Best Known (51−30, 51, s)-Nets in Base 32
(51−30, 51, 128)-Net over F32 — Constructive and digital
Digital (21, 51, 128)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (3, 33, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 18, 64)-net over F32, using
(51−30, 51, 185)-Net over F32 — Digital
Digital (21, 51, 185)-net over F32, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 21 and N(F) ≥ 185, using
(51−30, 51, 257)-Net in Base 32 — Constructive
(21, 51, 257)-net in base 32, using
- 5 times m-reduction [i] based on (21, 56, 257)-net in base 32, 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
(51−30, 51, 27151)-Net in Base 32 — Upper bound on s
There is no (21, 51, 27152)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 57909 307398 982216 256711 068795 290772 554631 136475 710340 494300 446977 980803 297983 > 3251 [i]