Information on Result #1197318
Digital (19, 26, 177150)-net over F27, using net defined by OOA based on linear OOA(2726, 177150, F27, 7, 7) (dual of [(177150, 7), 1240024, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2726, 531451, F27, 7) (dual of [531451, 531425, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(2725, 531442, F27, 7) (dual of [531442, 531417, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2717, 531442, F27, 5) (dual of [531442, 531425, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 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
Mode: Constructive and 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 | Digital (78, 92, 1375521)-net over F27 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (82, 97, 1375521)-net over F27 | [i] | ||