Best Known (65−40, 65, s)-Nets in Base 128
(65−40, 65, 345)-Net over F128 — Constructive and digital
Digital (25, 65, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 20, 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
- digital (5, 45, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (0, 20, 129)-net over F128, using
(65−40, 65, 513)-Net over F128 — Digital
Digital (25, 65, 513)-net over F128, using
- t-expansion [i] based on digital (24, 65, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(65−40, 65, 461238)-Net in Base 128 — Upper bound on s
There is no (25, 65, 461239)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 93036 229976 887895 898566 770296 901468 916932 125118 746077 365780 767853 812897 293688 315787 792416 390829 904300 167910 125117 113240 646374 933727 555609 > 12865 [i]