Information on Result #1190788
Digital (63, 82, 1868)-net over F7, using net defined by OOA based on linear OOA(782, 1868, F7, 19, 19) (dual of [(1868, 19), 35410, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(782, 16813, F7, 19) (dual of [16813, 16731, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(782, 16819, F7, 19) (dual of [16819, 16737, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(781, 16808, F7, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(771, 16808, F7, 17) (dual of [16808, 16737, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(782, 16819, F7, 19) (dual of [16819, 16737, 20]-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 (64, 83, 1868)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (73, 92, 1881)-net over F7 | [i] | (u, u+v)-Construction for Nets | |