Information on Result #1197570
Digital (31, 42, 106290)-net over F27, using net defined by OOA based on linear OOA(2742, 106290, F27, 11, 11) (dual of [(106290, 11), 1169148, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2742, 531451, F27, 11) (dual of [531451, 531409, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(2741, 531442, F27, 11) (dual of [531442, 531401, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2733, 531442, F27, 9) (dual of [531442, 531409, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 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([0,5]) ⊂ C([0,4]) [i] based on
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 (32, 43, 106290)-net over F27 | [i] | Net Duplication | |
| 2 | Digital (38, 49, 106641)-net over F27 | [i] | (u, u+v)-Construction for Nets | |