Information on Result #547151
There is no linear OA(4153, 224, F4, 112) (dual of [224, 71, 113]-code), because residual code would yield OA(441, 111, S4, 28), but
- the linear programming bound shows that M ≥ 7709 702911 510783 693838 831699 200582 723072 520355 840000 / 1472 084210 434687 540905 417611 > 441 [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(4154, 225, F4, 113) (dual of [225, 71, 114]-code) | [i] | Truncation | |
| 2 | No linear OA(4155, 226, F4, 114) (dual of [226, 71, 115]-code) | [i] | ||
| 3 | No linear OA(4156, 227, F4, 115) (dual of [227, 71, 116]-code) | [i] | ||
| 4 | No linear OOA(4154, 224, F4, 2, 113) (dual of [(224, 2), 294, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4155, 224, F4, 2, 114) (dual of [(224, 2), 293, 115]-NRT-code) | [i] | ||
| 6 | No linear OOA(4156, 224, F4, 2, 115) (dual of [(224, 2), 292, 116]-NRT-code) | [i] | ||
| 7 | No linear OOA(4153, 224, F4, 2, 112) (dual of [(224, 2), 295, 113]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4153, 224, F4, 3, 112) (dual of [(224, 3), 519, 113]-NRT-code) | [i] | ||
| 9 | No digital (41, 153, 224)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |