Best Known (57−37, 57, s)-Nets in Base 32
(57−37, 57, 120)-Net over F32 — Constructive and digital
Digital (20, 57, 120)-net over F32, using
- t-expansion [i] based on digital (11, 57, 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
(57−37, 57, 177)-Net over F32 — Digital
Digital (20, 57, 177)-net over F32, using
- net from sequence [i] based on digital (20, 176)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 20 and N(F) ≥ 177, using
(57−37, 57, 192)-Net in Base 32 — Constructive
(20, 57, 192)-net in base 32, using
- 321 times duplication [i] based on (19, 56, 192)-net in base 32, using
- base change [i] based on digital (3, 40, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 40, 192)-net over F128, using
(57−37, 57, 225)-Net in Base 32
(20, 57, 225)-net in base 32, using
- 3 times m-reduction [i] based on (20, 60, 225)-net in base 32, using
- base change [i] based on digital (10, 50, 225)-net over F64, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- base change [i] based on digital (10, 50, 225)-net over F64, using
(57−37, 57, 11725)-Net in Base 32 — Upper bound on s
There is no (20, 57, 11726)-net in base 32, because
- 1 times m-reduction [i] would yield (20, 56, 11726)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 944992 040253 590862 970038 557640 161148 846619 182746 299087 122030 377850 844150 161218 663784 > 3256 [i]