Information on Result #548011
There is no linear OA(8165, 182, F8, 144) (dual of [182, 17, 145]-code), because construction Y1 would yield
- linear OA(8164, 170, F8, 144) (dual of [170, 6, 145]-code), but
- construction Y1 [i] would yield
- linear OA(8163, 166, F8, 144) (dual of [166, 3, 145]-code), but
- OA(86, 170, 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, 182, 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(8166, 183, F8, 145) (dual of [183, 17, 146]-code) | [i] | Truncation | |
| 2 | No linear OA(8167, 184, F8, 146) (dual of [184, 17, 147]-code) | [i] | ||
| 3 | No linear OA(8168, 185, F8, 147) (dual of [185, 17, 148]-code) | [i] | ||
| 4 | No linear OA(8169, 186, F8, 148) (dual of [186, 17, 149]-code) | [i] | ||
| 5 | No linear OA(8170, 187, F8, 149) (dual of [187, 17, 150]-code) | [i] | ||
| 6 | No linear OA(8171, 188, F8, 150) (dual of [188, 17, 151]-code) | [i] | ||
| 7 | No linear OA(8172, 189, F8, 151) (dual of [189, 17, 152]-code) | [i] | ||
| 8 | No linear OOA(8166, 182, F8, 2, 145) (dual of [(182, 2), 198, 146]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8167, 182, F8, 2, 146) (dual of [(182, 2), 197, 147]-NRT-code) | [i] | ||
| 10 | No linear OOA(8168, 182, F8, 2, 147) (dual of [(182, 2), 196, 148]-NRT-code) | [i] | ||
| 11 | No linear OOA(8169, 182, F8, 2, 148) (dual of [(182, 2), 195, 149]-NRT-code) | [i] | ||
| 12 | No linear OOA(8170, 182, F8, 2, 149) (dual of [(182, 2), 194, 150]-NRT-code) | [i] | ||
| 13 | No linear OOA(8171, 182, F8, 2, 150) (dual of [(182, 2), 193, 151]-NRT-code) | [i] | ||
| 14 | No linear OOA(8172, 182, F8, 2, 151) (dual of [(182, 2), 192, 152]-NRT-code) | [i] | ||
| 15 | No linear OOA(8165, 182, F8, 2, 144) (dual of [(182, 2), 199, 145]-NRT-code) | [i] | Depth Reduction | |
| 16 | No linear OOA(8165, 182, F8, 3, 144) (dual of [(182, 3), 381, 145]-NRT-code) | [i] | ||
| 17 | No digital (21, 165, 182)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |