Best Known (128, 128+104, s)-Nets in Base 2
(128, 128+104, 63)-Net over F2 — Constructive and digital
Digital (128, 232, 63)-net over F2, using
- 2 times m-reduction [i] based on digital (128, 234, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 74, 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, 160, 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, 74, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(128, 128+104, 81)-Net over F2 — Digital
Digital (128, 232, 81)-net over F2, using
- t-expansion [i] based on digital (126, 232, 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
(128, 128+104, 289)-Net in Base 2 — Upper bound on s
There is no (128, 232, 290)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2232, 290, S2, 104), but
- the linear programming bound shows that M ≥ 31248 188163 173073 124141 552213 221428 911836 972514 149010 859356 835121 130605 760735 093805 023232 / 4 506159 960385 549875 > 2232 [i]