Information on Result #548595
There is no linear OA(3149, 166, F3, 99) (dual of [166, 17, 100]-code), because construction Y1 would yield
- linear OA(3148, 158, F3, 99) (dual of [158, 10, 100]-code), but
- residual code [i] would yield linear OA(349, 58, F3, 33) (dual of [58, 9, 34]-code), but
- residual code [i] would yield linear OA(316, 24, F3, 11) (dual of [24, 8, 12]-code), but
- residual code [i] would yield linear OA(349, 58, F3, 33) (dual of [58, 9, 34]-code), but
- OA(317, 166, S3, 8), but
- discarding factors would yield OA(317, 119, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 129 270891 > 317 [i]
- discarding factors would yield OA(317, 119, S3, 8), 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(3150, 167, F3, 100) (dual of [167, 17, 101]-code) | [i] | Truncation | |
| 2 | No linear OA(3151, 168, F3, 101) (dual of [168, 17, 102]-code) | [i] | ||
| 3 | No linear OOA(3150, 166, F3, 2, 100) (dual of [(166, 2), 182, 101]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3151, 166, F3, 2, 101) (dual of [(166, 2), 181, 102]-NRT-code) | [i] | ||
| 5 | No linear OOA(3149, 166, F3, 2, 99) (dual of [(166, 2), 183, 100]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3149, 166, F3, 3, 99) (dual of [(166, 3), 349, 100]-NRT-code) | [i] | ||
| 7 | No linear OOA(3149, 166, F3, 4, 99) (dual of [(166, 4), 515, 100]-NRT-code) | [i] | ||
| 8 | No linear OOA(3149, 166, F3, 5, 99) (dual of [(166, 5), 681, 100]-NRT-code) | [i] | ||
| 9 | No digital (50, 149, 166)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |