Information on Result #547220
There is no linear OA(4184, 237, F4, 136) (dual of [237, 53, 137]-code), because residual code would yield OA(448, 100, S4, 34), but
- the linear programming bound shows that M ≥ 9058 957890 512598 877597 243353 229194 029550 244654 789588 151723 066658 722038 162924 682285 684121 927080 009184 894902 538211 707610 394949 320704 / 112877 238751 180015 015346 131872 600873 922049 184597 216985 800847 416342 964009 902792 675071 874309 392551 306831 > 448 [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(4185, 238, F4, 137) (dual of [238, 53, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(4186, 239, F4, 138) (dual of [239, 53, 139]-code) | [i] | ||
| 3 | No linear OA(4187, 240, F4, 139) (dual of [240, 53, 140]-code) | [i] | ||
| 4 | No linear OOA(4185, 237, F4, 2, 137) (dual of [(237, 2), 289, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4186, 237, F4, 2, 138) (dual of [(237, 2), 288, 139]-NRT-code) | [i] | ||
| 6 | No linear OOA(4187, 237, F4, 2, 139) (dual of [(237, 2), 287, 140]-NRT-code) | [i] | ||
| 7 | No linear OOA(4184, 237, F4, 2, 136) (dual of [(237, 2), 290, 137]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4184, 237, F4, 3, 136) (dual of [(237, 3), 527, 137]-NRT-code) | [i] | ||
| 9 | No digital (48, 184, 237)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |