Best Known (57, 57+36, s)-Nets in Base 8
(57, 57+36, 354)-Net over F8 — Constructive and digital
Digital (57, 93, 354)-net over F8, using
- 7 times m-reduction [i] based on digital (57, 100, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 50, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 50, 177)-net over F64, using
(57, 57+36, 384)-Net in Base 8 — Constructive
(57, 93, 384)-net in base 8, using
- 1 times m-reduction [i] based on (57, 94, 384)-net in base 8, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
- 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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
- base change [i] based on digital (3, 42, 192)-net over F128, using
- 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
(57, 57+36, 516)-Net over F8 — Digital
Digital (57, 93, 516)-net over F8, using
(57, 57+36, 49992)-Net in Base 8 — Upper bound on s
There is no (57, 93, 49993)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 971673 108491 713140 846774 470858 066860 380421 264232 745005 872240 774238 229772 492986 410000 > 893 [i]