Information on Result #560152
There is no linear OOA(4180, 199, F4, 2, 135) (dual of [(199, 2), 218, 136]-NRT-code), because 3 step m-reduction would yield linear OA(4177, 199, F4, 132) (dual of [199, 22, 133]-code), but
- construction Y1 [i] would yield
- linear OA(4176, 187, F4, 132) (dual of [187, 11, 133]-code), but
- construction Y1 [i] would yield
- linear OA(4175, 181, F4, 132) (dual of [181, 6, 133]-code), but
- construction Y1 [i] would yield
- linear OA(4174, 178, F4, 132) (dual of [178, 4, 133]-code), but
- linear OA(46, 181, F4, 3) (dual of [181, 175, 4]-code or 181-cap in PG(5,4)), but
- construction Y1 [i] would yield
- OA(411, 187, S4, 6), but
- discarding factors would yield OA(411, 99, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 278880 > 411 [i]
- discarding factors would yield OA(411, 99, S4, 6), but
- linear OA(4175, 181, F4, 132) (dual of [181, 6, 133]-code), but
- construction Y1 [i] would yield
- OA(422, 199, S4, 12), but
- discarding factors would yield OA(422, 164, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 187369 733464 > 422 [i]
- discarding factors would yield OA(422, 164, S4, 12), but
- linear OA(4176, 187, F4, 132) (dual of [187, 11, 133]-code), 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 OOA(4180, 199, F4, 3, 135) (dual of [(199, 3), 417, 136]-NRT-code) | [i] | Depth Reduction | |