Best Known (65−27, 65, s)-Nets in Base 8
(65−27, 65, 256)-Net over F8 — Constructive and digital
Digital (38, 65, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (38, 66, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
(65−27, 65, 258)-Net in Base 8 — Constructive
(38, 65, 258)-net in base 8, using
- 1 times m-reduction [i] based on (38, 66, 258)-net in base 8, using
- trace code for nets [i] based on (5, 33, 129)-net in base 64, using
- 2 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- 2 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- trace code for nets [i] based on (5, 33, 129)-net in base 64, using
(65−27, 65, 285)-Net over F8 — Digital
Digital (38, 65, 285)-net over F8, using
(65−27, 65, 22601)-Net in Base 8 — Upper bound on s
There is no (38, 65, 22602)-net in base 8, because
- 1 times m-reduction [i] would yield (38, 64, 22602)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 6278 640601 418759 667471 575694 412986 955952 986477 197808 671664 > 864 [i]