Best Known (23, 23+12, s)-Nets in Base 25
(23, 23+12, 2605)-Net over F25 — Constructive and digital
Digital (23, 35, 2605)-net over F25, using
- net defined by OOA [i] based on linear OOA(2535, 2605, F25, 12, 12) (dual of [(2605, 12), 31225, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2535, 15630, F25, 12) (dual of [15630, 15595, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2535, 15632, F25, 12) (dual of [15632, 15597, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2535, 15632, F25, 12) (dual of [15632, 15597, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2535, 15630, F25, 12) (dual of [15630, 15595, 13]-code), using
(23, 23+12, 10680)-Net over F25 — Digital
Digital (23, 35, 10680)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2535, 10680, F25, 12) (dual of [10680, 10645, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2535, 15632, F25, 12) (dual of [15632, 15597, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2535, 15632, F25, 12) (dual of [15632, 15597, 13]-code), using
(23, 23+12, large)-Net in Base 25 — Upper bound on s
There is no (23, 35, large)-net in base 25, because
- 10 times m-reduction [i] would yield (23, 25, large)-net in base 25, but