Best Known (122, 122+99, s)-Nets in Base 2
(122, 122+99, 62)-Net over F2 — Constructive and digital
Digital (122, 221, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 68, 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, 153, 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, 68, 20)-net over F2, using
(122, 122+99, 80)-Net over F2 — Digital
Digital (122, 221, 80)-net over F2, using
- t-expansion [i] based on digital (121, 221, 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
(122, 122+99, 296)-Net in Base 2 — Upper bound on s
There is no (122, 221, 297)-net in base 2, because
- 1 times m-reduction [i] would yield (122, 220, 297)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2220, 297, S2, 98), but
- 3 times code embedding in larger space [i] would yield OA(2223, 300, S2, 98), but
- the linear programming bound shows that M ≥ 1 797227 776840 883681 896516 291018 079602 556004 736527 384481 376471 307374 972535 986485 205069 933364 379648 / 112622 624143 760877 566730 935625 > 2223 [i]
- 3 times code embedding in larger space [i] would yield OA(2223, 300, S2, 98), but
- extracting embedded orthogonal array [i] would yield OA(2220, 297, S2, 98), but