Best Known (81−54, 81, s)-Nets in Base 32
(81−54, 81, 120)-Net over F32 — Constructive and digital
Digital (27, 81, 120)-net over F32, using
- t-expansion [i] based on digital (11, 81, 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
(81−54, 81, 192)-Net in Base 32 — Constructive
(27, 81, 192)-net in base 32, using
- 3 times m-reduction [i] based on (27, 84, 192)-net in base 32, using
- base change [i] based on digital (3, 60, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 60, 192)-net over F128, using
(81−54, 81, 225)-Net over F32 — Digital
Digital (27, 81, 225)-net over F32, using
- t-expansion [i] based on digital (24, 81, 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
(81−54, 81, 257)-Net in Base 32
(27, 81, 257)-net in base 32, using
- 9 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
(81−54, 81, 11533)-Net in Base 32 — Upper bound on s
There is no (27, 81, 11534)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 82 666805 916620 891233 702690 340543 905350 336924 111759 631672 123553 153709 096095 039439 898936 617828 439190 404636 373907 918105 239712 > 3281 [i]