Best Known (29−10, 29, s)-Nets in Base 25
(29−10, 29, 3126)-Net over F25 — Constructive and digital
Digital (19, 29, 3126)-net over F25, using
- net defined by OOA [i] based on linear OOA(2529, 3126, F25, 10, 10) (dual of [(3126, 10), 31231, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2529, 15630, F25, 10) (dual of [15630, 15601, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2529, 15632, F25, 10) (dual of [15632, 15603, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(251, 7, F25, 1) (dual of [7, 6, 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(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2529, 15632, F25, 10) (dual of [15632, 15603, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2529, 15630, F25, 10) (dual of [15630, 15601, 11]-code), using
(29−10, 29, 12250)-Net over F25 — Digital
Digital (19, 29, 12250)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2529, 12250, F25, 10) (dual of [12250, 12221, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2529, 15632, F25, 10) (dual of [15632, 15603, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(251, 7, F25, 1) (dual of [7, 6, 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(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2529, 15632, F25, 10) (dual of [15632, 15603, 11]-code), using
(29−10, 29, large)-Net in Base 25 — Upper bound on s
There is no (19, 29, large)-net in base 25, because
- 8 times m-reduction [i] would yield (19, 21, large)-net in base 25, but