Information on Result #548009
There is no linear OA(8156, 173, F8, 136) (dual of [173, 17, 137]-code), because construction Y1 would yield
- linear OA(8155, 161, F8, 136) (dual of [161, 6, 137]-code), but
- construction Y1 [i] 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
- construction Y1 [i] would yield
- OA(817, 173, 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(8157, 174, F8, 137) (dual of [174, 17, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(8158, 175, F8, 138) (dual of [175, 17, 139]-code) | [i] | ||
| 3 | No linear OA(8159, 176, F8, 139) (dual of [176, 17, 140]-code) | [i] | ||
| 4 | No linear OA(8160, 177, F8, 140) (dual of [177, 17, 141]-code) | [i] | ||
| 5 | No linear OA(8161, 178, F8, 141) (dual of [178, 17, 142]-code) | [i] | ||
| 6 | No linear OA(8162, 179, F8, 142) (dual of [179, 17, 143]-code) | [i] | ||
| 7 | No linear OA(8163, 180, F8, 143) (dual of [180, 17, 144]-code) | [i] | ||
| 8 | No linear OOA(8157, 173, F8, 2, 137) (dual of [(173, 2), 189, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8158, 173, F8, 2, 138) (dual of [(173, 2), 188, 139]-NRT-code) | [i] | ||
| 10 | No linear OOA(8159, 173, F8, 2, 139) (dual of [(173, 2), 187, 140]-NRT-code) | [i] | ||
| 11 | No linear OOA(8160, 173, F8, 2, 140) (dual of [(173, 2), 186, 141]-NRT-code) | [i] | ||
| 12 | No linear OOA(8161, 173, F8, 2, 141) (dual of [(173, 2), 185, 142]-NRT-code) | [i] | ||
| 13 | No linear OOA(8162, 173, F8, 2, 142) (dual of [(173, 2), 184, 143]-NRT-code) | [i] | ||
| 14 | No linear OOA(8163, 173, F8, 2, 143) (dual of [(173, 2), 183, 144]-NRT-code) | [i] | ||
| 15 | No linear OOA(8156, 173, F8, 2, 136) (dual of [(173, 2), 190, 137]-NRT-code) | [i] | Depth Reduction | |
| 16 | No linear OOA(8156, 173, F8, 3, 136) (dual of [(173, 3), 363, 137]-NRT-code) | [i] | ||
| 17 | No digital (20, 156, 173)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |