Best Known (229−104, 229, s)-Nets in Base 2
(229−104, 229, 62)-Net over F2 — Constructive and digital
Digital (125, 229, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 71, 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, 158, 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, 71, 20)-net over F2, using
(229−104, 229, 80)-Net over F2 — Digital
Digital (125, 229, 80)-net over F2, using
- t-expansion [i] based on digital (121, 229, 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
(229−104, 229, 276)-Net in Base 2 — Upper bound on s
There is no (125, 229, 277)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2229, 277, S2, 104), but
- the linear programming bound shows that M ≥ 288 210741 112781 803449 096818 045883 935285 349639 863224 227722 405271 447495 793972 948510 965760 / 328748 659445 352861 > 2229 [i]