Information on Result #546862
There is no linear OA(3213, 340, F3, 135) (dual of [340, 127, 136]-code), because residual code would yield OA(378, 204, S3, 45), but
- 3 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(3214, 341, F3, 136) (dual of [341, 127, 137]-code) | [i] | Truncation | |
| 2 | No linear OA(3215, 342, F3, 137) (dual of [342, 127, 138]-code) | [i] | ||
| 3 | No linear OOA(3214, 340, F3, 2, 136) (dual of [(340, 2), 466, 137]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3215, 340, F3, 2, 137) (dual of [(340, 2), 465, 138]-NRT-code) | [i] | ||
| 5 | No linear OOA(3213, 340, F3, 2, 135) (dual of [(340, 2), 467, 136]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3213, 340, F3, 3, 135) (dual of [(340, 3), 807, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(3213, 340, F3, 4, 135) (dual of [(340, 4), 1147, 136]-NRT-code) | [i] | ||
| 8 | No linear OOA(3213, 340, F3, 5, 135) (dual of [(340, 5), 1487, 136]-NRT-code) | [i] | ||
| 9 | No digital (78, 213, 340)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |