Best Known (48−14, 48, s)-Nets in Base 8
(48−14, 48, 354)-Net over F8 — Constructive and digital
Digital (34, 48, 354)-net over F8, using
- 6 times m-reduction [i] based on 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
(48−14, 48, 538)-Net in Base 8 — Constructive
(34, 48, 538)-net in base 8, using
- base change [i] based on digital (22, 36, 538)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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
- trace code for nets [i] based on digital (0, 14, 257)-net over F256, using
- digital (1, 8, 24)-net over F16, using
- (u, u+v)-construction [i] based on
(48−14, 48, 1755)-Net over F8 — Digital
Digital (34, 48, 1755)-net over F8, using
(48−14, 48, 752376)-Net in Base 8 — Upper bound on s
There is no (34, 48, 752377)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 22 300801 989165 330862 600825 500293 350087 750408 > 848 [i]