Information on Result #546677
There is no linear OA(3153, 168, F3, 102) (dual of [168, 15, 103]-code), because residual code would yield OA(351, 65, S3, 34), but
- the linear programming bound shows that M ≥ 342 054256 122719 546156 841781 498869 / 115 101637 > 351 [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(3154, 169, F3, 103) (dual of [169, 15, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3155, 170, F3, 104) (dual of [170, 15, 105]-code) | [i] | ||
| 3 | No linear OOA(3154, 168, F3, 2, 103) (dual of [(168, 2), 182, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3155, 168, F3, 2, 104) (dual of [(168, 2), 181, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3153, 168, F3, 2, 102) (dual of [(168, 2), 183, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3153, 168, F3, 3, 102) (dual of [(168, 3), 351, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3153, 168, F3, 4, 102) (dual of [(168, 4), 519, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3153, 168, F3, 5, 102) (dual of [(168, 5), 687, 103]-NRT-code) | [i] | ||
| 9 | No digital (51, 153, 168)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |