Best Known (123, 225, s)-Nets in Base 2
(123, 225, 59)-Net over F2 — Constructive and digital
Digital (123, 225, 59)-net over F2, using
- 6 times m-reduction [i] based on digital (123, 231, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 69, 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, 162, 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, 69, 17)-net over F2, using
- (u, u+v)-construction [i] based on
(123, 225, 80)-Net over F2 — Digital
Digital (123, 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
(123, 225, 273)-Net in Base 2 — Upper bound on s
There is no (123, 225, 274)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2225, 274, S2, 102), but
- the linear programming bound shows that M ≥ 79251 474134 724391 586869 601191 635900 410863 158513 985921 008566 726865 186491 734549 331968 / 1468 716875 920935 > 2225 [i]