Best Known (57−36, 57, s)-Nets in Base 128
(57−36, 57, 321)-Net over F128 — Constructive and digital
Digital (21, 57, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 18, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (3, 39, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (0, 18, 129)-net over F128, using
(57−36, 57, 386)-Net over F128 — Digital
Digital (21, 57, 386)-net over F128, using
- t-expansion [i] based on digital (15, 57, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(57−36, 57, 513)-Net in Base 128
(21, 57, 513)-net in base 128, using
- t-expansion [i] based on (17, 57, 513)-net in base 128, using
- 15 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- 15 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(57−36, 57, 279991)-Net in Base 128 — Upper bound on s
There is no (21, 57, 279992)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 291184 892957 724203 175295 412111 472406 186860 852498 049610 709746 252311 291356 074932 582899 747023 238032 752412 240780 120167 981335 > 12857 [i]