Best Known (48, 48+26, s)-Nets in Base 25
(48, 48+26, 1202)-Net over F25 — Constructive and digital
Digital (48, 74, 1202)-net over F25, using
- net defined by OOA [i] based on linear OOA(2574, 1202, F25, 26, 26) (dual of [(1202, 26), 31178, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2574, 15626, F25, 26) (dual of [15626, 15552, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(251, 4, F25, 1) (dual of [4, 3, 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(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2574, 15626, F25, 26) (dual of [15626, 15552, 27]-code), using
(48, 48+26, 7814)-Net over F25 — Digital
Digital (48, 74, 7814)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2574, 7814, F25, 2, 26) (dual of [(7814, 2), 15554, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2574, 15628, F25, 26) (dual of [15628, 15554, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(251, 4, F25, 1) (dual of [4, 3, 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(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- OOA 2-folding [i] based on linear OA(2574, 15628, F25, 26) (dual of [15628, 15554, 27]-code), using
(48, 48+26, large)-Net in Base 25 — Upper bound on s
There is no (48, 74, large)-net in base 25, because
- 24 times m-reduction [i] would yield (48, 50, large)-net in base 25, but