Best Known (13, 13+14, s)-Nets in Base 256
(13, 13+14, 9362)-Net over F256 — Constructive and digital
Digital (13, 27, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25627, 9362, F256, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25627, 65534, F256, 14) (dual of [65534, 65507, 15]-code), using
(13, 13+14, 16384)-Net over F256 — Digital
Digital (13, 27, 16384)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25627, 16384, F256, 4, 14) (dual of [(16384, 4), 65509, 15]-NRT-code), using
- OOA 4-folding [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]
- OOA 4-folding [i] based on linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using
(13, 13+14, large)-Net in Base 256 — Upper bound on s
There is no (13, 27, large)-net in base 256, because
- 12 times m-reduction [i] would yield (13, 15, large)-net in base 256, but