Information on Result #547150
There is no linear OA(4152, 209, F4, 112) (dual of [209, 57, 113]-code), because residual code would yield OA(440, 96, S4, 28), but
- the linear programming bound shows that M ≥ 3 041221 052768 594873 805769 980859 249005 438281 138205 879215 063040 / 2 375396 786313 270370 198219 858144 081283 > 440 [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(4153, 210, F4, 113) (dual of [210, 57, 114]-code) | [i] | Truncation | |
| 2 | No linear OA(4154, 211, F4, 114) (dual of [211, 57, 115]-code) | [i] | ||
| 3 | No linear OA(4155, 212, F4, 115) (dual of [212, 57, 116]-code) | [i] | ||
| 4 | No linear OOA(4153, 209, F4, 2, 113) (dual of [(209, 2), 265, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4154, 209, F4, 2, 114) (dual of [(209, 2), 264, 115]-NRT-code) | [i] | ||
| 6 | No linear OOA(4155, 209, F4, 2, 115) (dual of [(209, 2), 263, 116]-NRT-code) | [i] | ||
| 7 | No linear OOA(4152, 209, F4, 2, 112) (dual of [(209, 2), 266, 113]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4152, 209, F4, 3, 112) (dual of [(209, 3), 475, 113]-NRT-code) | [i] | ||
| 9 | No digital (40, 152, 209)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |