Best Known (10−7, 10, s)-Nets in Base 128
(10−7, 10, 258)-Net over F128 — Constructive and digital
Digital (3, 10, 258)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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 (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 3, 129)-net over F128, using
(10−7, 10, 289)-Net in Base 128
(3, 10, 289)-net in base 128, using
- 6 times m-reduction [i] based on (3, 16, 289)-net in base 128, using
- base change [i] based on digital (1, 14, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 14, 289)-net over F256, using
(10−7, 10, 30005)-Net in Base 128 — Upper bound on s
There is no (3, 10, 30006)-net in base 128, because
- 1 times m-reduction [i] would yield (3, 9, 30006)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 9 224199 185482 212862 > 1289 [i]