Information on Result #548017
There is no linear OA(931, 85, F9, 27) (dual of [85, 54, 28]-code), because construction Y1 would yield
- linear OA(930, 37, F9, 27) (dual of [37, 7, 28]-code), but
- construction Y1 [i] would yield
- OA(929, 31, S9, 27), but
- the (dual) Plotkin bound shows that M ≥ 42391 158275 216203 514294 433201 / 7 > 929 [i]
- OA(97, 37, S9, 6), but
- the linear programming bound shows that M ≥ 8306 954271 / 1613 > 97 [i]
- OA(929, 31, S9, 27), but
- construction Y1 [i] would yield
- OA(954, 85, S9, 48), but
- discarding factors would yield OA(954, 83, S9, 48), but
- the linear programming bound shows that M ≥ 10132 927410 689078 360872 417149 617665 028299 664062 593121 142935 280521 657389 / 2 927120 765949 062837 > 954 [i]
- discarding factors would yield OA(954, 83, S9, 48), 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(932, 86, F9, 28) (dual of [86, 54, 29]-code) | [i] | Truncation | |
| 2 | No linear OA(933, 87, F9, 29) (dual of [87, 54, 30]-code) | [i] | ||
| 3 | No linear OOA(932, 85, F9, 2, 28) (dual of [(85, 2), 138, 29]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(933, 85, F9, 2, 29) (dual of [(85, 2), 137, 30]-NRT-code) | [i] | ||
| 5 | No linear OOA(934, 85, F9, 2, 30) (dual of [(85, 2), 136, 31]-NRT-code) | [i] | ||
| 6 | No linear OOA(931, 85, F9, 2, 27) (dual of [(85, 2), 139, 28]-NRT-code) | [i] | Depth Reduction | |
| 7 | No linear OOA(931, 85, F9, 3, 27) (dual of [(85, 3), 224, 28]-NRT-code) | [i] | ||
| 8 | No digital (4, 31, 85)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |