Best Known (36−31, 36, s)-Nets in Base 128
(36−31, 36, 216)-Net over F128 — Constructive and digital
Digital (5, 36, 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
(36−31, 36, 227)-Net over F128 — Digital
Digital (5, 36, 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
(36−31, 36, 257)-Net in Base 128 — Constructive
(5, 36, 257)-net in base 128, using
- 4 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
(36−31, 36, 4169)-Net in Base 128 — Upper bound on s
There is no (5, 36, 4170)-net in base 128, because
- 1 times m-reduction [i] would yield (5, 35, 4170)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 56 715757 636841 723963 037310 009519 892770 015171 772985 117405 500273 471240 095200 > 12835 [i]