Information on Result #547461
There is no linear OA(4252, 431, F4, 180) (dual of [431, 179, 181]-code), because residual code would yield OA(472, 250, S4, 45), but
- the linear programming bound shows that M ≥ 844 253129 128337 968002 738138 104958 795392 851484 110411 486022 086287 533951 460726 969110 480212 292670 586880 / 36 177347 187970 342236 372937 633185 534214 836452 245739 305493 > 472 [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(4253, 432, F4, 181) (dual of [432, 179, 182]-code) | [i] | Truncation | |
| 2 | No linear OA(4254, 433, F4, 182) (dual of [433, 179, 183]-code) | [i] | ||
| 3 | No linear OA(4255, 434, F4, 183) (dual of [434, 179, 184]-code) | [i] | ||
| 4 | No linear OOA(4253, 431, F4, 2, 181) (dual of [(431, 2), 609, 182]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4254, 431, F4, 2, 182) (dual of [(431, 2), 608, 183]-NRT-code) | [i] | ||
| 6 | No linear OOA(4255, 431, F4, 2, 183) (dual of [(431, 2), 607, 184]-NRT-code) | [i] | ||
| 7 | No linear OOA(4252, 431, F4, 2, 180) (dual of [(431, 2), 610, 181]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4252, 431, F4, 3, 180) (dual of [(431, 3), 1041, 181]-NRT-code) | [i] | ||
| 9 | No digital (72, 252, 431)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |