Best Known (39, 39+16, s)-Nets in Base 8
(39, 39+16, 368)-Net over F8 — Constructive and digital
Digital (39, 55, 368)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (30, 46, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 23, 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, 23, 177)-net over F64, using
- digital (1, 9, 14)-net over F8, using
(39, 39+16, 538)-Net in Base 8 — Constructive
(39, 55, 538)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 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
- (28, 44, 514)-net in base 8, using
- base change [i] based on digital (17, 33, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (17, 34, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 17, 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, 17, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (17, 34, 514)-net over F16, using
- base change [i] based on digital (17, 33, 514)-net over F16, using
- digital (3, 11, 24)-net over F8, using
(39, 39+16, 1887)-Net over F8 — Digital
Digital (39, 55, 1887)-net over F8, using
(39, 39+16, 869627)-Net in Base 8 — Upper bound on s
There is no (39, 55, 869628)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 46 768179 238168 640081 120064 851782 708570 955494 048783 > 855 [i]