Best Known (228−104, 228, s)-Nets in Base 2
(228−104, 228, 59)-Net over F2 — Constructive and digital
Digital (124, 228, 59)-net over F2, using
- 6 times m-reduction [i] based on digital (124, 234, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 70, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- digital (54, 164, 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
- digital (15, 70, 17)-net over F2, using
- (u, u+v)-construction [i] based on
(228−104, 228, 80)-Net over F2 — Digital
Digital (124, 228, 80)-net over F2, using
- t-expansion [i] based on digital (121, 228, 80)-net over F2, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 121 and N(F) ≥ 80, using
- net from sequence [i] based on digital (121, 79)-sequence over F2, using
(228−104, 228, 274)-Net in Base 2 — Upper bound on s
There is no (124, 228, 275)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2228, 275, S2, 104), but
- the linear programming bound shows that M ≥ 251264 125746 691665 140945 653724 331420 478748 637190 708022 716362 001460 206075 835028 865024 / 507 147920 958861 > 2228 [i]