Best Known (124, 124+106, s)-Nets in Base 2
(124, 124+106, 59)-Net over F2 — Constructive and digital
Digital (124, 230, 59)-net over F2, using
- 4 times m-reduction [i] based on digital (124, 234, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 70, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- digital (54, 164, 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 (15, 70, 17)-net over F2, using
- (u, u+v)-construction [i] based on
(124, 124+106, 80)-Net over F2 — Digital
Digital (124, 230, 80)-net over F2, using
- t-expansion [i] based on digital (121, 230, 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
(124, 124+106, 271)-Net in Base 2 — Upper bound on s
There is no (124, 230, 272)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2230, 272, S2, 106), but
- the linear programming bound shows that M ≥ 87012 566779 043893 467251 609745 916741 198255 732639 555128 908104 132777 714444 392973 991936 / 37 326782 728125 > 2230 [i]