Best Known (63−39, 63, s)-Nets in Base 32
(63−39, 63, 120)-Net over F32 — Constructive and digital
Digital (24, 63, 120)-net over F32, using
- t-expansion [i] based on digital (11, 63, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(63−39, 63, 225)-Net over F32 — Digital
Digital (24, 63, 225)-net over F32, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
(63−39, 63, 257)-Net in Base 32 — Constructive
(24, 63, 257)-net in base 32, using
- 1 times m-reduction [i] based on (24, 64, 257)-net in base 32, using
- base change [i] based on digital (0, 40, 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, 40, 257)-net over F256, using
(63−39, 63, 20854)-Net in Base 32 — Upper bound on s
There is no (24, 63, 20855)-net in base 32, because
- 1 times m-reduction [i] would yield (24, 62, 20855)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2087 245207 922718 422957 544647 193600 392032 375768 320761 544265 480102 291327 734554 966281 363550 982228 > 3262 [i]