Best Known (85−58, 85, s)-Nets in Base 32
(85−58, 85, 120)-Net over F32 — Constructive and digital
Digital (27, 85, 120)-net over F32, using
- t-expansion [i] based on digital (11, 85, 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
(85−58, 85, 177)-Net in Base 32 — Constructive
(27, 85, 177)-net in base 32, using
- t-expansion [i] based on (25, 85, 177)-net in base 32, using
- 23 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 90, 177)-net over F64, using
- 23 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
(85−58, 85, 225)-Net over F32 — Digital
Digital (27, 85, 225)-net over F32, using
- t-expansion [i] based on digital (24, 85, 225)-net over F32, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
(85−58, 85, 257)-Net in Base 32
(27, 85, 257)-net in base 32, using
- 5 times m-reduction [i] based on (27, 90, 257)-net in base 32, using
- base change [i] based on digital (12, 75, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 75, 257)-net over F64, using
(85−58, 85, 9699)-Net in Base 32 — Upper bound on s
There is no (27, 85, 9700)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 86 836344 348679 229370 357956 034222 640088 972818 098286 754391 010079 047006 881779 661694 255865 067004 761150 410809 856063 873611 493060 314264 > 3285 [i]