Information on Result #547900
There is no linear OA(4186, 218, F4, 139) (dual of [218, 32, 140]-code), because construction Y1 would yield
- linear OA(4185, 200, F4, 139) (dual of [200, 15, 140]-code), but
- construction Y1 [i] would yield
- linear OA(4184, 192, F4, 139) (dual of [192, 8, 140]-code), but
- construction Y1 [i] would yield
- linear OA(4183, 188, F4, 139) (dual of [188, 5, 140]-code), but
- OA(48, 192, 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
- construction Y1 [i] would yield
- OA(415, 200, 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(4184, 192, F4, 139) (dual of [192, 8, 140]-code), but
- construction Y1 [i] would yield
- OA(432, 218, S4, 18), but
- discarding factors would yield OA(432, 195, S4, 18), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 632959 071185 877328 > 432 [i]
- discarding factors would yield OA(432, 195, S4, 18), 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 OOA(4186, 218, F4, 2, 139) (dual of [(218, 2), 250, 140]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(4186, 218, F4, 3, 139) (dual of [(218, 3), 468, 140]-NRT-code) | [i] | ||
| 3 | No digital (47, 186, 218)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |