Best Known (15, 15+36, s)-Nets in Base 128
(15, 15+36, 288)-Net over F128 — Constructive and digital
Digital (15, 51, 288)-net over F128, using
- t-expansion [i] based on digital (9, 51, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(15, 15+36, 386)-Net over F128 — Digital
Digital (15, 51, 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
(15, 15+36, 513)-Net in Base 128
(15, 51, 513)-net in base 128, using
- 5 times m-reduction [i] based on (15, 56, 513)-net in base 128, using
- base change [i] based on digital (8, 49, 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, 49, 513)-net over F256, using
(15, 15+36, 55550)-Net in Base 128 — Upper bound on s
There is no (15, 51, 55551)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 293626 858391 077563 116456 515458 652456 464269 570371 127908 639843 711993 345821 571328 966329 881599 031345 372251 317379 > 12851 [i]