Information on Result #547783
There is no linear OA(3135, 164, F3, 87) (dual of [164, 29, 88]-code), because construction Y1 would yield
- OA(3134, 150, S3, 87), but
- the linear programming bound shows that M ≥ 1998 191076 053927 805178 143382 564872 985089 052204 487349 698881 740338 723055 870219 / 227413 116931 > 3134 [i]
- OA(329, 164, S3, 14), but
- discarding factors would yield OA(329, 163, S3, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 69 685080 318363 > 329 [i]
- discarding factors would yield OA(329, 163, S3, 14), but
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(3136, 165, F3, 88) (dual of [165, 29, 89]-code) | [i] | Truncation | |
| 2 | No linear OOA(3136, 164, F3, 2, 88) (dual of [(164, 2), 192, 89]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(3135, 164, F3, 2, 87) (dual of [(164, 2), 193, 88]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(3135, 164, F3, 3, 87) (dual of [(164, 3), 357, 88]-NRT-code) | [i] | ||
| 5 | No linear OOA(3135, 164, F3, 4, 87) (dual of [(164, 4), 521, 88]-NRT-code) | [i] | ||
| 6 | No linear OOA(3135, 164, F3, 5, 87) (dual of [(164, 5), 685, 88]-NRT-code) | [i] | ||
| 7 | No digital (48, 135, 164)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 8 | No linear OA(3136, 198, F3, 87) (dual of [198, 62, 88]-code) | [i] | Construction Y1 (Bound) | |