Best Known (53, 53+31, s)-Nets in Base 8
(53, 53+31, 354)-Net over F8 — Constructive and digital
Digital (53, 84, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (53, 92, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 46, 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, 46, 177)-net over F64, using
(53, 53+31, 514)-Net in Base 8 — Constructive
(53, 84, 514)-net in base 8, using
- base change [i] based on digital (32, 63, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (32, 64, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 32, 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, 32, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (32, 64, 514)-net over F16, using
(53, 53+31, 596)-Net over F8 — Digital
Digital (53, 84, 596)-net over F8, using
(53, 53+31, 91142)-Net in Base 8 — Upper bound on s
There is no (53, 84, 91143)-net in base 8, because
- 1 times m-reduction [i] would yield (53, 83, 91143)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 904 636714 818118 480229 096511 773164 172066 602486 095138 038612 844185 465963 427840 > 883 [i]