base 2, because
- 13 times m-reduction [i] would yield (11, 52, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(252, 19, S2, 3, 41), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 117093 590311 632896 / 21 > 252 [i]
- extracting embedded OOA [i] would yield OOA(252, 19, S2, 3, 41), but