Best Known (54−36, 54, s)-Nets in Base 32
(54−36, 54, 120)-Net over F32 — Constructive and digital
Digital (18, 54, 120)-net over F32, using
- t-expansion [i] based on digital (11, 54, 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
(54−36, 54, 161)-Net over F32 — Digital
Digital (18, 54, 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
(54−36, 54, 177)-Net in Base 32 — Constructive
(18, 54, 177)-net in base 32, using
- 12 times m-reduction [i] based on (18, 66, 177)-net in base 32, using
- base change [i] based on digital (7, 55, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 55, 177)-net over F64, using
(54−36, 54, 209)-Net in Base 32
(18, 54, 209)-net in base 32, using
- base change [i] based on digital (9, 45, 209)-net over F64, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
(54−36, 54, 7974)-Net in Base 32 — Upper bound on s
There is no (18, 54, 7975)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1897 648030 156082 780763 358083 363718 308096 733953 186847 626358 829188 917030 918846 812306 > 3254 [i]