Information on Result #547173
There is no linear OA(4165, 251, F4, 120) (dual of [251, 86, 121]-code), because residual code would yield OA(445, 130, S4, 30), but
- the linear programming bound shows that M ≥ 18361 010361 194259 039988 478818 345052 021927 082904 773350 916096 / 14 690690 202506 322671 084018 635999 > 445 [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(4166, 252, F4, 121) (dual of [252, 86, 122]-code) | [i] | Truncation | |
| 2 | No linear OA(4167, 253, F4, 122) (dual of [253, 86, 123]-code) | [i] | ||
| 3 | No linear OA(4168, 254, F4, 123) (dual of [254, 86, 124]-code) | [i] | ||
| 4 | No linear OOA(4166, 251, F4, 2, 121) (dual of [(251, 2), 336, 122]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4167, 251, F4, 2, 122) (dual of [(251, 2), 335, 123]-NRT-code) | [i] | ||
| 6 | No linear OOA(4168, 251, F4, 2, 123) (dual of [(251, 2), 334, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(4165, 251, F4, 2, 120) (dual of [(251, 2), 337, 121]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4165, 251, F4, 3, 120) (dual of [(251, 3), 588, 121]-NRT-code) | [i] | ||
| 9 | No digital (45, 165, 251)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |