Information on Result #547836
There is no linear OA(448, 57, F4, 36) (dual of [57, 9, 37]-code), because construction Y1 would yield
- linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- OA(49, 57, S4, 6), but
- discarding factors would yield OA(49, 40, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 273901 > 49 [i]
- discarding factors would yield OA(49, 40, S4, 6), 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 OOA(450, 57, F4, 2, 38) (dual of [(57, 2), 64, 39]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(451, 57, F4, 2, 39) (dual of [(57, 2), 63, 40]-NRT-code) | [i] | ||
| 3 | No linear OOA(448, 57, F4, 2, 36) (dual of [(57, 2), 66, 37]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(448, 57, F4, 3, 36) (dual of [(57, 3), 123, 37]-NRT-code) | [i] | ||
| 5 | No digital (12, 48, 57)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |