Information on Result #546931
There is no linear OA(3216, 228, F3, 144) (dual of [228, 12, 145]-code), because residual code would yield OA(372, 83, S3, 48), but
- the linear programming bound shows that M ≥ 342768 675411 868196 169996 964468 602867 136719 / 13 555360 > 372 [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(3217, 229, F3, 145) (dual of [229, 12, 146]-code) | [i] | Truncation | |
| 2 | No linear OA(3218, 230, F3, 146) (dual of [230, 12, 147]-code) | [i] | ||
| 3 | No linear OOA(3217, 228, F3, 2, 145) (dual of [(228, 2), 239, 146]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3218, 228, F3, 2, 146) (dual of [(228, 2), 238, 147]-NRT-code) | [i] | ||
| 5 | No linear OOA(3216, 228, F3, 2, 144) (dual of [(228, 2), 240, 145]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3216, 228, F3, 3, 144) (dual of [(228, 3), 468, 145]-NRT-code) | [i] | ||
| 7 | No linear OOA(3216, 228, F3, 4, 144) (dual of [(228, 4), 696, 145]-NRT-code) | [i] | ||
| 8 | No linear OOA(3216, 228, F3, 5, 144) (dual of [(228, 5), 924, 145]-NRT-code) | [i] | ||
| 9 | No digital (72, 216, 228)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |