Information on Result #546724
There is no linear OA(3176, 285, F3, 111) (dual of [285, 109, 112]-code), because residual code would yield OA(365, 173, S3, 37), but
- the linear programming bound shows that M ≥ 1453 422171 176186 751809 127162 493016 603191 312063 081521 426831 231947 464953 600000 / 134 521851 774696 965469 262634 050207 937701 652681 > 365 [i]
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 OA(3177, 286, F3, 112) (dual of [286, 109, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3178, 287, F3, 113) (dual of [287, 109, 114]-code) | [i] | ||
| 3 | No linear OOA(3177, 285, F3, 2, 112) (dual of [(285, 2), 393, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3178, 285, F3, 2, 113) (dual of [(285, 2), 392, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3176, 285, F3, 2, 111) (dual of [(285, 2), 394, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3176, 285, F3, 3, 111) (dual of [(285, 3), 679, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3176, 285, F3, 4, 111) (dual of [(285, 4), 964, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3176, 285, F3, 5, 111) (dual of [(285, 5), 1249, 112]-NRT-code) | [i] | ||
| 9 | No digital (65, 176, 285)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |