Best Known (36, 36+13, s)-Nets in Base 25
(36, 36+13, 65104)-Net over F25 — Constructive and digital
Digital (36, 49, 65104)-net over F25, using
- net defined by OOA [i] based on linear OOA(2549, 65104, F25, 13, 13) (dual of [(65104, 13), 846303, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
(36, 36+13, 257571)-Net over F25 — Digital
Digital (36, 49, 257571)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2549, 257571, F25, 13) (dual of [257571, 257522, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using
(36, 36+13, large)-Net in Base 25 — Upper bound on s
There is no (36, 49, large)-net in base 25, because
- 11 times m-reduction [i] would yield (36, 38, large)-net in base 25, but