Best Known (55−14, 55, s)-Nets in Base 25
(55−14, 55, 55805)-Net over F25 — Constructive and digital
Digital (41, 55, 55805)-net over F25, using
- net defined by OOA [i] based on linear OOA(2555, 55805, F25, 14, 14) (dual of [(55805, 14), 781215, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2555, 390635, F25, 14) (dual of [390635, 390580, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2555, 390639, F25, 14) (dual of [390639, 390584, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2541, 390625, F25, 11) (dual of [390625, 390584, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(2555, 390639, F25, 14) (dual of [390639, 390584, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2555, 390635, F25, 14) (dual of [390635, 390580, 15]-code), using
(55−14, 55, 390639)-Net over F25 — Digital
Digital (41, 55, 390639)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2555, 390639, F25, 14) (dual of [390639, 390584, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2541, 390625, F25, 11) (dual of [390625, 390584, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
(55−14, 55, large)-Net in Base 25 — Upper bound on s
There is no (41, 55, large)-net in base 25, because
- 12 times m-reduction [i] would yield (41, 43, large)-net in base 25, but