Best Known (17, 17+7, s)-Nets in Base 25
(17, 17+7, 6743)-Net over F25 — Constructive and digital
Digital (17, 24, 6743)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 1534)-net over F25, using
- net defined by OOA [i] based on linear OOA(255, 1534, F25, 3, 3) (dual of [(1534, 3), 4597, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(255, 1534, F25, 2, 3) (dual of [(1534, 2), 3063, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(255, 1534, F25, 3, 3) (dual of [(1534, 3), 4597, 4]-NRT-code), using
- 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 (2, 5, 1534)-net over F25, using
(17, 17+7, 48730)-Net over F25 — Digital
Digital (17, 24, 48730)-net over F25, using
(17, 17+7, large)-Net in Base 25 — Upper bound on s
There is no (17, 24, large)-net in base 25, because
- 5 times m-reduction [i] would yield (17, 19, large)-net in base 25, but