Information on Result #547357
There is no linear OA(4220, 242, F4, 164) (dual of [242, 22, 165]-code), because residual code would yield OA(456, 77, S4, 41), but
- the linear programming bound shows that M ≥ 2852 409624 643877 869804 773184 242737 249513 373696 / 530979 549763 > 456 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4221, 243, F4, 165) (dual of [243, 22, 166]-code) | [i] | Truncation | |
| 2 | No linear OA(4222, 244, F4, 166) (dual of [244, 22, 167]-code) | [i] | ||
| 3 | No linear OA(4223, 245, F4, 167) (dual of [245, 22, 168]-code) | [i] | ||
| 4 | No linear OOA(4221, 242, F4, 2, 165) (dual of [(242, 2), 263, 166]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4222, 242, F4, 2, 166) (dual of [(242, 2), 262, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(4223, 242, F4, 2, 167) (dual of [(242, 2), 261, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(4220, 242, F4, 2, 164) (dual of [(242, 2), 264, 165]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4220, 242, F4, 3, 164) (dual of [(242, 3), 506, 165]-NRT-code) | [i] | ||
| 9 | No digital (56, 220, 242)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |