Best Known (48, 83, s)-Nets in Base 32
(48, 83, 273)-Net over F32 — Constructive and digital
Digital (48, 83, 273)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 17, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (1, 12, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 5, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 24, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 42, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (6, 17, 77)-net over F32, using
(48, 83, 513)-Net in Base 32 — Constructive
(48, 83, 513)-net in base 32, using
- t-expansion [i] based on (46, 83, 513)-net in base 32, using
- 25 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
- 25 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(48, 83, 2080)-Net over F32 — Digital
Digital (48, 83, 2080)-net over F32, using
(48, 83, 4214225)-Net in Base 32 — Upper bound on s
There is no (48, 83, 4214226)-net in base 32, because
- 1 times m-reduction [i] would yield (48, 82, 4214226)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2644 223942 755358 766859 616900 629743 064251 014717 051704 755616 466191 087857 199103 845786 858849 217891 982733 907592 322147 544194 331787 > 3282 [i]