Best Known (58, 58+55, s)-Nets in Base 2
(58, 58+55, 42)-Net over F2 — Constructive and digital
Digital (58, 113, 42)-net over F2, using
- t-expansion [i] based on digital (54, 113, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(58, 58+55, 132)-Net in Base 2 — Upper bound on s
There is no (58, 113, 133)-net in base 2, because
- 1 times m-reduction [i] would yield (58, 112, 133)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2112, 133, S2, 54), but
- the linear programming bound shows that M ≥ 665 839379 951072 155772 236727 273868 230656 / 115995 > 2112 [i]
- extracting embedded orthogonal array [i] would yield OA(2112, 133, S2, 54), but