Best Known (108−89, 108, s)-Nets in Base 32
(108−89, 108, 120)-Net over F32 — Constructive and digital
Digital (19, 108, 120)-net over F32, using
- t-expansion [i] based on digital (11, 108, 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
(108−89, 108, 172)-Net over F32 — Digital
Digital (19, 108, 172)-net over F32, using
- net from sequence [i] based on digital (19, 171)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 19 and N(F) ≥ 172, using
(108−89, 108, 2522)-Net in Base 32 — Upper bound on s
There is no (19, 108, 2523)-net in base 32, because
- 1 times m-reduction [i] would yield (19, 107, 2523)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 112758 536362 382822 129655 363344 006497 214757 070961 009122 606279 149251 198408 769199 371312 009888 124402 672060 161952 782733 370715 596327 742922 408672 458779 277520 794439 130568 > 32107 [i]