Best Known (40−29, 40, s)-Nets in Base 2
(40−29, 40, 14)-Net over F2 — Constructive and digital
Digital (11, 40, 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
(40−29, 40, 21)-Net in Base 2 — Upper bound on s
There is no (11, 40, 22)-net in base 2, because
- 7 times m-reduction [i] would yield (11, 33, 22)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(233, 22, S2, 2, 22), but
- the linear programming bound for OOAs shows that M ≥ 192877 381548 009288 892416 / 19 614878 395771 > 233 [i]
- extracting embedded OOA [i] would yield OOA(233, 22, S2, 2, 22), but