Best Known (45−27, 45, s)-Nets in Base 32
(45−27, 45, 120)-Net over F32 — Constructive and digital
Digital (18, 45, 120)-net over F32, using
- t-expansion [i] based on digital (11, 45, 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
(45−27, 45, 161)-Net over F32 — Digital
Digital (18, 45, 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
(45−27, 45, 257)-Net in Base 32 — Constructive
(18, 45, 257)-net in base 32, using
- 3 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
(45−27, 45, 22713)-Net in Base 32 — Upper bound on s
There is no (18, 45, 22714)-net in base 32, because
- 1 times m-reduction [i] would yield (18, 44, 22714)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 685908 720256 668835 820294 926695 855929 133734 039088 674682 310079 470284 > 3244 [i]