Best Known (29−15, 29, s)-Nets in Base 256
(29−15, 29, 9362)-Net over F256 — Constructive and digital
Digital (14, 29, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25629, 9362, F256, 15, 15) (dual of [(9362, 15), 140401, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
(29−15, 29, 16384)-Net over F256 — Digital
Digital (14, 29, 16384)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25629, 16384, F256, 4, 15) (dual of [(16384, 4), 65507, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 4-folding [i] based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
(29−15, 29, large)-Net in Base 256 — Upper bound on s
There is no (14, 29, large)-net in base 256, because
- 13 times m-reduction [i] would yield (14, 16, large)-net in base 256, but