Information on Result #548015
There is no linear OA(928, 58, F9, 25) (dual of [58, 30, 26]-code), because construction Y1 would yield
- OA(927, 31, S9, 25), but
- the linear programming bound shows that M ≥ 25644 034018 340666 323462 064529 / 377 > 927 [i]
- linear OA(930, 58, F9, 27) (dual of [58, 28, 28]-code), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- residual code [i] would yield OA(93, 11, S9, 3), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), 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(929, 59, F9, 26) (dual of [59, 30, 27]-code) | [i] | Truncation | |
| 2 | No linear OOA(929, 58, F9, 2, 26) (dual of [(58, 2), 87, 27]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(928, 58, F9, 2, 25) (dual of [(58, 2), 88, 26]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(928, 58, F9, 3, 25) (dual of [(58, 3), 146, 26]-NRT-code) | [i] | ||
| 5 | No digital (3, 28, 58)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(938, 66, F9, 34) (dual of [66, 28, 35]-code) | [i] | Construction Y1 (Bound) | |