Best Known (47, 47+20, s)-Nets in Base 8
(47, 47+20, 378)-Net over F8 — Constructive and digital
Digital (47, 67, 378)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (34, 54, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 27, 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, 27, 177)-net over F64, using
- digital (3, 13, 24)-net over F8, using
(47, 47+20, 538)-Net in Base 8 — Constructive
(47, 67, 538)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- (34, 54, 514)-net in base 8, using
- trace code for nets [i] based on (7, 27, 257)-net in base 64, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- trace code for nets [i] based on (7, 27, 257)-net in base 64, using
- digital (3, 13, 24)-net over F8, using
(47, 47+20, 1742)-Net over F8 — Digital
Digital (47, 67, 1742)-net over F8, using
(47, 47+20, 727072)-Net in Base 8 — Upper bound on s
There is no (47, 67, 727073)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 213904 389788 558769 191614 126082 547635 539053 017428 884712 828656 > 867 [i]