Best Known (32−23, 32, s)-Nets in Base 32
(32−23, 32, 104)-Net over F32 — Constructive and digital
Digital (9, 32, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
(32−23, 32, 108)-Net over F32 — Digital
Digital (9, 32, 108)-net over F32, using
- net from sequence [i] based on digital (9, 107)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 108, using
(32−23, 32, 113)-Net in Base 32
(9, 32, 113)-net in base 32, using
- 4 times m-reduction [i] based on (9, 36, 113)-net in base 32, using
- base change [i] based on digital (3, 30, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- base change [i] based on digital (3, 30, 113)-net over F64, using
(32−23, 32, 2758)-Net in Base 32 — Upper bound on s
There is no (9, 32, 2759)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 31, 2759)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 45851 159933 631538 072338 881014 008449 479153 108960 > 3231 [i]