Best Known (104−16, 104, s)-Nets in Base 25
(104−16, 104, 1052782)-Net over F25 — Constructive and digital
Digital (88, 104, 1052782)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (20, 28, 4207)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(256, 300, F25, 4, 4) (dual of [(300, 4), 1194, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- 1 times truncation [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- net defined by OOA [i] based on linear OOA(256, 300, F25, 4, 4) (dual of [(300, 4), 1194, 5]-NRT-code), using
- digital (14, 22, 3907)-net over F25, using
- net defined by OOA [i] based on linear OOA(2522, 3907, F25, 8, 8) (dual of [(3907, 8), 31234, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2522, 15628, F25, 8) (dual of [15628, 15606, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2522, 15625, F25, 8) (dual of [15625, 15603, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(2522, 15628, F25, 8) (dual of [15628, 15606, 9]-code), using
- net defined by OOA [i] based on linear OOA(2522, 3907, F25, 8, 8) (dual of [(3907, 8), 31234, 9]-NRT-code), using
- digital (2, 6, 300)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (60, 76, 1048575)-net over F25, using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (20, 28, 4207)-net over F25, using
(104−16, 104, large)-Net over F25 — Digital
Digital (88, 104, large)-net over F25, using
- t-expansion [i] based on digital (85, 104, large)-net over F25, using
- 3 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
- 3 times m-reduction [i] based on digital (85, 107, large)-net over F25, using
(104−16, 104, large)-Net in Base 25 — Upper bound on s
There is no (88, 104, large)-net in base 25, because
- 14 times m-reduction [i] would yield (88, 90, large)-net in base 25, but