Best Known (25, 25+30, s)-Nets in Base 32
(25, 25+30, 162)-Net over F32 — Constructive and digital
Digital (25, 55, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 37, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (3, 18, 64)-net over F32, using
(25, 25+30, 280)-Net over F32 — Digital
Digital (25, 55, 280)-net over F32, using
(25, 25+30, 288)-Net in Base 32 — Constructive
(25, 55, 288)-net in base 32, using
- 1 times m-reduction [i] based on (25, 56, 288)-net in base 32, using
- base change [i] based on digital (9, 40, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 40, 288)-net over F128, using
(25, 25+30, 321)-Net in Base 32
(25, 55, 321)-net in base 32, using
- 5 times m-reduction [i] based on (25, 60, 321)-net in base 32, using
- base change [i] based on (15, 50, 321)-net in base 64, using
- 2 times m-reduction [i] based on (15, 52, 321)-net in base 64, using
- base change [i] based on digital (2, 39, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 39, 321)-net over F256, using
- 2 times m-reduction [i] based on (15, 52, 321)-net in base 64, using
- base change [i] based on (15, 50, 321)-net in base 64, using
(25, 25+30, 68429)-Net in Base 32 — Upper bound on s
There is no (25, 55, 68430)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 60720 633100 814447 110968 403286 422340 478145 150233 061149 004108 991814 041975 751876 478368 > 3255 [i]