Best Known (60−45, 60, s)-Nets in Base 32
(60−45, 60, 120)-Net over F32 — Constructive and digital
Digital (15, 60, 120)-net over F32, using
- t-expansion [i] based on digital (11, 60, 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
(60−45, 60, 128)-Net in Base 32 — Constructive
(15, 60, 128)-net in base 32, using
- base change [i] based on digital (5, 50, 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
(60−45, 60, 158)-Net over F32 — Digital
Digital (15, 60, 158)-net over F32, using
- net from sequence [i] based on digital (15, 157)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
(60−45, 60, 3165)-Net in Base 32 — Upper bound on s
There is no (15, 60, 3166)-net in base 32, because
- 1 times m-reduction [i] would yield (15, 59, 3166)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 63705 018588 314676 797401 221175 560014 488227 411862 693345 332519 411764 716515 223950 200791 696508 > 3259 [i]