Information on Result #547881
There is no linear OA(4151, 185, F4, 112) (dual of [185, 34, 113]-code), because construction Y1 would yield
- linear OA(4150, 165, F4, 112) (dual of [165, 15, 113]-code), but
- construction Y1 [i] would yield
- linear OA(4149, 157, F4, 112) (dual of [157, 8, 113]-code), but
- construction Y1 [i] would yield
- linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- OA(48, 157, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 4), but
- linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- construction Y1 [i] would yield
- OA(415, 165, S4, 8), but
- discarding factors would yield OA(415, 135, S4, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1082 768311 > 415 [i]
- discarding factors would yield OA(415, 135, S4, 8), but
- linear OA(4149, 157, F4, 112) (dual of [157, 8, 113]-code), but
- construction Y1 [i] would yield
- OA(434, 185, S4, 20), but
- discarding factors would yield OA(434, 173, S4, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 305 996090 287239 486286 > 434 [i]
- discarding factors would yield OA(434, 173, S4, 20), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4152, 186, F4, 113) (dual of [186, 34, 114]-code) | [i] | Truncation | |
| 2 | No linear OA(4153, 187, F4, 114) (dual of [187, 34, 115]-code) | [i] | ||
| 3 | No linear OA(4154, 188, F4, 115) (dual of [188, 34, 116]-code) | [i] | ||
| 4 | No linear OOA(4152, 185, F4, 2, 113) (dual of [(185, 2), 218, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4153, 185, F4, 2, 114) (dual of [(185, 2), 217, 115]-NRT-code) | [i] | ||
| 6 | No linear OOA(4154, 185, F4, 2, 115) (dual of [(185, 2), 216, 116]-NRT-code) | [i] | ||
| 7 | No linear OOA(4151, 185, F4, 2, 112) (dual of [(185, 2), 219, 113]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4151, 185, F4, 3, 112) (dual of [(185, 3), 404, 113]-NRT-code) | [i] | ||
| 9 | No digital (39, 151, 185)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |