Information on Result #547736
There is no linear OA(321, 26, F3, 15) (dual of [26, 5, 16]-code), because construction Y1 would yield
- OA(320, 23, S3, 15), but
- the (dual) Plotkin bound shows that M ≥ 31381 059609 / 8 > 320 [i]
- linear OA(35, 26, F3, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,3)), but
- discarding factors / shortening the dual code would yield linear OA(35, 21, F3, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), 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(322, 27, F3, 16) (dual of [27, 5, 17]-code) | [i] | Truncation | |
| 2 | No linear OOA(321, 26, F3, 2, 15) (dual of [(26, 2), 31, 16]-NRT-code) | [i] | Depth Reduction | |
| 3 | No linear OOA(321, 26, F3, 3, 15) (dual of [(26, 3), 57, 16]-NRT-code) | [i] | ||
| 4 | No linear OOA(321, 26, F3, 4, 15) (dual of [(26, 4), 83, 16]-NRT-code) | [i] | ||
| 5 | No linear OOA(321, 26, F3, 5, 15) (dual of [(26, 5), 109, 16]-NRT-code) | [i] | ||
| 6 | No digital (6, 21, 26)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 7 | No linear OA(322, 34, F3, 15) (dual of [34, 12, 16]-code) | [i] | Construction Y1 (Bound) | |