Best Known (47−12, 47, s)-Nets in Base 25
(47−12, 47, 65106)-Net over F25 — Constructive and digital
Digital (35, 47, 65106)-net over F25, using
- net defined by OOA [i] based on linear OOA(2547, 65106, F25, 12, 12) (dual of [(65106, 12), 781225, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2547, 390636, F25, 12) (dual of [390636, 390589, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2547, 390639, F25, 12) (dual of [390639, 390592, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2533, 390625, F25, 9) (dual of [390625, 390592, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2547, 390639, F25, 12) (dual of [390639, 390592, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2547, 390636, F25, 12) (dual of [390636, 390589, 13]-code), using
(47−12, 47, 390639)-Net over F25 — Digital
Digital (35, 47, 390639)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2547, 390639, F25, 12) (dual of [390639, 390592, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2533, 390625, F25, 9) (dual of [390625, 390592, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
(47−12, 47, large)-Net in Base 25 — Upper bound on s
There is no (35, 47, large)-net in base 25, because
- 10 times m-reduction [i] would yield (35, 37, large)-net in base 25, but