Information on Result #548010
There is no linear OA(8164, 170, F8, 144) (dual of [170, 6, 145]-code), because construction Y1 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
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(8165, 171, F8, 145) (dual of [171, 6, 146]-code) | [i] | Truncation | |
| 2 | No linear OA(8166, 172, F8, 146) (dual of [172, 6, 147]-code) | [i] | ||
| 3 | No linear OA(8167, 173, F8, 147) (dual of [173, 6, 148]-code) | [i] | ||
| 4 | No linear OA(8168, 174, F8, 148) (dual of [174, 6, 149]-code) | [i] | ||
| 5 | No linear OA(8169, 175, F8, 149) (dual of [175, 6, 150]-code) | [i] | ||
| 6 | No linear OA(8170, 176, F8, 150) (dual of [176, 6, 151]-code) | [i] | ||
| 7 | No linear OA(8171, 177, F8, 151) (dual of [177, 6, 152]-code) | [i] | ||
| 8 | No linear OOA(8165, 170, F8, 2, 145) (dual of [(170, 2), 175, 146]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8166, 170, F8, 2, 146) (dual of [(170, 2), 174, 147]-NRT-code) | [i] | ||
| 10 | No linear OOA(8167, 170, F8, 2, 147) (dual of [(170, 2), 173, 148]-NRT-code) | [i] | ||
| 11 | No linear OOA(8168, 170, F8, 2, 148) (dual of [(170, 2), 172, 149]-NRT-code) | [i] | ||
| 12 | No linear OOA(8169, 170, F8, 2, 149) (dual of [(170, 2), 171, 150]-NRT-code) | [i] | ||
| 13 | No linear OOA(8170, 170, F8, 2, 150) (dual of [(170, 2), 170, 151]-NRT-code) | [i] | ||
| 14 | No linear OOA(8171, 170, F8, 2, 151) (dual of [(170, 2), 169, 152]-NRT-code) | [i] | ||
| 15 | No linear OOA(8172, 170, F8, 2, 152) (dual of [(170, 2), 168, 153]-NRT-code) | [i] | ||
| 16 | No linear OOA(8173, 170, F8, 2, 153) (dual of [(170, 2), 167, 154]-NRT-code) | [i] | ||
| 17 | No linear OOA(8164, 170, F8, 2, 144) (dual of [(170, 2), 176, 145]-NRT-code) | [i] | Depth Reduction | |
| 18 | No linear OOA(8164, 170, F8, 3, 144) (dual of [(170, 3), 346, 145]-NRT-code) | [i] | ||
| 19 | No digital (20, 164, 170)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 20 | No linear OA(8165, 182, F8, 144) (dual of [182, 17, 145]-code) | [i] | Construction Y1 (Bound) | |