Best Known (115−57, 115, s)-Nets in Base 2
(115−57, 115, 42)-Net over F2 — Constructive and digital
Digital (58, 115, 42)-net over F2, using
- t-expansion [i] based on digital (54, 115, 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
(115−57, 115, 129)-Net in Base 2 — Upper bound on s
There is no (58, 115, 130)-net in base 2, because
- 1 times m-reduction [i] would yield (58, 114, 130)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2114, 130, S2, 56), but
- the linear programming bound shows that M ≥ 76811 433578 425041 089555 846688 890131 841024 / 3 537275 > 2114 [i]
- extracting embedded orthogonal array [i] would yield OA(2114, 130, S2, 56), but