Best Known (70−61, 70, s)-Nets in Base 32
(70−61, 70, 104)-Net over F32 — Constructive and digital
Digital (9, 70, 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
(70−61, 70, 108)-Net over F32 — Digital
Digital (9, 70, 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
(70−61, 70, 1109)-Net in Base 32 — Upper bound on s
There is no (9, 70, 1110)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 69, 1110)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 71 886821 275393 535206 000639 356268 580841 536308 075334 410439 572512 232279 116477 278742 934649 696131 593993 366368 > 3269 [i]