Best Known (3, 3+15, s)-Nets in Base 128
(3, 3+15, 192)-Net over F128 — Constructive and digital
Digital (3, 18, 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+15, 257)-Net in Base 128 — Constructive
(3, 18, 257)-net in base 128, using
- 6 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+15, 3485)-Net in Base 128 — Upper bound on s
There is no (3, 18, 3486)-net in base 128, because
- 1 times m-reduction [i] would yield (3, 17, 3486)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 665502 637306 166901 199784 321339 361268 > 12817 [i]