Best Known (64−26, 64, s)-Nets in Base 8
(64−26, 64, 256)-Net over F8 — Constructive and digital
Digital (38, 64, 256)-net over F8, using
- 2 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
(64−26, 64, 300)-Net in Base 8 — Constructive
(38, 64, 300)-net in base 8, using
- trace code for nets [i] based on (6, 32, 150)-net in base 64, using
- 3 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- 3 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
(64−26, 64, 322)-Net over F8 — Digital
Digital (38, 64, 322)-net over F8, using
- trace code for nets [i] based on digital (6, 32, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
(64−26, 64, 22601)-Net in Base 8 — Upper bound on s
There is no (38, 64, 22602)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6278 640601 418759 667471 575694 412986 955952 986477 197808 671664 > 864 [i]