Information on Result #1185682
Digital (211, 248, 3282)-net over F3, using net defined by OOA based on linear OOA(3248, 3282, F3, 37, 37) (dual of [(3282, 37), 121186, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(3248, 59077, F3, 37) (dual of [59077, 58829, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3247, 59076, F3, 37) (dual of [59076, 58829, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(3241, 59050, F3, 37) (dual of [59050, 58809, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3221, 59050, F3, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(36, 26, F3, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3247, 59076, F3, 37) (dual of [59076, 58829, 38]-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 (212, 248, 3282)-net over F3 | [i] | t-Expansion | |
| 2 | Digital (212, 249, 3282)-net over F3 | [i] | Net Duplication | |
| 3 | Digital (213, 250, 3282)-net over F3 | [i] | ||
| 4 | Digital (211, 247, 3282)-net over F3 | [i] | m-Reduction | |