Best Known (12, 12+25, s)-Nets in Base 32
(12, 12+25, 120)-Net over F32 — Constructive and digital
Digital (12, 37, 120)-net over F32, using
- t-expansion [i] based on digital (11, 37, 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
(12, 12+25, 129)-Net in Base 32 — Constructive
(12, 37, 129)-net in base 32, using
- 5 times m-reduction [i] based on (12, 42, 129)-net in base 32, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
(12, 12+25, 129)-Net over F32 — Digital
Digital (12, 37, 129)-net over F32, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 12 and N(F) ≥ 129, using
(12, 12+25, 133)-Net in Base 32
(12, 37, 133)-net in base 32, using
- 5 times m-reduction [i] based on (12, 42, 133)-net in base 32, using
- base change [i] based on digital (5, 35, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- base change [i] based on digital (5, 35, 133)-net over F64, using
(12, 12+25, 5584)-Net in Base 32 — Upper bound on s
There is no (12, 37, 5585)-net in base 32, because
- 1 times m-reduction [i] would yield (12, 36, 5585)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 533806 832307 906700 998101 795633 865570 688056 499980 018188 > 3236 [i]