Best Known (92−32, 92, s)-Nets in Base 25
(92−32, 92, 977)-Net over F25 — Constructive and digital
Digital (60, 92, 977)-net over F25, using
- net defined by OOA [i] based on linear OOA(2592, 977, F25, 32, 32) (dual of [(977, 32), 31172, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(31) ⊂ Ce(29) [i] based on
- OA 16-folding and stacking [i] based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
(92−32, 92, 8714)-Net over F25 — Digital
Digital (60, 92, 8714)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2592, 8714, F25, 32) (dual of [8714, 8622, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(31) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
(92−32, 92, large)-Net in Base 25 — Upper bound on s
There is no (60, 92, large)-net in base 25, because
- 30 times m-reduction [i] would yield (60, 62, large)-net in base 25, but