Information on Result #547536
There is no linear OA(5131, 271, F5, 100) (dual of [271, 140, 101]-code), because residual code 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(5132, 272, F5, 101) (dual of [272, 140, 102]-code) | [i] | Truncation | |
| 2 | No linear OA(5133, 273, F5, 102) (dual of [273, 140, 103]-code) | [i] | ||
| 3 | No linear OA(5134, 274, F5, 103) (dual of [274, 140, 104]-code) | [i] | ||
| 4 | No linear OA(5135, 275, F5, 104) (dual of [275, 140, 105]-code) | [i] | ||
| 5 | No linear OOA(5132, 271, F5, 2, 101) (dual of [(271, 2), 410, 102]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(5133, 271, F5, 2, 102) (dual of [(271, 2), 409, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(5134, 271, F5, 2, 103) (dual of [(271, 2), 408, 104]-NRT-code) | [i] | ||
| 8 | No linear OOA(5135, 271, F5, 2, 104) (dual of [(271, 2), 407, 105]-NRT-code) | [i] | ||
| 9 | No linear OOA(5131, 271, F5, 2, 100) (dual of [(271, 2), 411, 101]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(5131, 271, F5, 3, 100) (dual of [(271, 3), 682, 101]-NRT-code) | [i] | ||
| 11 | No digital (31, 131, 271)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |