Best Known (30−7, 30, s)-Nets in Base 25
(30−7, 30, 131743)-Net over F25 — Constructive and digital
Digital (23, 30, 131743)-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 (18, 25, 130209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2525, 130209, F25, 7, 7) (dual of [(130209, 7), 911438, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2525, 390628, F25, 7) (dual of [390628, 390603, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2525, 390629, F25, 7) (dual of [390629, 390604, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(2525, 390625, F25, 7) (dual of [390625, 390600, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 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
- discarding factors / shortening the dual code based on linear OA(2525, 390629, F25, 7) (dual of [390629, 390604, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2525, 390628, F25, 7) (dual of [390628, 390603, 8]-code), using
- net defined by OOA [i] based on linear OOA(2525, 130209, F25, 7, 7) (dual of [(130209, 7), 911438, 8]-NRT-code), using
- digital (2, 5, 1534)-net over F25, using
(30−7, 30, 1218181)-Net over F25 — Digital
Digital (23, 30, 1218181)-net over F25, using
(30−7, 30, large)-Net in Base 25 — Upper bound on s
There is no (23, 30, large)-net in base 25, because
- 5 times m-reduction [i] would yield (23, 25, large)-net in base 25, but