Information on Result #1179690
Digital (9, 14, 265724)-net over F81, using net defined by OOA based on linear OOA(8114, 265724, F81, 5, 5) (dual of [(265724, 5), 1328606, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(8114, 265724, F81, 4, 5) (dual of [(265724, 4), 1062882, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8114, 531449, F81, 5) (dual of [531449, 531435, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- 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(817, 531442, F81, 3) (dual of [531442, 531435, 4]-code or 531442-cap in PG(6,81)), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (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([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(8114, 531449, F81, 5) (dual of [531449, 531435, 6]-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 (41, 51, 1943444)-net over F81 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (44, 55, 1943444)-net over F81 | [i] | ||