Best Known (80−54, 80, s)-Nets in Base 32
(80−54, 80, 120)-Net over F32 — Constructive and digital
Digital (26, 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
(80−54, 80, 177)-Net in Base 32 — Constructive
(26, 80, 177)-net in base 32, using
- t-expansion [i] based on (25, 80, 177)-net in base 32, using
- 28 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
- 28 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
(80−54, 80, 225)-Net over F32 — Digital
Digital (26, 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
(80−54, 80, 257)-Net in Base 32
(26, 80, 257)-net in base 32, using
- 4 times m-reduction [i] based on (26, 84, 257)-net in base 32, using
- base change [i] based on digital (12, 70, 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, 70, 257)-net over F64, using
(80−54, 80, 10142)-Net in Base 32 — Upper bound on s
There is no (26, 80, 10143)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 584023 260796 690874 486203 596476 527182 125760 534805 317996 846934 349469 438943 873258 277778 689571 725963 653369 798241 868865 320036 > 3280 [i]