Information on Result #546772
There is no linear OA(3188, 223, F3, 123) (dual of [223, 35, 124]-code), because residual code would yield OA(365, 99, S3, 41), but
- the linear programming bound shows that M ≥ 1 398289 528640 015865 013744 903134 488973 245855 682309 745191 / 125126 745302 260144 143218 > 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(3189, 224, F3, 124) (dual of [224, 35, 125]-code) | [i] | Truncation | |
| 2 | No linear OA(3190, 225, F3, 125) (dual of [225, 35, 126]-code) | [i] | ||
| 3 | No linear OOA(3189, 223, F3, 2, 124) (dual of [(223, 2), 257, 125]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3190, 223, F3, 2, 125) (dual of [(223, 2), 256, 126]-NRT-code) | [i] | ||
| 5 | No linear OOA(3188, 223, F3, 2, 123) (dual of [(223, 2), 258, 124]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3188, 223, F3, 3, 123) (dual of [(223, 3), 481, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(3188, 223, F3, 4, 123) (dual of [(223, 4), 704, 124]-NRT-code) | [i] | ||
| 8 | No linear OOA(3188, 223, F3, 5, 123) (dual of [(223, 5), 927, 124]-NRT-code) | [i] | ||
| 9 | No digital (65, 188, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |