Best Known (57−48, 57, s)-Nets in Base 256
(57−48, 57, 266)-Net over F256 — Constructive and digital
Digital (9, 57, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(57−48, 57, 513)-Net over F256 — Digital
Digital (9, 57, 513)-net over F256, using
- t-expansion [i] based on digital (8, 57, 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
(57−48, 57, 20143)-Net in Base 256 — Upper bound on s
There is no (9, 57, 20144)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 186102 633233 453916 409265 342373 113184 040252 072930 041356 690891 807168 608938 509568 813874 779532 513463 770993 692244 476074 536424 898654 883074 810406 > 25657 [i]