Best Known (47, 47+47, s)-Nets in Base 32
(47, 47+47, 240)-Net over F32 — Constructive and digital
Digital (47, 94, 240)-net over F32, using
- 3 times m-reduction [i] based on digital (47, 97, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 36, 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
- digital (11, 61, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 36, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(47, 47+47, 513)-Net in Base 32 — Constructive
(47, 94, 513)-net in base 32, using
- t-expansion [i] based on (46, 94, 513)-net in base 32, using
- 14 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 14 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(47, 47+47, 713)-Net over F32 — Digital
Digital (47, 94, 713)-net over F32, using
(47, 47+47, 370784)-Net in Base 32 — Upper bound on s
There is no (47, 94, 370785)-net in base 32, because
- 1 times m-reduction [i] would yield (47, 93, 370785)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 95 268745 363088 206191 107453 150916 909959 792111 217413 189271 721136 924898 223405 414350 893519 395010 180280 812808 735267 640706 051228 781657 934572 886688 > 3293 [i]