Best Known (73−26, 73, s)-Nets in Base 25
(73−26, 73, 1201)-Net over F25 — Constructive and digital
Digital (47, 73, 1201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2573, 1201, F25, 26, 26) (dual of [(1201, 26), 31153, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2573, 15613, F25, 26) (dual of [15613, 15540, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2573, 15613, F25, 26) (dual of [15613, 15540, 27]-code), using
(73−26, 73, 7812)-Net over F25 — Digital
Digital (47, 73, 7812)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2573, 7812, F25, 2, 26) (dual of [(7812, 2), 15551, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2573, 15624, F25, 26) (dual of [15624, 15551, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- OOA 2-folding [i] based on linear OA(2573, 15624, F25, 26) (dual of [15624, 15551, 27]-code), using
(73−26, 73, large)-Net in Base 25 — Upper bound on s
There is no (47, 73, large)-net in base 25, because
- 24 times m-reduction [i] would yield (47, 49, large)-net in base 25, but