Information on Result #547460
There is no linear OA(4251, 410, F4, 180) (dual of [410, 159, 181]-code), because residual code would yield OA(471, 229, S4, 45), but
- the linear programming bound shows that M ≥ 877 912702 924905 625680 913013 034326 550228 995916 587809 875578 704494 502776 185113 709858 393246 285168 640000 / 155 079140 374101 434134 168939 696571 367080 998053 409783 569671 > 471 [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(4252, 411, F4, 181) (dual of [411, 159, 182]-code) | [i] | Truncation | |
| 2 | No linear OA(4253, 412, F4, 182) (dual of [412, 159, 183]-code) | [i] | ||
| 3 | No linear OA(4254, 413, F4, 183) (dual of [413, 159, 184]-code) | [i] | ||
| 4 | No linear OOA(4252, 410, F4, 2, 181) (dual of [(410, 2), 568, 182]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4253, 410, F4, 2, 182) (dual of [(410, 2), 567, 183]-NRT-code) | [i] | ||
| 6 | No linear OOA(4254, 410, F4, 2, 183) (dual of [(410, 2), 566, 184]-NRT-code) | [i] | ||
| 7 | No linear OOA(4251, 410, F4, 2, 180) (dual of [(410, 2), 569, 181]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4251, 410, F4, 3, 180) (dual of [(410, 3), 979, 181]-NRT-code) | [i] | ||
| 9 | No digital (71, 251, 410)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |