Information on Result #547369
There is no linear OA(4232, 443, F4, 164) (dual of [443, 211, 165]-code), because residual code would yield OA(468, 278, S4, 41), but
- the linear programming bound shows that M ≥ 9751 854148 120896 570793 936092 472808 488071 901083 469159 873923 045115 979366 400000 000000 000000 / 106042 296287 604630 552636 245594 756356 027986 690833 > 468 [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(4233, 444, F4, 165) (dual of [444, 211, 166]-code) | [i] | Truncation | |
| 2 | No linear OA(4234, 445, F4, 166) (dual of [445, 211, 167]-code) | [i] | ||
| 3 | No linear OA(4235, 446, F4, 167) (dual of [446, 211, 168]-code) | [i] | ||
| 4 | No linear OOA(4233, 443, F4, 2, 165) (dual of [(443, 2), 653, 166]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4234, 443, F4, 2, 166) (dual of [(443, 2), 652, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(4235, 443, F4, 2, 167) (dual of [(443, 2), 651, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(4232, 443, F4, 2, 164) (dual of [(443, 2), 654, 165]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4232, 443, F4, 3, 164) (dual of [(443, 3), 1097, 165]-NRT-code) | [i] | ||
| 9 | No digital (68, 232, 443)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |