Information on Result #526545
There is no linear OA(36, 57, F3, 3) (dual of [57, 51, 4]-code or 57-cap in PG(5,3)), because doubling the cap would yield 114-cap in AG(6,3), but
- discarding factors / shortening the dual code would yield 113-cap in AG(6,3), 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 OOA(36, 57, F3, 2, 3) (dual of [(57, 2), 108, 4]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(36, 57, F3, 3, 3) (dual of [(57, 3), 165, 4]-NRT-code) | [i] | ||
| 3 | No linear OOA(36, 57, F3, 4, 3) (dual of [(57, 4), 222, 4]-NRT-code) | [i] | ||
| 4 | No linear OOA(36, 57, F3, 5, 3) (dual of [(57, 5), 279, 4]-NRT-code) | [i] | ||
| 5 | No digital (3, 6, 57)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(353, 59, F3, 36) (dual of [59, 6, 37]-code) | [i] | Construction Y1 (Bound) | |
| 7 | No linear OA(357, 63, F3, 39) (dual of [63, 6, 40]-code) | [i] | ||
| 8 | No linear OA(361, 67, F3, 42) (dual of [67, 6, 43]-code) | [i] | ||
| 9 | No linear OA(366, 72, F3, 45) (dual of [72, 6, 46]-code) | [i] | ||
| 10 | No linear OA(370, 76, F3, 48) (dual of [76, 6, 49]-code) | [i] | ||