Information on Result #547539
There is no linear OA(5136, 252, F5, 105) (dual of [252, 116, 106]-code), because residual code would yield OA(531, 146, S5, 21), but
- 1 times truncation [i] would yield OA(530, 145, S5, 20), but
- the linear programming bound shows that M ≥ 34078 027381 828650 342719 814777 374267 578125 / 36 570326 005604 057357 > 530 [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(5137, 253, F5, 106) (dual of [253, 116, 107]-code) | [i] | Truncation | |
| 2 | No linear OA(5138, 254, F5, 107) (dual of [254, 116, 108]-code) | [i] | ||
| 3 | No linear OA(5139, 255, F5, 108) (dual of [255, 116, 109]-code) | [i] | ||
| 4 | No linear OOA(5137, 252, F5, 2, 106) (dual of [(252, 2), 367, 107]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(5138, 252, F5, 2, 107) (dual of [(252, 2), 366, 108]-NRT-code) | [i] | ||
| 6 | No linear OOA(5139, 252, F5, 2, 108) (dual of [(252, 2), 365, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(5136, 252, F5, 2, 105) (dual of [(252, 2), 368, 106]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(5136, 252, F5, 3, 105) (dual of [(252, 3), 620, 106]-NRT-code) | [i] | ||
| 9 | No digital (31, 136, 252)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(5116, 252, F5, 88) (dual of [252, 136, 89]-code) | [i] | Construction Y1 (Bound) | |