Best Known (127, 231, s)-Nets in Base 2
(127, 231, 63)-Net over F2 — Constructive and digital
Digital (127, 231, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 73, 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, 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 (21, 73, 21)-net over F2, using
(127, 231, 81)-Net over F2 — Digital
Digital (127, 231, 81)-net over F2, using
- t-expansion [i] based on digital (126, 231, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(127, 231, 287)-Net in Base 2 — Upper bound on s
There is no (127, 231, 288)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2231, 288, S2, 104), but
- the linear programming bound shows that M ≥ 2321 079489 842758 634889 781394 169856 121560 276403 191987 107319 707767 179739 505587 999240 880128 / 557056 853379 564615 > 2231 [i]