Best Known (68, 68+44, s)-Nets in Base 8
(68, 68+44, 354)-Net over F8 — Constructive and digital
Digital (68, 112, 354)-net over F8, using
- 10 times m-reduction [i] based on digital (68, 122, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 61, 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, 61, 177)-net over F64, using
(68, 68+44, 384)-Net in Base 8 — Constructive
(68, 112, 384)-net in base 8, using
- t-expansion [i] based on (67, 112, 384)-net in base 8, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
(68, 68+44, 552)-Net over F8 — Digital
Digital (68, 112, 552)-net over F8, using
(68, 68+44, 51190)-Net in Base 8 — Upper bound on s
There is no (68, 112, 51191)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 140021 777704 447248 440885 592262 437292 328434 532016 189441 708378 785635 380801 997604 473811 624881 997448 450267 > 8112 [i]