Information on Result #546706
There is no linear OA(3166, 212, F3, 108) (dual of [212, 46, 109]-code), because residual code would yield OA(358, 103, S3, 36), but
- the linear programming bound shows that M ≥ 10156 978991 001331 162956 096121 250957 052835 549981 966253 500685 908151 917037 752938 447734 452120 610565 247729 783614 274683 456708 473505 647028 881750 777661 / 2 150100 658067 421186 781820 643305 293437 760326 405421 945649 628834 598190 514781 560026 381075 663150 228993 281922 344503 352960 > 358 [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(3167, 213, F3, 109) (dual of [213, 46, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3168, 214, F3, 110) (dual of [214, 46, 111]-code) | [i] | ||
| 3 | No linear OOA(3167, 212, F3, 2, 109) (dual of [(212, 2), 257, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3168, 212, F3, 2, 110) (dual of [(212, 2), 256, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3166, 212, F3, 2, 108) (dual of [(212, 2), 258, 109]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3166, 212, F3, 3, 108) (dual of [(212, 3), 470, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(3166, 212, F3, 4, 108) (dual of [(212, 4), 682, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(3166, 212, F3, 5, 108) (dual of [(212, 5), 894, 109]-NRT-code) | [i] | ||
| 9 | No digital (58, 166, 212)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |