Information on Result #1190792
Digital (66, 85, 1870)-net over F7, using net defined by OOA based on linear OOA(785, 1870, F7, 19, 19) (dual of [(1870, 19), 35445, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(785, 16831, F7, 19) (dual of [16831, 16746, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(785, 16832, F7, 19) (dual of [16832, 16747, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [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(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(785, 16832, F7, 19) (dual of [16832, 16747, 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 (67, 86, 1870)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (68, 87, 1870)-net over F7 | [i] | ||
| 3 | Digital (69, 88, 1870)-net over F7 | [i] | ||