Information on Result #547563
There is no linear OA(741, 66, F7, 35) (dual of [66, 25, 36]-code), because residual code would yield OA(76, 30, S7, 5), but
- 1 times truncation [i] would yield OA(75, 29, S7, 4), but
- the linear programming bound shows that M ≥ 3 384381 / 197 > 75 [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(742, 67, F7, 36) (dual of [67, 25, 37]-code) | [i] | Truncation | |
| 2 | No linear OOA(742, 66, F7, 2, 36) (dual of [(66, 2), 90, 37]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(741, 66, F7, 2, 35) (dual of [(66, 2), 91, 36]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(741, 66, F7, 3, 35) (dual of [(66, 3), 157, 36]-NRT-code) | [i] | ||
| 5 | No digital (6, 41, 66)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |