Best Known (47, 47+16, s)-Nets in Base 25
(47, 47+16, 48829)-Net over F25 — Constructive and digital
Digital (47, 63, 48829)-net over F25, using
- 251 times duplication [i] based on digital (46, 62, 48829)-net over F25, using
- net defined by OOA [i] based on linear OOA(2562, 48829, F25, 16, 16) (dual of [(48829, 16), 781202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 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(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
- net defined by OOA [i] based on linear OOA(2562, 48829, F25, 16, 16) (dual of [(48829, 16), 781202, 17]-NRT-code), using
(47, 47+16, 390639)-Net over F25 — Digital
Digital (47, 63, 390639)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2563, 390639, F25, 16) (dual of [390639, 390576, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 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]
- 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(15) ⊂ Ce(12) [i] based on
(47, 47+16, large)-Net in Base 25 — Upper bound on s
There is no (47, 63, large)-net in base 25, because
- 14 times m-reduction [i] would yield (47, 49, large)-net in base 25, but