Best Known (25−13, 25, s)-Nets in Base 256
(25−13, 25, 10922)-Net over F256 — Constructive and digital
Digital (12, 25, 10922)-net over F256, using
- net defined by OOA [i] based on linear OOA(25625, 10922, F256, 13, 13) (dual of [(10922, 13), 141961, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25625, 65533, F256, 13) (dual of [65533, 65508, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25625, 65533, F256, 13) (dual of [65533, 65508, 14]-code), using
(25−13, 25, 16384)-Net over F256 — Digital
Digital (12, 25, 16384)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25625, 16384, F256, 4, 13) (dual of [(16384, 4), 65511, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 4-folding [i] based on linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using
(25−13, 25, large)-Net in Base 256 — Upper bound on s
There is no (12, 25, large)-net in base 256, because
- 11 times m-reduction [i] would yield (12, 14, large)-net in base 256, but