Information on Result #548579
There is no linear OA(323, 37, F3, 15) (dual of [37, 14, 16]-code), because construction Y1 would yield
- linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- linear OA(314, 37, F3, 9) (dual of [37, 23, 10]-code), but
- discarding factors / shortening the dual code would yield linear OA(314, 31, F3, 9) (dual of [31, 17, 10]-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(324, 38, F3, 16) (dual of [38, 14, 17]-code) | [i] | Truncation | |
| 2 | No linear OOA(324, 37, F3, 2, 16) (dual of [(37, 2), 50, 17]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(323, 37, F3, 2, 15) (dual of [(37, 2), 51, 16]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(323, 37, F3, 3, 15) (dual of [(37, 3), 88, 16]-NRT-code) | [i] | ||
| 5 | No linear OOA(323, 37, F3, 4, 15) (dual of [(37, 4), 125, 16]-NRT-code) | [i] | ||
| 6 | No linear OOA(323, 37, F3, 5, 15) (dual of [(37, 5), 162, 16]-NRT-code) | [i] | ||
| 7 | No digital (8, 23, 37)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 8 | No linear OA(324, 62, F3, 15) (dual of [62, 38, 16]-code) | [i] | Construction Y1 (Bound) | |
| 9 | No linear OA(319, 42, F3, 12) (dual of [42, 23, 13]-code) | [i] | ||