Information on Result #547153
There is no linear OA(4155, 252, F4, 112) (dual of [252, 97, 113]-code), because residual code would yield OA(443, 139, S4, 28), but
- the linear programming bound shows that M ≥ 1035 121114 338894 134286 782748 220018 948622 504479 948800 000000 / 12 858495 004117 038732 982555 334443 > 443 [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(4156, 253, F4, 113) (dual of [253, 97, 114]-code) | [i] | Truncation | |
| 2 | No linear OA(4157, 254, F4, 114) (dual of [254, 97, 115]-code) | [i] | ||
| 3 | No linear OA(4158, 255, F4, 115) (dual of [255, 97, 116]-code) | [i] | ||
| 4 | No linear OOA(4156, 252, F4, 2, 113) (dual of [(252, 2), 348, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4157, 252, F4, 2, 114) (dual of [(252, 2), 347, 115]-NRT-code) | [i] | ||
| 6 | No linear OOA(4158, 252, F4, 2, 115) (dual of [(252, 2), 346, 116]-NRT-code) | [i] | ||
| 7 | No linear OOA(4155, 252, F4, 2, 112) (dual of [(252, 2), 349, 113]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4155, 252, F4, 3, 112) (dual of [(252, 3), 601, 113]-NRT-code) | [i] | ||
| 9 | No digital (43, 155, 252)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |