Best Known (108−40, 108, s)-Nets in Base 8
(108−40, 108, 354)-Net over F8 — Constructive and digital
Digital (68, 108, 354)-net over F8, using
- 14 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
(108−40, 108, 514)-Net in Base 8 — Constructive
(68, 108, 514)-net in base 8, using
- base change [i] based on digital (41, 81, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (41, 82, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 41, 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, 41, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (41, 82, 514)-net over F16, using
(108−40, 108, 716)-Net over F8 — Digital
Digital (68, 108, 716)-net over F8, using
(108−40, 108, 89296)-Net in Base 8 — Upper bound on s
There is no (68, 108, 89297)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 34 180262 775893 428031 362515 612347 488544 533197 187512 571170 791244 007231 119145 556200 845698 946923 644496 > 8108 [i]