Best Known (39−34, 39, s)-Nets in Base 128
(39−34, 39, 216)-Net over F128 — Constructive and digital
Digital (5, 39, 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
(39−34, 39, 227)-Net over F128 — Digital
Digital (5, 39, 227)-net over F128, using
- net from sequence [i] based on digital (5, 226)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 227, using
(39−34, 39, 257)-Net in Base 128 — Constructive
(5, 39, 257)-net in base 128, using
- 1 times m-reduction [i] based on (5, 40, 257)-net in base 128, using
- base change [i] based on digital (0, 35, 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, 35, 257)-net over F256, using
(39−34, 39, 3849)-Net in Base 128 — Upper bound on s
There is no (5, 39, 3850)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 15205 552645 039686 326181 348324 285681 298883 276544 667770 811093 355583 819894 005475 638736 > 12839 [i]