Best Known (72−68, 72, s)-Nets in Base 32
(72−68, 72, 64)-Net over F32 — Constructive and digital
Digital (4, 72, 64)-net over F32, using
- t-expansion [i] based on digital (3, 72, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
(72−68, 72, 71)-Net over F32 — Digital
Digital (4, 72, 71)-net over F32, using
- net from sequence [i] based on digital (4, 70)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 4 and N(F) ≥ 71, using
(72−68, 72, 526)-Net in Base 32 — Upper bound on s
There is no (4, 72, 527)-net in base 32, because
- 36 times m-reduction [i] would yield (4, 36, 527)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 565609 455691 255002 140952 023254 084028 302343 434446 899744 > 3236 [i]