Best Known (18, 18+29, s)-Nets in Base 32
(18, 18+29, 120)-Net over F32 — Constructive and digital
Digital (18, 47, 120)-net over F32, using
- t-expansion [i] based on digital (11, 47, 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
(18, 18+29, 161)-Net over F32 — Digital
Digital (18, 47, 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
(18, 18+29, 257)-Net in Base 32 — Constructive
(18, 47, 257)-net in base 32, using
- 1 times m-reduction [i] based on (18, 48, 257)-net in base 32, using
- base change [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
(18, 18+29, 17195)-Net in Base 32 — Upper bound on s
There is no (18, 47, 17196)-net in base 32, because
- 1 times m-reduction [i] would yield (18, 46, 17196)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1726 222136 425834 643940 211452 393411 343467 038648 761332 005588 206399 869096 > 3246 [i]