Best Known (64−55, 64, s)-Nets in Base 32
(64−55, 64, 104)-Net over F32 — Constructive and digital
Digital (9, 64, 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
(64−55, 64, 108)-Net over F32 — Digital
Digital (9, 64, 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
(64−55, 64, 1131)-Net in Base 32 — Upper bound on s
There is no (9, 64, 1132)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 63, 1132)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 66999 689116 289850 818003 018913 209862 031947 905172 969892 558086 176547 832434 835078 185983 334791 986426 > 3263 [i]