Information on Result #547183
There is no linear OA(4170, 253, F4, 124) (dual of [253, 83, 125]-code), because residual code would yield OA(446, 128, S4, 31), but
- the linear programming bound shows that M ≥ 267 358960 125089 320834 735810 320865 223199 249308 916618 499694 277322 342400 / 51948 589430 472776 062424 380928 571484 419011 > 446 [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(4171, 254, F4, 125) (dual of [254, 83, 126]-code) | [i] | Truncation | |
| 2 | No linear OA(4172, 255, F4, 126) (dual of [255, 83, 127]-code) | [i] | ||
| 3 | No linear OA(4173, 256, F4, 127) (dual of [256, 83, 128]-code) | [i] | ||
| 4 | No linear OOA(4171, 253, F4, 2, 125) (dual of [(253, 2), 335, 126]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4172, 253, F4, 2, 126) (dual of [(253, 2), 334, 127]-NRT-code) | [i] | ||
| 6 | No linear OOA(4173, 253, F4, 2, 127) (dual of [(253, 2), 333, 128]-NRT-code) | [i] | ||
| 7 | No linear OOA(4170, 253, F4, 2, 124) (dual of [(253, 2), 336, 125]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4170, 253, F4, 3, 124) (dual of [(253, 3), 589, 125]-NRT-code) | [i] | ||
| 9 | No digital (46, 170, 253)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |