Information on Result #546788
There is no linear OA(3191, 213, F3, 126) (dual of [213, 22, 127]-code), because residual code would yield OA(365, 86, S3, 42), but
- the linear programming bound shows that M ≥ 105639 517822 541973 415942 878050 095499 770611 / 8844 615395 > 365 [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(3192, 214, F3, 127) (dual of [214, 22, 128]-code) | [i] | Truncation | |
| 2 | No linear OA(3193, 215, F3, 128) (dual of [215, 22, 129]-code) | [i] | ||
| 3 | No linear OOA(3192, 213, F3, 2, 127) (dual of [(213, 2), 234, 128]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3193, 213, F3, 2, 128) (dual of [(213, 2), 233, 129]-NRT-code) | [i] | ||
| 5 | No linear OOA(3191, 213, F3, 2, 126) (dual of [(213, 2), 235, 127]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3191, 213, F3, 3, 126) (dual of [(213, 3), 448, 127]-NRT-code) | [i] | ||
| 7 | No linear OOA(3191, 213, F3, 4, 126) (dual of [(213, 4), 661, 127]-NRT-code) | [i] | ||
| 8 | No linear OOA(3191, 213, F3, 5, 126) (dual of [(213, 5), 874, 127]-NRT-code) | [i] | ||
| 9 | No digital (65, 191, 213)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |