Best Known (3, 3+18, s)-Nets in Base 128
(3, 3+18, 192)-Net over F128 — Constructive and digital
Digital (3, 21, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
(3, 3+18, 257)-Net in Base 128 — Constructive
(3, 21, 257)-net in base 128, using
- 3 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
(3, 3+18, 2692)-Net in Base 128 — Upper bound on s
There is no (3, 21, 2693)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 178 854442 265563 324128 933466 210857 193126 505536 > 12821 [i]