Best Known (129, 129+106, s)-Nets in Base 2
(129, 129+106, 63)-Net over F2 — Constructive and digital
Digital (129, 235, 63)-net over F2, using
- 2 times m-reduction [i] based on digital (129, 237, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 75, 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, 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 (21, 75, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(129, 129+106, 81)-Net over F2 — Digital
Digital (129, 235, 81)-net over F2, using
- t-expansion [i] based on digital (126, 235, 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
(129, 129+106, 288)-Net in Base 2 — Upper bound on s
There is no (129, 235, 289)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2235, 289, S2, 106), but
- the linear programming bound shows that M ≥ 8949 517916 154748 572183 271892 040894 535562 140457 040985 596436 787586 086568 019064 359340 736512 / 134224 403570 228439 > 2235 [i]