Information on Result #546680
There is no linear OA(3156, 194, F3, 102) (dual of [194, 38, 103]-code), because residual code would yield OA(354, 91, S3, 34), but
- the linear programming bound shows that M ≥ 474 977782 539634 784051 796341 060967 928894 025210 202817 107183 513784 170892 978866 150753 / 7 995136 378245 997436 849186 466159 148790 740510 898632 999345 > 354 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3157, 195, F3, 103) (dual of [195, 38, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3158, 196, F3, 104) (dual of [196, 38, 105]-code) | [i] | ||
| 3 | No linear OOA(3157, 194, F3, 2, 103) (dual of [(194, 2), 231, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3158, 194, F3, 2, 104) (dual of [(194, 2), 230, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3156, 194, F3, 2, 102) (dual of [(194, 2), 232, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3156, 194, F3, 3, 102) (dual of [(194, 3), 426, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3156, 194, F3, 4, 102) (dual of [(194, 4), 620, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3156, 194, F3, 5, 102) (dual of [(194, 5), 814, 103]-NRT-code) | [i] | ||
| 9 | No digital (54, 156, 194)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |