Information on Result #1202020
Digital (13, 20, 177149)-net over F81, using net defined by OOA based on linear OOA(8120, 177149, F81, 7, 7) (dual of [(177149, 7), 1240023, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8120, 531448, F81, 7) (dual of [531448, 531428, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 531449, F81, 7) (dual of [531449, 531429, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(8113, 531442, F81, 5) (dual of [531442, 531429, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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
- discarding factors / shortening the dual code based on linear OA(8120, 531449, F81, 7) (dual of [531449, 531429, 8]-code), using
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 (59, 73, 1375520)-net over F81 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (62, 77, 1375520)-net over F81 | [i] | ||