Best Known (58−49, 58, s)-Nets in Base 32
(58−49, 58, 104)-Net over F32 — Constructive and digital
Digital (9, 58, 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
(58−49, 58, 108)-Net over F32 — Digital
Digital (9, 58, 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
(58−49, 58, 1175)-Net in Base 32 — Upper bound on s
There is no (9, 58, 1176)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 57, 1176)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 62 766900 998747 632154 352638 289791 997597 784993 760359 414731 812522 539568 636599 753560 062896 > 3257 [i]