Best Known (65−17, 65, s)-Nets in Base 25
(65−17, 65, 48828)-Net over F25 — Constructive and digital
Digital (48, 65, 48828)-net over F25, using
- net defined by OOA [i] based on linear OOA(2565, 48828, F25, 17, 17) (dual of [(48828, 17), 830011, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
(65−17, 65, 246653)-Net over F25 — Digital
Digital (48, 65, 246653)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2565, 246653, F25, 17) (dual of [246653, 246588, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using
(65−17, 65, large)-Net in Base 25 — Upper bound on s
There is no (48, 65, large)-net in base 25, because
- 15 times m-reduction [i] would yield (48, 50, large)-net in base 25, but