Best Known (47−16, 47, s)-Nets in Base 25
(47−16, 47, 1954)-Net over F25 — Constructive and digital
Digital (31, 47, 1954)-net over F25, using
- net defined by OOA [i] based on linear OOA(2547, 1954, F25, 16, 16) (dual of [(1954, 16), 31217, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2547, 15632, F25, 16) (dual of [15632, 15585, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 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
- OA 8-folding and stacking [i] based on linear OA(2547, 15632, F25, 16) (dual of [15632, 15585, 17]-code), using
(47−16, 47, 9867)-Net over F25 — Digital
Digital (31, 47, 9867)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2547, 9867, F25, 16) (dual of [9867, 9820, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2547, 15632, F25, 16) (dual of [15632, 15585, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 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(2547, 15632, F25, 16) (dual of [15632, 15585, 17]-code), using
(47−16, 47, large)-Net in Base 25 — Upper bound on s
There is no (31, 47, large)-net in base 25, because
- 14 times m-reduction [i] would yield (31, 33, large)-net in base 25, but