Information on Result #547192
There is no linear OA(4174, 237, F4, 128) (dual of [237, 63, 129]-code), because residual code would yield OA(446, 108, S4, 32), but
- the linear programming bound shows that M ≥ 7521 585930 885377 473826 532410 438434 365147 619053 743009 472248 914222 591788 142097 858560 000000 / 1 441569 793884 706534 073896 273915 521544 945772 995787 416063 963723 > 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(4175, 238, F4, 129) (dual of [238, 63, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(4176, 239, F4, 130) (dual of [239, 63, 131]-code) | [i] | ||
| 3 | No linear OA(4177, 240, F4, 131) (dual of [240, 63, 132]-code) | [i] | ||
| 4 | No linear OOA(4175, 237, F4, 2, 129) (dual of [(237, 2), 299, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4176, 237, F4, 2, 130) (dual of [(237, 2), 298, 131]-NRT-code) | [i] | ||
| 6 | No linear OOA(4177, 237, F4, 2, 131) (dual of [(237, 2), 297, 132]-NRT-code) | [i] | ||
| 7 | No linear OOA(4174, 237, F4, 2, 128) (dual of [(237, 2), 300, 129]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4174, 237, F4, 3, 128) (dual of [(237, 3), 537, 129]-NRT-code) | [i] | ||
| 9 | No digital (46, 174, 237)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |