Information on Result #548008
There is no linear OA(8155, 161, F8, 136) (dual of [161, 6, 137]-code), because construction Y1 would yield
- linear OA(8154, 157, F8, 136) (dual of [157, 3, 137]-code), but
- OA(86, 161, 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(8156, 162, F8, 137) (dual of [162, 6, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(8157, 163, F8, 138) (dual of [163, 6, 139]-code) | [i] | ||
| 3 | No linear OA(8158, 164, F8, 139) (dual of [164, 6, 140]-code) | [i] | ||
| 4 | No linear OA(8159, 165, F8, 140) (dual of [165, 6, 141]-code) | [i] | ||
| 5 | No linear OA(8160, 166, F8, 141) (dual of [166, 6, 142]-code) | [i] | ||
| 6 | No linear OA(8161, 167, F8, 142) (dual of [167, 6, 143]-code) | [i] | ||
| 7 | No linear OA(8162, 168, F8, 143) (dual of [168, 6, 144]-code) | [i] | ||
| 8 | No linear OOA(8156, 161, F8, 2, 137) (dual of [(161, 2), 166, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8157, 161, F8, 2, 138) (dual of [(161, 2), 165, 139]-NRT-code) | [i] | ||
| 10 | No linear OOA(8158, 161, F8, 2, 139) (dual of [(161, 2), 164, 140]-NRT-code) | [i] | ||
| 11 | No linear OOA(8159, 161, F8, 2, 140) (dual of [(161, 2), 163, 141]-NRT-code) | [i] | ||
| 12 | No linear OOA(8160, 161, F8, 2, 141) (dual of [(161, 2), 162, 142]-NRT-code) | [i] | ||
| 13 | No linear OOA(8161, 161, F8, 2, 142) (dual of [(161, 2), 161, 143]-NRT-code) | [i] | ||
| 14 | No linear OOA(8162, 161, F8, 2, 143) (dual of [(161, 2), 160, 144]-NRT-code) | [i] | ||
| 15 | No linear OOA(8163, 161, F8, 2, 144) (dual of [(161, 2), 159, 145]-NRT-code) | [i] | ||
| 16 | No linear OOA(8164, 161, F8, 2, 145) (dual of [(161, 2), 158, 146]-NRT-code) | [i] | ||
| 17 | No linear OOA(8165, 161, F8, 2, 146) (dual of [(161, 2), 157, 147]-NRT-code) | [i] | ||
| 18 | No linear OOA(8166, 161, F8, 2, 147) (dual of [(161, 2), 156, 148]-NRT-code) | [i] | ||
| 19 | No linear OOA(8167, 161, F8, 2, 148) (dual of [(161, 2), 155, 149]-NRT-code) | [i] | ||
| 20 | No linear OOA(8168, 161, F8, 2, 149) (dual of [(161, 2), 154, 150]-NRT-code) | [i] | ||
| 21 | No linear OOA(8169, 161, F8, 2, 150) (dual of [(161, 2), 153, 151]-NRT-code) | [i] | ||
| 22 | No linear OOA(8170, 161, F8, 2, 151) (dual of [(161, 2), 152, 152]-NRT-code) | [i] | ||
| 23 | No linear OOA(8171, 161, F8, 2, 152) (dual of [(161, 2), 151, 153]-NRT-code) | [i] | ||
| 24 | No linear OOA(8172, 161, F8, 2, 153) (dual of [(161, 2), 150, 154]-NRT-code) | [i] | ||
| 25 | No linear OOA(8173, 161, F8, 2, 154) (dual of [(161, 2), 149, 155]-NRT-code) | [i] | ||
| 26 | No linear OOA(8155, 161, F8, 2, 136) (dual of [(161, 2), 167, 137]-NRT-code) | [i] | Depth Reduction | |
| 27 | No linear OOA(8155, 161, F8, 3, 136) (dual of [(161, 3), 328, 137]-NRT-code) | [i] | ||
| 28 | No digital (19, 155, 161)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 29 | No linear OA(8156, 173, F8, 136) (dual of [173, 17, 137]-code) | [i] | Construction Y1 (Bound) | |