Best Known (225−100, 225, s)-Nets in Base 2
(225−100, 225, 63)-Net over F2 — Constructive and digital
Digital (125, 225, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 71, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (54, 154, 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 (21, 71, 21)-net over F2, using
(225−100, 225, 80)-Net over F2 — Digital
Digital (125, 225, 80)-net over F2, using
- t-expansion [i] based on digital (121, 225, 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
(225−100, 225, 291)-Net in Base 2 — Upper bound on s
There is no (125, 225, 292)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2225, 292, S2, 100), but
- the linear programming bound shows that M ≥ 1 973220 369394 871195 412336 709261 295688 333325 962966 455512 445345 028087 951464 847607 282918 227968 / 29934 775001 778432 660225 > 2225 [i]