Best Known (54−33, 54, s)-Nets in Base 32
(54−33, 54, 120)-Net over F32 — Constructive and digital
Digital (21, 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
(54−33, 54, 185)-Net over F32 — Digital
Digital (21, 54, 185)-net over F32, using
- net from sequence [i] based on digital (21, 184)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 21 and N(F) ≥ 185, using
(54−33, 54, 257)-Net in Base 32 — Constructive
(21, 54, 257)-net in base 32, using
- 2 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- base change [i] based on digital (0, 35, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 35, 257)-net over F256, using
(54−33, 54, 21223)-Net in Base 32 — Upper bound on s
There is no (21, 54, 21224)-net in base 32, because
- 1 times m-reduction [i] would yield (21, 53, 21224)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 59 296225 491283 017345 939964 365027 706429 607765 535813 245956 902495 499097 974491 840930 > 3253 [i]