Information on Result #548583
There is no linear OA(332, 45, F3, 21) (dual of [45, 13, 22]-code), because construction Y1 would yield
- linear OA(331, 37, F3, 21) (dual of [37, 6, 22]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- OA(313, 45, S3, 8), but
- discarding factors would yield OA(313, 41, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 708963 > 313 [i]
- discarding factors would yield OA(313, 41, S3, 8), 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(333, 46, F3, 22) (dual of [46, 13, 23]-code) | [i] | Truncation | |
| 2 | No linear OOA(333, 45, F3, 2, 22) (dual of [(45, 2), 57, 23]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(334, 45, F3, 2, 23) (dual of [(45, 2), 56, 24]-NRT-code) | [i] | ||
| 4 | No linear OOA(332, 45, F3, 2, 21) (dual of [(45, 2), 58, 22]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(332, 45, F3, 3, 21) (dual of [(45, 3), 103, 22]-NRT-code) | [i] | ||
| 6 | No linear OOA(332, 45, F3, 4, 21) (dual of [(45, 4), 148, 22]-NRT-code) | [i] | ||
| 7 | No linear OOA(332, 45, F3, 5, 21) (dual of [(45, 5), 193, 22]-NRT-code) | [i] | ||
| 8 | No digital (11, 32, 45)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 9 | No linear OA(333, 67, F3, 21) (dual of [67, 34, 22]-code) | [i] | Construction Y1 (Bound) | |