Best Known (25, 25+28, s)-Nets in Base 32
(25, 25+28, 162)-Net over F32 — Constructive and digital
Digital (25, 53, 162)-net over F32, using
- 2 times m-reduction [i] based on 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
- (u, u+v)-construction [i] based on
(25, 25+28, 288)-Net in Base 32 — Constructive
(25, 53, 288)-net in base 32, using
- 3 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+28, 337)-Net over F32 — Digital
Digital (25, 53, 337)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3253, 337, F32, 28) (dual of [337, 284, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3253, 341, F32, 28) (dual of [341, 288, 29]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(3253, 341, F32, 28) (dual of [341, 288, 29]-code), using
(25, 25+28, 97304)-Net in Base 32 — Upper bound on s
There is no (25, 53, 97305)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 59 290062 709326 239177 897991 915458 666411 402784 933916 529627 750679 620084 815896 061224 > 3253 [i]