Best Known (12, 17, s)-Nets in Base 25
(12, 17, 195314)-Net over F25 — Constructive and digital
Digital (12, 17, 195314)-net over F25, using
- net defined by OOA [i] based on linear OOA(2517, 195314, F25, 5, 5) (dual of [(195314, 5), 976553, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2517, 390629, F25, 5) (dual of [390629, 390612, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(2517, 390629, F25, 5) (dual of [390629, 390612, 6]-code), using
(12, 17, 390629)-Net over F25 — Digital
Digital (12, 17, 390629)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2517, 390629, F25, 5) (dual of [390629, 390612, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
(12, 17, large)-Net in Base 25 — Upper bound on s
There is no (12, 17, large)-net in base 25, because
- 3 times m-reduction [i] would yield (12, 14, large)-net in base 25, but