Information on Result #547543
There is no linear OA(5141, 229, F5, 110) (dual of [229, 88, 111]-code), because residual code would yield OA(531, 118, S5, 22), but
- the linear programming bound shows that M ≥ 2 310642 313094 154045 260009 765625 000000 000000 / 481 569852 057372 130117 > 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(5142, 230, F5, 111) (dual of [230, 88, 112]-code) | [i] | Truncation | |
| 2 | No linear OA(5143, 231, F5, 112) (dual of [231, 88, 113]-code) | [i] | ||
| 3 | No linear OA(5144, 232, F5, 113) (dual of [232, 88, 114]-code) | [i] | ||
| 4 | No linear OA(5145, 233, F5, 114) (dual of [233, 88, 115]-code) | [i] | ||
| 5 | No linear OOA(5142, 229, F5, 2, 111) (dual of [(229, 2), 316, 112]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(5143, 229, F5, 2, 112) (dual of [(229, 2), 315, 113]-NRT-code) | [i] | ||
| 7 | No linear OOA(5144, 229, F5, 2, 113) (dual of [(229, 2), 314, 114]-NRT-code) | [i] | ||
| 8 | No linear OOA(5145, 229, F5, 2, 114) (dual of [(229, 2), 313, 115]-NRT-code) | [i] | ||
| 9 | No linear OOA(5141, 229, F5, 2, 110) (dual of [(229, 2), 317, 111]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(5141, 229, F5, 3, 110) (dual of [(229, 3), 546, 111]-NRT-code) | [i] | ||
| 11 | No digital (31, 141, 229)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 12 | No linear OA(5112, 253, F5, 85) (dual of [253, 141, 86]-code) | [i] | Construction Y1 (Bound) | |