Best Known (6, 6+10, s)-Nets in Base 128
(6, 6+10, 279)-Net over F128 — Constructive and digital
Digital (6, 16, 279)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (1, 11, 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
- digital (0, 5, 129)-net over F128, using
(6, 6+10, 321)-Net in Base 128
(6, 16, 321)-net in base 128, using
- 16 times m-reduction [i] based on (6, 32, 321)-net in base 128, using
- base change [i] based on digital (2, 28, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 28, 321)-net over F256, using
(6, 6+10, 113526)-Net in Base 128 — Upper bound on s
There is no (6, 16, 113527)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 5192 448214 512128 138218 713509 707538 > 12816 [i]