Best Known (25, 25+52, s)-Nets in Base 32
(25, 25+52, 120)-Net over F32 — Constructive and digital
Digital (25, 77, 120)-net over F32, using
- t-expansion [i] based on digital (11, 77, 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+52, 192)-Net in Base 32 — Constructive
(25, 77, 192)-net in base 32, using
- base change [i] based on digital (3, 55, 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
(25, 25+52, 225)-Net over F32 — Digital
Digital (25, 77, 225)-net over F32, using
- t-expansion [i] based on digital (24, 77, 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+52, 257)-Net in Base 32
(25, 77, 257)-net in base 32, using
- 1 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+52, 9747)-Net in Base 32 — Upper bound on s
There is no (25, 77, 9748)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 78 890434 458059 350630 670369 118917 941573 636486 129145 095291 064398 283728 130987 457948 298439 038737 229993 058233 202130 735424 > 3277 [i]