Best Known (127, 127+106, s)-Nets in Base 2
(127, 127+106, 62)-Net over F2 — Constructive and digital
Digital (127, 233, 62)-net over F2, using
- 2 times m-reduction [i] based on digital (127, 235, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 73, 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, 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 (19, 73, 20)-net over F2, using
- (u, u+v)-construction [i] based on
(127, 127+106, 81)-Net over F2 — Digital
Digital (127, 233, 81)-net over F2, using
- t-expansion [i] based on digital (126, 233, 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, 127+106, 280)-Net in Base 2 — Upper bound on s
There is no (127, 233, 281)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2233, 281, S2, 106), but
- the linear programming bound shows that M ≥ 96255 071560 945144 825845 753186 529299 549319 657197 345428 176368 791637 411331 289766 066166 693888 / 6 100003 838212 464375 > 2233 [i]