Information on Result #1197682
Digital (13, 26, 122)-net over F27, using net defined by OOA based on linear OOA(2726, 122, F27, 13, 13) (dual of [(122, 13), 1560, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2726, 733, F27, 13) (dual of [733, 707, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2726, 735, F27, 13) (dual of [735, 709, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(2725, 730, F27, 13) (dual of [730, 705, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2721, 730, F27, 11) (dual of [730, 709, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(271, 5, F27, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2726, 735, F27, 13) (dual of [735, 709, 14]-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 (47, 73, 250)-net over F27 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (47, 74, 250)-net over F27 | [i] | ||
| 3 | Digital (49, 76, 262)-net over F27 | [i] | ||