Information on Result #546887
There is no linear OA(3217, 344, F3, 138) (dual of [344, 127, 139]-code), because residual code would yield OA(379, 205, S3, 46), but
- 4 times truncation [i] would yield OA(375, 201, S3, 42), but
- the linear programming bound shows that M ≥ 70 125936 773107 976834 379244 843784 716640 335910 577502 309916 609029 015855 123273 912868 189563 572000 000000 / 109 901819 499502 271926 662008 620205 982068 132289 165070 372767 942049 > 375 [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(3218, 345, F3, 139) (dual of [345, 127, 140]-code) | [i] | Truncation | |
| 2 | No linear OA(3219, 346, F3, 140) (dual of [346, 127, 141]-code) | [i] | ||
| 3 | No linear OOA(3218, 344, F3, 2, 139) (dual of [(344, 2), 470, 140]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3219, 344, F3, 2, 140) (dual of [(344, 2), 469, 141]-NRT-code) | [i] | ||
| 5 | No linear OOA(3217, 344, F3, 2, 138) (dual of [(344, 2), 471, 139]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3217, 344, F3, 3, 138) (dual of [(344, 3), 815, 139]-NRT-code) | [i] | ||
| 7 | No linear OOA(3217, 344, F3, 4, 138) (dual of [(344, 4), 1159, 139]-NRT-code) | [i] | ||
| 8 | No linear OOA(3217, 344, F3, 5, 138) (dual of [(344, 5), 1503, 139]-NRT-code) | [i] | ||
| 9 | No digital (79, 217, 344)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |