Information on Result #556131
There is no linear OOA(3117, 117, F3, 2, 81) (dual of [(117, 2), 117, 82]-NRT-code), because 9 step m-reduction would yield linear OA(3108, 117, F3, 72) (dual of [117, 9, 73]-code), but
- construction Y1 [i] would yield
- linear OA(3107, 113, F3, 72) (dual of [113, 6, 73]-code), but
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- “vE1†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- OA(39, 117, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, S3, 4), but
- linear OA(3107, 113, F3, 72) (dual of [113, 6, 73]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(3117, 117, F3, 3, 81) (dual of [(117, 3), 234, 82]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3117, 117, F3, 4, 81) (dual of [(117, 4), 351, 82]-NRT-code) | [i] | ||
| 3 | No linear OOA(3117, 117, F3, 5, 81) (dual of [(117, 5), 468, 82]-NRT-code) | [i] | ||