Best Known (14, 14+14, s)-Nets in Base 256
(14, 14+14, 9363)-Net over F256 — Constructive and digital
Digital (14, 28, 9363)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 9363, F256, 14, 14) (dual of [(9363, 14), 131054, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25628, 65541, F256, 14) (dual of [65541, 65513, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- OA 7-folding and stacking [i] based on linear OA(25628, 65541, F256, 14) (dual of [65541, 65513, 15]-code), using
(14, 14+14, 18618)-Net over F256 — Digital
Digital (14, 28, 18618)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 18618, F256, 3, 14) (dual of [(18618, 3), 55826, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25628, 21847, F256, 3, 14) (dual of [(21847, 3), 65513, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25628, 65541, F256, 14) (dual of [65541, 65513, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- OOA 3-folding [i] based on linear OA(25628, 65541, F256, 14) (dual of [65541, 65513, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(25628, 21847, F256, 3, 14) (dual of [(21847, 3), 65513, 15]-NRT-code), using
(14, 14+14, large)-Net in Base 256 — Upper bound on s
There is no (14, 28, large)-net in base 256, because
- 12 times m-reduction [i] would yield (14, 16, large)-net in base 256, but