Best Known (25, 25+10, s)-Nets in Base 32
(25, 25+10, 7050)-Net over F32 — Constructive and digital
Digital (25, 35, 7050)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- digital (18, 28, 6554)-net over F32, using
- net defined by OOA [i] based on linear OOA(3228, 6554, F32, 10, 10) (dual of [(6554, 10), 65512, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- net defined by OOA [i] based on linear OOA(3228, 6554, F32, 10, 10) (dual of [(6554, 10), 65512, 11]-NRT-code), using
- digital (2, 7, 496)-net over F32, using
(25, 25+10, 52430)-Net in Base 32 — Constructive
(25, 35, 52430)-net in base 32, using
- net defined by OOA [i] based on OOA(3235, 52430, S32, 10, 10), using
- OA 5-folding and stacking [i] based on OA(3235, 262150, S32, 10), using
- discarding factors based on OA(3235, 262151, S32, 10), using
- discarding parts of the base [i] based on linear OA(6429, 262151, F64, 10) (dual of [262151, 262122, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- 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(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding parts of the base [i] based on linear OA(6429, 262151, F64, 10) (dual of [262151, 262122, 11]-code), using
- discarding factors based on OA(3235, 262151, S32, 10), using
- OA 5-folding and stacking [i] based on OA(3235, 262150, S32, 10), using
(25, 25+10, 95449)-Net over F32 — Digital
Digital (25, 35, 95449)-net over F32, using
(25, 25+10, large)-Net in Base 32 — Upper bound on s
There is no (25, 35, large)-net in base 32, because
- 8 times m-reduction [i] would yield (25, 27, large)-net in base 32, but