Best Known (63, 99, s)-Nets in Base 8
(63, 99, 354)-Net over F8 — Constructive and digital
Digital (63, 99, 354)-net over F8, using
- 13 times m-reduction [i] based on digital (63, 112, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 56, 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, 56, 177)-net over F64, using
(63, 99, 514)-Net in Base 8 — Constructive
(63, 99, 514)-net in base 8, using
- 1 times m-reduction [i] based on (63, 100, 514)-net in base 8, using
- base change [i] based on digital (38, 75, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (38, 76, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 38, 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, 38, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (38, 76, 514)-net over F16, using
- base change [i] based on digital (38, 75, 514)-net over F16, using
(63, 99, 730)-Net over F8 — Digital
Digital (63, 99, 730)-net over F8, using
(63, 99, 99995)-Net in Base 8 — Upper bound on s
There is no (63, 99, 99996)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 254669 212432 135231 436780 678431 226999 043225 419177 317178 437017 444098 671378 028627 548094 160737 > 899 [i]