Information on Result #547193
There is no linear OA(4175, 250, F4, 128) (dual of [250, 75, 129]-code), because residual code would yield OA(447, 121, S4, 32), but
- the linear programming bound shows that M ≥ 365 129709 190376 390301 373618 637040 010384 793045 585047 102752 276086 784000 / 18163 087858 506659 594163 938688 475283 050507 > 447 [i]
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(4176, 251, F4, 129) (dual of [251, 75, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(4177, 252, F4, 130) (dual of [252, 75, 131]-code) | [i] | ||
| 3 | No linear OA(4178, 253, F4, 131) (dual of [253, 75, 132]-code) | [i] | ||
| 4 | No linear OOA(4176, 250, F4, 2, 129) (dual of [(250, 2), 324, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4177, 250, F4, 2, 130) (dual of [(250, 2), 323, 131]-NRT-code) | [i] | ||
| 6 | No linear OOA(4178, 250, F4, 2, 131) (dual of [(250, 2), 322, 132]-NRT-code) | [i] | ||
| 7 | No linear OOA(4175, 250, F4, 2, 128) (dual of [(250, 2), 325, 129]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4175, 250, F4, 3, 128) (dual of [(250, 3), 575, 129]-NRT-code) | [i] | ||
| 9 | No digital (47, 175, 250)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |