Best Known (34, 34+13, s)-Nets in Base 32
(34, 34+13, 5538)-Net over F32 — Constructive and digital
Digital (34, 47, 5538)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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, 7, 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, 3, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (24, 37, 5461)-net over F32, using
- net defined by OOA [i] based on linear OOA(3237, 5461, F32, 13, 13) (dual of [(5461, 13), 70956, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
- net defined by OOA [i] based on linear OOA(3237, 5461, F32, 13, 13) (dual of [(5461, 13), 70956, 14]-NRT-code), using
- digital (4, 10, 77)-net over F32, using
(34, 34+13, 43692)-Net in Base 32 — Constructive
(34, 47, 43692)-net in base 32, using
- net defined by OOA [i] based on OOA(3247, 43692, S32, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3247, 262153, S32, 13), using
- discarding factors based on OA(3247, 262155, S32, 13), using
- discarding parts of the base [i] based on linear OA(6439, 262155, F64, 13) (dual of [262155, 262116, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(6439, 262155, F64, 13) (dual of [262155, 262116, 14]-code), using
- discarding factors based on OA(3247, 262155, S32, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3247, 262153, S32, 13), using
(34, 34+13, 134026)-Net over F32 — Digital
Digital (34, 47, 134026)-net over F32, using
(34, 34+13, large)-Net in Base 32 — Upper bound on s
There is no (34, 47, large)-net in base 32, because
- 11 times m-reduction [i] would yield (34, 36, large)-net in base 32, but