Information on Result #547227
There is no linear OA(4192, 374, F4, 136) (dual of [374, 182, 137]-code), because residual code would yield OA(456, 237, S4, 34), but
- the linear programming bound shows that M ≥ 227 819482 170490 726334 286831 192651 607943 130369 749048 513507 843112 960000 000000 / 43777 691396 586787 052635 611770 906797 710989 > 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4193, 375, F4, 137) (dual of [375, 182, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(4194, 376, F4, 138) (dual of [376, 182, 139]-code) | [i] | ||
| 3 | No linear OA(4195, 377, F4, 139) (dual of [377, 182, 140]-code) | [i] | ||
| 4 | No linear OOA(4193, 374, F4, 2, 137) (dual of [(374, 2), 555, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4194, 374, F4, 2, 138) (dual of [(374, 2), 554, 139]-NRT-code) | [i] | ||
| 6 | No linear OOA(4195, 374, F4, 2, 139) (dual of [(374, 2), 553, 140]-NRT-code) | [i] | ||
| 7 | No linear OOA(4192, 374, F4, 2, 136) (dual of [(374, 2), 556, 137]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4192, 374, F4, 3, 136) (dual of [(374, 3), 930, 137]-NRT-code) | [i] | ||
| 9 | No digital (56, 192, 374)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |