Information on Result #1708082
Digital (7, 14, 32771)-net over F256, using net defined by OOA based on linear OOA(25614, 32771, F256, 7, 7) (dual of [(32771, 7), 229383, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25614, 32771, F256, 6, 7) (dual of [(32771, 6), 196612, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25614, 32771, F256, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2569, 65537, F256, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 2-folding [i] based on linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25614, 32771, F256, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | (9, 16, 32771)-net in base 128 | [i] | Base Change | |