Best Known (51−37, 51, s)-Nets in Base 32
(51−37, 51, 120)-Net over F32 — Constructive and digital
Digital (14, 51, 120)-net over F32, using
- t-expansion [i] based on digital (11, 51, 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
(51−37, 51, 128)-Net in Base 32 — Constructive
(14, 51, 128)-net in base 32, using
- 3 times m-reduction [i] based on (14, 54, 128)-net in base 32, using
- base change [i] based on digital (5, 45, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- base change [i] based on digital (5, 45, 128)-net over F64, using
(51−37, 51, 146)-Net over F32 — Digital
Digital (14, 51, 146)-net over F32, using
- net from sequence [i] based on digital (14, 145)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
(51−37, 51, 3686)-Net in Base 32 — Upper bound on s
There is no (14, 51, 3687)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 50, 3687)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1809 275701 745259 596812 649821 040352 118973 761978 283157 809557 124943 939829 000790 > 3250 [i]