Information on Result #546886
There is no linear OA(3216, 334, F3, 138) (dual of [334, 118, 139]-code), because residual code would yield OA(378, 195, S3, 46), but
- 4 times truncation [i] would yield OA(374, 191, S3, 42), but
- the linear programming bound shows that M ≥ 7425 373872 326041 246958 413277 162396 664697 868093 270451 580073 051722 485491 109207 030427 537458 984375 / 32911 891840 780579 755648 777011 603243 208306 897748 202179 983781 > 374 [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(3217, 335, F3, 139) (dual of [335, 118, 140]-code) | [i] | Truncation | |
| 2 | No linear OA(3218, 336, F3, 140) (dual of [336, 118, 141]-code) | [i] | ||
| 3 | No linear OOA(3217, 334, F3, 2, 139) (dual of [(334, 2), 451, 140]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3218, 334, F3, 2, 140) (dual of [(334, 2), 450, 141]-NRT-code) | [i] | ||
| 5 | No linear OOA(3216, 334, F3, 2, 138) (dual of [(334, 2), 452, 139]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3216, 334, F3, 3, 138) (dual of [(334, 3), 786, 139]-NRT-code) | [i] | ||
| 7 | No linear OOA(3216, 334, F3, 4, 138) (dual of [(334, 4), 1120, 139]-NRT-code) | [i] | ||
| 8 | No linear OOA(3216, 334, F3, 5, 138) (dual of [(334, 5), 1454, 139]-NRT-code) | [i] | ||
| 9 | No digital (78, 216, 334)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |