Best Known (124, 124+102, s)-Nets in Base 2
(124, 124+102, 62)-Net over F2 — Constructive and digital
Digital (124, 226, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 70, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- digital (54, 156, 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 (19, 70, 20)-net over F2, using
(124, 124+102, 80)-Net over F2 — Digital
Digital (124, 226, 80)-net over F2, using
- t-expansion [i] based on digital (121, 226, 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
(124, 124+102, 278)-Net in Base 2 — Upper bound on s
There is no (124, 226, 279)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2226, 279, S2, 102), but
- the linear programming bound shows that M ≥ 701407 263458 729570 124673 658590 276691 356786 681751 788848 857862 560164 911267 552464 774505 693184 / 5736 774963 361499 182125 > 2226 [i]