Information on Result #547128
There is no linear OA(4139, 245, F4, 100) (dual of [245, 106, 101]-code), because residual code would yield OA(439, 144, S4, 25), but
- the linear programming bound shows that M ≥ 451 194621 572690 925216 028943 220812 151783 424000 / 1452 353674 315137 592771 > 439 [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(4140, 246, F4, 101) (dual of [246, 106, 102]-code) | [i] | Truncation | |
| 2 | No linear OA(4141, 247, F4, 102) (dual of [247, 106, 103]-code) | [i] | ||
| 3 | No linear OA(4142, 248, F4, 103) (dual of [248, 106, 104]-code) | [i] | ||
| 4 | No linear OOA(4140, 245, F4, 2, 101) (dual of [(245, 2), 350, 102]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4141, 245, F4, 2, 102) (dual of [(245, 2), 349, 103]-NRT-code) | [i] | ||
| 6 | No linear OOA(4142, 245, F4, 2, 103) (dual of [(245, 2), 348, 104]-NRT-code) | [i] | ||
| 7 | No linear OOA(4139, 245, F4, 2, 100) (dual of [(245, 2), 351, 101]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4139, 245, F4, 3, 100) (dual of [(245, 3), 596, 101]-NRT-code) | [i] | ||
| 9 | No digital (39, 139, 245)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |