Best Known (12, 12+30, s)-Nets in Base 2
(12, 12+30, 14)-Net over F2 — Constructive and digital
Digital (12, 42, 14)-net over F2, using
- t-expansion [i] based on digital (11, 42, 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
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
(12, 12+30, 22)-Net in Base 2 — Upper bound on s
There is no (12, 42, 23)-net in base 2, because
- 5 times m-reduction [i] would yield (12, 37, 23)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(237, 23, S2, 2, 25), but
- the linear programming bound for OOAs shows that M ≥ 701 058921 791488 / 4361 > 237 [i]
- extracting embedded OOA [i] would yield OOA(237, 23, S2, 2, 25), but