Information on Result #547574
There is no linear OA(837, 68, F8, 32) (dual of [68, 31, 33]-code), because residual code would yield OA(85, 35, S8, 4), but
- the linear programming bound shows that M ≥ 1 306624 / 39 > 85 [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(838, 69, F8, 33) (dual of [69, 31, 34]-code) | [i] | Truncation | |
| 2 | No linear OA(839, 70, F8, 34) (dual of [70, 31, 35]-code) | [i] | ||
| 3 | No linear OA(840, 71, F8, 35) (dual of [71, 31, 36]-code) | [i] | ||
| 4 | No linear OOA(838, 68, F8, 2, 33) (dual of [(68, 2), 98, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(839, 68, F8, 2, 34) (dual of [(68, 2), 97, 35]-NRT-code) | [i] | ||
| 6 | No linear OOA(840, 68, F8, 2, 35) (dual of [(68, 2), 96, 36]-NRT-code) | [i] | ||
| 7 | No linear OOA(837, 68, F8, 2, 32) (dual of [(68, 2), 99, 33]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(837, 68, F8, 3, 32) (dual of [(68, 3), 167, 33]-NRT-code) | [i] | ||
| 9 | No digital (5, 37, 68)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |