Best Known (30−8, 30, s)-Nets in Base 25
(30−8, 30, 97658)-Net over F25 — Constructive and digital
Digital (22, 30, 97658)-net over F25, using
- net defined by OOA [i] based on linear OOA(2530, 97658, F25, 8, 8) (dual of [(97658, 8), 781234, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2530, 390632, F25, 8) (dual of [390632, 390602, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2530, 390634, F25, 8) (dual of [390634, 390604, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(2529, 390625, F25, 8) (dual of [390625, 390596, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(2530, 390634, F25, 8) (dual of [390634, 390604, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2530, 390632, F25, 8) (dual of [390632, 390602, 9]-code), using
(30−8, 30, 390635)-Net over F25 — Digital
Digital (22, 30, 390635)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2530, 390635, F25, 8) (dual of [390635, 390605, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(2529, 390625, F25, 8) (dual of [390625, 390596, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(259, 10, F25, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
- dual of repetition code with length 10 [i]
- linear OA(251, 10, F25, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
(30−8, 30, large)-Net in Base 25 — Upper bound on s
There is no (22, 30, large)-net in base 25, because
- 6 times m-reduction [i] would yield (22, 24, large)-net in base 25, but