Best Known (71, 85, s)-Nets in Base 25
(71, 85, 1203580)-Net over F25 — Constructive and digital
Digital (71, 85, 1203580)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (12, 19, 5209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2519, 5209, F25, 7, 7) (dual of [(5209, 7), 36444, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2519, 15628, F25, 7) (dual of [15628, 15609, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(2519, 15625, F25, 7) (dual of [15625, 15606, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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
- OOA 3-folding and stacking with additional row [i] based on linear OA(2519, 15628, F25, 7) (dual of [15628, 15609, 8]-code), using
- net defined by OOA [i] based on linear OOA(2519, 5209, F25, 7, 7) (dual of [(5209, 7), 36444, 8]-NRT-code), using
- digital (52, 66, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (12, 19, 5209)-net over F25, using
(71, 85, large)-Net over F25 — Digital
Digital (71, 85, large)-net over F25, using
- t-expansion [i] based on digital (69, 85, large)-net over F25, using
- 2 times m-reduction [i] based on digital (69, 87, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2587, large, F25, 18) (dual of [large, large−87, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times code embedding in larger space [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2587, large, F25, 18) (dual of [large, large−87, 19]-code), using
- 2 times m-reduction [i] based on digital (69, 87, large)-net over F25, using
(71, 85, large)-Net in Base 25 — Upper bound on s
There is no (71, 85, large)-net in base 25, because
- 12 times m-reduction [i] would yield (71, 73, large)-net in base 25, but