Best Known (47, 72, s)-Nets in Base 25
(47, 72, 1301)-Net over F25 — Constructive and digital
Digital (47, 72, 1301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2572, 1301, F25, 25, 25) (dual of [(1301, 25), 32453, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2572, 15613, F25, 25) (dual of [15613, 15541, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2572, 15613, F25, 25) (dual of [15613, 15541, 26]-code), using
(47, 72, 8110)-Net over F25 — Digital
Digital (47, 72, 8110)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2572, 8110, F25, 25) (dual of [8110, 8038, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
(47, 72, large)-Net in Base 25 — Upper bound on s
There is no (47, 72, large)-net in base 25, because
- 23 times m-reduction [i] would yield (47, 49, large)-net in base 25, but