Information on Result #548007
There is no linear OA(8147, 164, F8, 128) (dual of [164, 17, 129]-code), because construction Y1 would yield
- linear OA(8146, 152, F8, 128) (dual of [152, 6, 129]-code), but
- construction Y1 [i] would yield
- linear OA(8145, 148, F8, 128) (dual of [148, 3, 129]-code), but
- OA(86, 152, S8, 4), but
- discarding factors would yield OA(86, 104, S8, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 263173 > 86 [i]
- discarding factors would yield OA(86, 104, S8, 4), but
- construction Y1 [i] would yield
- OA(817, 164, S8, 12), but
- discarding factors would yield OA(817, 158, S8, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 2322 300560 650316 > 817 [i]
- discarding factors would yield OA(817, 158, S8, 12), 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 OA(8148, 165, F8, 129) (dual of [165, 17, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(8149, 166, F8, 130) (dual of [166, 17, 131]-code) | [i] | ||
| 3 | No linear OA(8150, 167, F8, 131) (dual of [167, 17, 132]-code) | [i] | ||
| 4 | No linear OA(8151, 168, F8, 132) (dual of [168, 17, 133]-code) | [i] | ||
| 5 | No linear OA(8152, 169, F8, 133) (dual of [169, 17, 134]-code) | [i] | ||
| 6 | No linear OA(8153, 170, F8, 134) (dual of [170, 17, 135]-code) | [i] | ||
| 7 | No linear OA(8154, 171, F8, 135) (dual of [171, 17, 136]-code) | [i] | ||
| 8 | No linear OOA(8148, 164, F8, 2, 129) (dual of [(164, 2), 180, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8149, 164, F8, 2, 130) (dual of [(164, 2), 179, 131]-NRT-code) | [i] | ||
| 10 | No linear OOA(8150, 164, F8, 2, 131) (dual of [(164, 2), 178, 132]-NRT-code) | [i] | ||
| 11 | No linear OOA(8151, 164, F8, 2, 132) (dual of [(164, 2), 177, 133]-NRT-code) | [i] | ||
| 12 | No linear OOA(8152, 164, F8, 2, 133) (dual of [(164, 2), 176, 134]-NRT-code) | [i] | ||
| 13 | No linear OOA(8153, 164, F8, 2, 134) (dual of [(164, 2), 175, 135]-NRT-code) | [i] | ||
| 14 | No linear OOA(8154, 164, F8, 2, 135) (dual of [(164, 2), 174, 136]-NRT-code) | [i] | ||
| 15 | No linear OOA(8147, 164, F8, 2, 128) (dual of [(164, 2), 181, 129]-NRT-code) | [i] | Depth Reduction | |
| 16 | No linear OOA(8147, 164, F8, 3, 128) (dual of [(164, 3), 345, 129]-NRT-code) | [i] | ||
| 17 | No digital (19, 147, 164)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |