Information on Result #547732
There is no linear OA(313, 19, F3, 9) (dual of [19, 6, 10]-code), because construction Y1 would yield
- linear OA(312, 15, F3, 9) (dual of [15, 3, 10]-code), but
- OA(36, 19, S3, 4), but
- the linear programming bound shows that M ≥ 51975 / 67 > 36 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(314, 20, F3, 10) (dual of [20, 6, 11]-code) | [i] | Truncation | |
| 2 | No linear OA(315, 21, F3, 11) (dual of [21, 6, 12]-code) | [i] | ||
| 3 | No linear OOA(314, 19, F3, 2, 10) (dual of [(19, 2), 24, 11]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(315, 19, F3, 2, 11) (dual of [(19, 2), 23, 12]-NRT-code) | [i] | ||
| 5 | No linear OOA(313, 19, F3, 2, 9) (dual of [(19, 2), 25, 10]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(313, 19, F3, 3, 9) (dual of [(19, 3), 44, 10]-NRT-code) | [i] | ||
| 7 | No linear OOA(313, 19, F3, 4, 9) (dual of [(19, 4), 63, 10]-NRT-code) | [i] | ||
| 8 | No linear OOA(313, 19, F3, 5, 9) (dual of [(19, 5), 82, 10]-NRT-code) | [i] | ||
| 9 | No digital (4, 13, 19)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(314, 30, F3, 9) (dual of [30, 16, 10]-code) | [i] | Construction Y1 (Bound) | |