Best Known (25, 25+43, s)-Nets in Base 32
(25, 25+43, 120)-Net over F32 — Constructive and digital
Digital (25, 68, 120)-net over F32, using
- t-expansion [i] based on digital (11, 68, 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
(25, 25+43, 216)-Net in Base 32 — Constructive
(25, 68, 216)-net in base 32, using
- 2 times m-reduction [i] based on (25, 70, 216)-net in base 32, using
- base change [i] based on digital (5, 50, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 50, 216)-net over F128, using
(25, 25+43, 225)-Net over F32 — Digital
Digital (25, 68, 225)-net over F32, using
- t-expansion [i] based on digital (24, 68, 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
(25, 25+43, 257)-Net in Base 32
(25, 68, 257)-net in base 32, using
- 10 times m-reduction [i] based on (25, 78, 257)-net in base 32, using
- base change [i] based on digital (12, 65, 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, 65, 257)-net over F64, using
(25, 25+43, 17742)-Net in Base 32 — Upper bound on s
There is no (25, 68, 17743)-net in base 32, because
- 1 times m-reduction [i] would yield (25, 67, 17743)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 70033 485651 137332 668958 370873 762675 332972 794270 323097 391763 496653 611318 726630 646895 044069 475048 096408 > 3267 [i]