Best Known (80−53, 80, s)-Nets in Base 32
(80−53, 80, 120)-Net over F32 — Constructive and digital
Digital (27, 80, 120)-net over F32, using
- t-expansion [i] based on digital (11, 80, 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
(80−53, 80, 192)-Net in Base 32 — Constructive
(27, 80, 192)-net in base 32, using
- 4 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
(80−53, 80, 225)-Net over F32 — Digital
Digital (27, 80, 225)-net over F32, using
- t-expansion [i] based on digital (24, 80, 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
(80−53, 80, 257)-Net in Base 32
(27, 80, 257)-net in base 32, using
- 10 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
(80−53, 80, 12729)-Net in Base 32 — Upper bound on s
There is no (27, 80, 12730)-net in base 32, because
- 1 times m-reduction [i] would yield (27, 79, 12730)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 80750 681254 440316 401114 614777 441980 122796 781212 229506 878426 700159 589482 857512 766031 847756 080928 866113 344143 430945 674096 > 3279 [i]