Best Known (97−34, 97, s)-Nets in Base 25
(97−34, 97, 919)-Net over F25 — Constructive and digital
Digital (63, 97, 919)-net over F25, using
- net defined by OOA [i] based on linear OOA(2597, 919, F25, 34, 34) (dual of [(919, 34), 31149, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(2597, 15623, F25, 34) (dual of [15623, 15526, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 15625, F25, 34) (dual of [15625, 15528, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(2597, 15625, F25, 34) (dual of [15625, 15528, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(2597, 15623, F25, 34) (dual of [15623, 15526, 35]-code), using
(97−34, 97, 8311)-Net over F25 — Digital
Digital (63, 97, 8311)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2597, 8311, F25, 34) (dual of [8311, 8214, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2597, 15625, F25, 34) (dual of [15625, 15528, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(2597, 15625, F25, 34) (dual of [15625, 15528, 35]-code), using
(97−34, 97, large)-Net in Base 25 — Upper bound on s
There is no (63, 97, large)-net in base 25, because
- 32 times m-reduction [i] would yield (63, 65, large)-net in base 25, but