Best Known (32−21, 32, s)-Nets in Base 32
(32−21, 32, 120)-Net over F32 — Constructive and digital
Digital (11, 32, 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
(32−21, 32, 150)-Net in Base 32 — Constructive
(11, 32, 150)-net in base 32, using
- 3 times m-reduction [i] based on (11, 35, 150)-net in base 32, using
- base change [i] based on digital (1, 25, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 25, 150)-net over F128, using
(32−21, 32, 6765)-Net in Base 32 — Upper bound on s
There is no (11, 32, 6766)-net in base 32, because
- 1 times m-reduction [i] would yield (11, 31, 6766)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 45737 003902 826033 658914 476948 059742 177289 172294 > 3231 [i]