Best Known (34, 34+30, s)-Nets in Base 32
(34, 34+30, 218)-Net over F32 — Constructive and digital
Digital (34, 64, 218)-net over F32, using
- 2 times m-reduction [i] based on digital (34, 66, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 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 (11, 43, 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
- digital (7, 23, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(34, 34+30, 301)-Net in Base 32 — Constructive
(34, 64, 301)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 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
- (18, 48, 257)-net in base 32, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- digital (1, 16, 44)-net over F32, using
(34, 34+30, 875)-Net over F32 — Digital
Digital (34, 64, 875)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3264, 875, F32, 30) (dual of [875, 811, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3264, 1041, F32, 30) (dual of [1041, 977, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(23) [i] based on
- linear OA(3259, 1024, F32, 30) (dual of [1024, 965, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3247, 1024, F32, 24) (dual of [1024, 977, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(29) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(3264, 1041, F32, 30) (dual of [1041, 977, 31]-code), using
(34, 34+30, 547485)-Net in Base 32 — Upper bound on s
There is no (34, 64, 547486)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 136043 615887 250514 358828 732617 913056 241950 429264 581032 922739 344678 916365 023118 134580 830709 204568 > 3264 [i]