Best Known (94, 106, s)-Nets in Base 25
(94, 106, 5153051)-Net over F25 — Constructive and digital
Digital (94, 106, 5153051)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 8, 958751)-net over F25, using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(258, 958751, F25, 3) (dual of [958751, 958743, 4]-code or 958751-cap in PG(7,25)), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 4]-NRT-code), using
- digital (12, 16, 1398100)-net over F25, using
- s-reduction based on digital (12, 16, 4194301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2516, 4194301, F25, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- net defined by OOA [i] based on linear OOA(2516, 4194301, F25, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- s-reduction based on digital (12, 16, 4194301)-net over F25, using
- digital (20, 26, 1398100)-net over F25, using
- s-reduction based on digital (20, 26, 2796201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- s-reduction based on digital (20, 26, 2796201)-net over F25, using
- digital (44, 56, 1398100)-net over F25, using
- net defined by OOA [i] based on linear OOA(2556, 1398100, F25, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2556, 8388600, F25, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2556, 8388600, F25, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(2556, 1398100, F25, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- digital (5, 8, 958751)-net over F25, using
(94, 106, large)-Net over F25 — Digital
Digital (94, 106, large)-net over F25, using
- t-expansion [i] based on digital (85, 106, large)-net over F25, using
- 1 times m-reduction [i] based on digital (85, 107, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
- 1 times m-reduction [i] based on digital (85, 107, large)-net over F25, using
(94, 106, large)-Net in Base 25 — Upper bound on s
There is no (94, 106, large)-net in base 25, because
- 10 times m-reduction [i] would yield (94, 96, large)-net in base 25, but