Best Known (43, 65, s)-Nets in Base 25
(43, 65, 1421)-Net over F25 — Constructive and digital
Digital (43, 65, 1421)-net over F25, using
- net defined by OOA [i] based on linear OOA(2565, 1421, F25, 22, 22) (dual of [(1421, 22), 31197, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2565, 15631, F25, 22) (dual of [15631, 15566, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2565, 15631, F25, 22) (dual of [15631, 15566, 23]-code), using
(43, 65, 10282)-Net over F25 — Digital
Digital (43, 65, 10282)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2565, 10282, F25, 22) (dual of [10282, 10217, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
(43, 65, large)-Net in Base 25 — Upper bound on s
There is no (43, 65, large)-net in base 25, because
- 20 times m-reduction [i] would yield (43, 45, large)-net in base 25, but