Best Known (54, 76, s)-Nets in Base 25
(54, 76, 1447)-Net over F25 — Constructive and digital
Digital (54, 76, 1447)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (42, 64, 1420)-net over F25, using
- net defined by OOA [i] based on linear OOA(2564, 1420, F25, 22, 22) (dual of [(1420, 22), 31176, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2564, 15620, F25, 22) (dual of [15620, 15556, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2564, 15620, F25, 22) (dual of [15620, 15556, 23]-code), using
- net defined by OOA [i] based on linear OOA(2564, 1420, F25, 22, 22) (dual of [(1420, 22), 31176, 23]-NRT-code), using
- digital (1, 12, 27)-net over F25, using
(54, 76, 41457)-Net over F25 — Digital
Digital (54, 76, 41457)-net over F25, using
(54, 76, large)-Net in Base 25 — Upper bound on s
There is no (54, 76, large)-net in base 25, because
- 20 times m-reduction [i] would yield (54, 56, large)-net in base 25, but