Best Known (70−52, 70, s)-Nets in Base 32
(70−52, 70, 120)-Net over F32 — Constructive and digital
Digital (18, 70, 120)-net over F32, using
- t-expansion [i] based on digital (11, 70, 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
(70−52, 70, 128)-Net in Base 32 — Constructive
(18, 70, 128)-net in base 32, using
- 8 times m-reduction [i] based on (18, 78, 128)-net in base 32, using
- base change [i] based on digital (5, 65, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- base change [i] based on digital (5, 65, 128)-net over F64, using
(70−52, 70, 161)-Net over F32 — Digital
Digital (18, 70, 161)-net over F32, using
- net from sequence [i] based on digital (18, 160)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 18 and N(F) ≥ 161, using
(70−52, 70, 3826)-Net in Base 32 — Upper bound on s
There is no (18, 70, 3827)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2308 676007 013323 212900 807056 180244 848796 770545 199043 833901 519506 447519 450199 668909 316687 485045 292146 182980 > 3270 [i]