Best Known (89−75, 89, s)-Nets in Base 32
(89−75, 89, 120)-Net over F32 — Constructive and digital
Digital (14, 89, 120)-net over F32, using
- t-expansion [i] based on digital (11, 89, 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
(89−75, 89, 146)-Net over F32 — Digital
Digital (14, 89, 146)-net over F32, using
- net from sequence [i] based on digital (14, 145)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
(89−75, 89, 1777)-Net in Base 32 — Upper bound on s
There is no (14, 89, 1778)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 88, 1778)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 892425 046729 074000 079751 785980 071611 139631 671100 406537 506636 258659 363602 248102 537978 045180 386673 492672 388986 599735 379922 854863 859796 > 3288 [i]