Best Known (46−22, 46, s)-Nets in Base 32
(46−22, 46, 175)-Net over F32 — Constructive and digital
Digital (24, 46, 175)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (1, 12, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 5, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 29, 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 (6, 17, 77)-net over F32, using
(46−22, 46, 288)-Net in Base 32 — Constructive
(24, 46, 288)-net in base 32, using
- t-expansion [i] based on (23, 46, 288)-net in base 32, using
- 3 times m-reduction [i] based on (23, 49, 288)-net in base 32, using
- base change [i] based on digital (9, 35, 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, 35, 288)-net over F128, using
- 3 times m-reduction [i] based on (23, 49, 288)-net in base 32, using
(46−22, 46, 643)-Net over F32 — Digital
Digital (24, 46, 643)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3246, 643, F32, 22) (dual of [643, 597, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 1035, F32, 22) (dual of [1035, 989, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(3243, 1024, F32, 22) (dual of [1024, 981, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3235, 1024, F32, 18) (dual of [1024, 989, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 1035, F32, 22) (dual of [1035, 989, 23]-code), using
(46−22, 46, 311823)-Net in Base 32 — Upper bound on s
There is no (24, 46, 311824)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1725 479769 582821 576065 402400 397033 838128 743170 692933 985699 787698 662635 > 3246 [i]