Best Known (71, 95, s)-Nets in Base 25
(71, 95, 32553)-Net over F25 — Constructive and digital
Digital (71, 95, 32553)-net over F25, using
- net defined by OOA [i] based on linear OOA(2595, 32553, F25, 24, 24) (dual of [(32553, 24), 781177, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2595, 390636, F25, 24) (dual of [390636, 390541, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2595, 390639, F25, 24) (dual of [390639, 390544, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] 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]
- linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(252, 14, F25, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2595, 390639, F25, 24) (dual of [390639, 390544, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2595, 390636, F25, 24) (dual of [390636, 390541, 25]-code), using
(71, 95, 354523)-Net over F25 — Digital
Digital (71, 95, 354523)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2595, 354523, F25, 24) (dual of [354523, 354428, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2595, 390639, F25, 24) (dual of [390639, 390544, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] 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]
- linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(252, 14, F25, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2595, 390639, F25, 24) (dual of [390639, 390544, 25]-code), using
(71, 95, large)-Net in Base 25 — Upper bound on s
There is no (71, 95, large)-net in base 25, because
- 22 times m-reduction [i] would yield (71, 73, large)-net in base 25, but