Best Known (224−102, 224, s)-Nets in Base 2
(224−102, 224, 59)-Net over F2 — Constructive and digital
Digital (122, 224, 59)-net over F2, using
- 4 times m-reduction [i] based on digital (122, 228, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 68, 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, 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 (15, 68, 17)-net over F2, using
- (u, u+v)-construction [i] based on
(224−102, 224, 80)-Net over F2 — Digital
Digital (122, 224, 80)-net over F2, using
- t-expansion [i] based on digital (121, 224, 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
(224−102, 224, 270)-Net in Base 2 — Upper bound on s
There is no (122, 224, 271)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2224, 271, S2, 102), but
- the linear programming bound shows that M ≥ 47 407138 423115 388183 966488 087080 744418 451432 367941 570177 125545 578341 545748 944836 886528 / 1 674805 719008 741319 > 2224 [i]