Best Known (92−11, 92, s)-Nets in Base 25
(92−11, 92, 7117781)-Net over F25 — Constructive and digital
Digital (81, 92, 7117781)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 5, 406901)-net over F25, using
- digital (4, 6, 1677720)-net over F25, using
- s-reduction based on digital (4, 6, large)-net over F25, using
- digital (6, 9, 1677720)-net over F25, using
- s-reduction based on digital (6, 9, large)-net over F25, using
- net defined by OOA [i] based on linear OOA(259, large, F25, 3, 3), using
- appending kth column [i] based on linear OOA(259, large, F25, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(259, large, F25, 3) (dual of [large, large−9, 4]-code), using
- appending kth column [i] based on linear OOA(259, large, F25, 2, 3), using
- net defined by OOA [i] based on linear OOA(259, large, F25, 3, 3), using
- s-reduction based on digital (6, 9, large)-net over F25, using
- digital (16, 21, 1677720)-net over F25, using
- s-reduction based on digital (16, 21, 4194301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- s-reduction based on digital (16, 21, 4194301)-net over F25, using
- digital (40, 51, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
(92−11, 92, large)-Net over F25 — Digital
Digital (81, 92, large)-net over F25, using
- 10 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
(92−11, 92, large)-Net in Base 25 — Upper bound on s
There is no (81, 92, large)-net in base 25, because
- 9 times m-reduction [i] would yield (81, 83, large)-net in base 25, but