Information on Result #547890
There is no linear OA(4171, 182, F4, 128) (dual of [182, 11, 129]-code), because construction Y1 would yield
- linear OA(4170, 176, F4, 128) (dual of [176, 6, 129]-code), but
- construction Y1 [i] would yield
- linear OA(4169, 173, F4, 128) (dual of [173, 4, 129]-code), but
- linear OA(46, 176, F4, 3) (dual of [176, 170, 4]-code or 176-cap in PG(5,4)), but
- construction Y1 [i] would yield
- OA(411, 182, 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
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(4172, 183, F4, 129) (dual of [183, 11, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(4173, 184, F4, 130) (dual of [184, 11, 131]-code) | [i] | ||
| 3 | No linear OA(4174, 185, F4, 131) (dual of [185, 11, 132]-code) | [i] | ||
| 4 | No linear OOA(4172, 182, F4, 2, 129) (dual of [(182, 2), 192, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4173, 182, F4, 2, 130) (dual of [(182, 2), 191, 131]-NRT-code) | [i] | ||
| 6 | No linear OOA(4174, 182, F4, 2, 131) (dual of [(182, 2), 190, 132]-NRT-code) | [i] | ||
| 7 | No linear OOA(4171, 182, F4, 2, 128) (dual of [(182, 2), 193, 129]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4171, 182, F4, 3, 128) (dual of [(182, 3), 375, 129]-NRT-code) | [i] | ||
| 9 | No digital (43, 171, 182)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(4172, 194, F4, 128) (dual of [194, 22, 129]-code) | [i] | Construction Y1 (Bound) | |