Best Known (69, 93, s)-Nets in Base 25
(69, 93, 32552)-Net over F25 — Constructive and digital
Digital (69, 93, 32552)-net over F25, using
- net defined by OOA [i] based on linear OOA(2593, 32552, F25, 24, 24) (dual of [(32552, 24), 781155, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2593, 390624, F25, 24) (dual of [390624, 390531, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2593, 390624, F25, 24) (dual of [390624, 390531, 25]-code), using
(69, 93, 264579)-Net over F25 — Digital
Digital (69, 93, 264579)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2593, 264579, F25, 24) (dual of [264579, 264486, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using
(69, 93, large)-Net in Base 25 — Upper bound on s
There is no (69, 93, large)-net in base 25, because
- 22 times m-reduction [i] would yield (69, 71, large)-net in base 25, but