Information on Result #547540
There is no linear OA(5137, 277, F5, 105) (dual of [277, 140, 106]-code), because residual code would yield OA(532, 171, S5, 21), but
- 1 times truncation [i] would yield OA(531, 170, S5, 20), but
- the linear programming bound shows that M ≥ 42216 069885 091800 891878 320552 825927 734375 / 8 765861 509813 289221 > 531 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(5138, 278, F5, 106) (dual of [278, 140, 107]-code) | [i] | Truncation | |
| 2 | No linear OA(5139, 279, F5, 107) (dual of [279, 140, 108]-code) | [i] | ||
| 3 | No linear OA(5140, 280, F5, 108) (dual of [280, 140, 109]-code) | [i] | ||
| 4 | No linear OA(5141, 281, F5, 109) (dual of [281, 140, 110]-code) | [i] | ||
| 5 | No linear OOA(5138, 277, F5, 2, 106) (dual of [(277, 2), 416, 107]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(5139, 277, F5, 2, 107) (dual of [(277, 2), 415, 108]-NRT-code) | [i] | ||
| 7 | No linear OOA(5140, 277, F5, 2, 108) (dual of [(277, 2), 414, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(5141, 277, F5, 2, 109) (dual of [(277, 2), 413, 110]-NRT-code) | [i] | ||
| 9 | No linear OOA(5137, 277, F5, 2, 105) (dual of [(277, 2), 417, 106]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(5137, 277, F5, 3, 105) (dual of [(277, 3), 694, 106]-NRT-code) | [i] | ||
| 11 | No digital (32, 137, 277)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |