Best Known (96−15, 96, s)-Nets in Base 25
(96−15, 96, 1328580)-Net over F25 — Constructive and digital
Digital (81, 96, 1328580)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (18, 25, 130209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2525, 130209, F25, 7, 7) (dual of [(130209, 7), 911438, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2525, 390628, F25, 7) (dual of [390628, 390603, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2525, 390629, F25, 7) (dual of [390629, 390604, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(2525, 390625, F25, 7) (dual of [390625, 390600, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(2525, 390629, F25, 7) (dual of [390629, 390604, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2525, 390628, F25, 7) (dual of [390628, 390603, 8]-code), using
- net defined by OOA [i] based on linear OOA(2525, 130209, F25, 7, 7) (dual of [(130209, 7), 911438, 8]-NRT-code), using
- digital (56, 71, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2571, 1198371, F25, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2571, 8388598, F25, 15) (dual of [8388598, 8388527, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2571, 8388598, F25, 15) (dual of [8388598, 8388527, 16]-code), using
- net defined by OOA [i] based on linear OOA(2571, 1198371, F25, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- digital (18, 25, 130209)-net over F25, using
(96−15, 96, large)-Net over F25 — Digital
Digital (81, 96, large)-net over F25, using
- 6 times m-reduction [i] based on digital (81, 102, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
(96−15, 96, large)-Net in Base 25 — Upper bound on s
There is no (81, 96, large)-net in base 25, because
- 13 times m-reduction [i] would yield (81, 83, large)-net in base 25, but