Information on Result #1205395
Digital (73, 84, 2305924)-net over F7, using trace code for nets based on digital (31, 42, 1152962)-net over F49, using
- net defined by OOA [i] based on linear OOA(4942, 1152962, F49, 11, 11) (dual of [(1152962, 11), 12682540, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4942, 5764811, F49, 11) (dual of [5764811, 5764769, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(4941, 5764802, F49, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(4933, 5764802, F49, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(4942, 5764811, F49, 11) (dual of [5764811, 5764769, 12]-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 (74, 85, 2305924)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (75, 86, 2305924)-net over F7 | [i] | ||