Information on Result #546888
There is no linear OA(3218, 356, F3, 138) (dual of [356, 138, 139]-code), because residual code would yield OA(380, 217, S3, 46), but
- 4 times truncation [i] would yield OA(376, 213, S3, 42), but
- the linear programming bound shows that M ≥ 24139 354386 854363 147378 476124 618112 504428 827791 667688 382538 767752 602863 057296 834401 801307 804700 / 12846 980782 406505 841743 696059 469546 157683 736221 588601 551817 > 376 [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(3219, 357, F3, 139) (dual of [357, 138, 140]-code) | [i] | Truncation | |
| 2 | No linear OA(3220, 358, F3, 140) (dual of [358, 138, 141]-code) | [i] | ||
| 3 | No linear OOA(3219, 356, F3, 2, 139) (dual of [(356, 2), 493, 140]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3220, 356, F3, 2, 140) (dual of [(356, 2), 492, 141]-NRT-code) | [i] | ||
| 5 | No linear OOA(3218, 356, F3, 2, 138) (dual of [(356, 2), 494, 139]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3218, 356, F3, 3, 138) (dual of [(356, 3), 850, 139]-NRT-code) | [i] | ||
| 7 | No linear OOA(3218, 356, F3, 4, 138) (dual of [(356, 4), 1206, 139]-NRT-code) | [i] | ||
| 8 | No linear OOA(3218, 356, F3, 5, 138) (dual of [(356, 5), 1562, 139]-NRT-code) | [i] | ||
| 9 | No digital (80, 218, 356)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |