Best Known (64−31, 64, s)-Nets in Base 2
(64−31, 64, 24)-Net over F2 — Constructive and digital
Digital (33, 64, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(64−31, 64, 28)-Net over F2 — Digital
Digital (33, 64, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(64−31, 64, 86)-Net in Base 2 — Upper bound on s
There is no (33, 64, 87)-net in base 2, because
- 1 times m-reduction [i] would yield (33, 63, 87)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(263, 87, S2, 30), but
- the linear programming bound shows that M ≥ 77 790362 480690 948193 910784 / 7 413705 > 263 [i]
- extracting embedded orthogonal array [i] would yield OA(263, 87, S2, 30), but