Best Known (7, 7+8, s)-Nets in Base 256
(7, 7+8, 16384)-Net over F256 — Constructive and digital
Digital (7, 15, 16384)-net over F256, using
- net defined by OOA [i] based on linear OOA(25615, 16384, F256, 8, 8) (dual of [(16384, 8), 131057, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
(7, 7+8, 21846)-Net over F256 — Digital
Digital (7, 15, 21846)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25615, 21846, F256, 3, 8) (dual of [(21846, 3), 65523, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OOA 3-folding [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
(7, 7+8, large)-Net in Base 256 — Upper bound on s
There is no (7, 15, large)-net in base 256, because
- 6 times m-reduction [i] would yield (7, 9, large)-net in base 256, but