Best Known (58−42, 58, s)-Nets in Base 128
(58−42, 58, 288)-Net over F128 — Constructive and digital
Digital (16, 58, 288)-net over F128, using
- t-expansion [i] based on digital (9, 58, 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
(58−42, 58, 386)-Net over F128 — Digital
Digital (16, 58, 386)-net over F128, using
- t-expansion [i] based on digital (15, 58, 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
(58−42, 58, 513)-Net in Base 128
(16, 58, 513)-net in base 128, using
- 6 times m-reduction [i] based on (16, 64, 513)-net in base 128, using
- base change [i] based on digital (8, 56, 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, 56, 513)-net over F256, using
(58−42, 58, 45134)-Net in Base 128 — Upper bound on s
There is no (16, 58, 45135)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 165 337112 347670 919366 242638 899405 654506 600843 919472 295352 703988 571272 771205 366821 839466 744248 872222 713547 299951 449850 069432 > 12858 [i]