Best Known (69−58, 69, s)-Nets in Base 2
(69−58, 69, 14)-Net over F2 — Constructive and digital
Digital (11, 69, 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
(69−58, 69, 17)-Net in Base 2 — Upper bound on s
There is no (11, 69, 18)-net in base 2, because
- 2 times m-reduction [i] would yield (11, 67, 18)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(267, 18, S2, 4, 56), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2951 479051 793528 258560 / 19 > 267 [i]
- extracting embedded OOA [i] would yield OOA(267, 18, S2, 4, 56), but