Information on Result #1197406
Digital (9, 18, 183)-net over F27, using net defined by OOA based on linear OOA(2718, 183, F27, 9, 9) (dual of [(183, 9), 1629, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2718, 733, F27, 9) (dual of [733, 715, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2718, 735, F27, 9) (dual of [735, 717, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(2717, 730, F27, 9) (dual of [730, 713, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2713, 730, F27, 7) (dual of [730, 717, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2718, 735, F27, 9) (dual of [735, 717, 10]-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 (86, 104, 932250)-net over F27 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (90, 109, 932249)-net over F27 | [i] | ||