Information on Result #547191
There is no linear OA(4173, 223, F4, 128) (dual of [223, 50, 129]-code), because residual code would yield OA(445, 94, S4, 32), but
- the linear programming bound shows that M ≥ 5620 184626 019067 545133 732595 852193 606492 239172 450795 055293 610024 696241 375244 513537 251173 048636 372484 511737 707886 460600 729196 298240 / 4 490354 977671 109171 977374 825515 463646 543995 191995 384881 187906 235255 501379 117691 433461 827076 002203 266473 > 445 [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(4174, 224, F4, 129) (dual of [224, 50, 130]-code) | [i] | Truncation | |
| 2 | No linear OA(4175, 225, F4, 130) (dual of [225, 50, 131]-code) | [i] | ||
| 3 | No linear OA(4176, 226, F4, 131) (dual of [226, 50, 132]-code) | [i] | ||
| 4 | No linear OOA(4174, 223, F4, 2, 129) (dual of [(223, 2), 272, 130]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4175, 223, F4, 2, 130) (dual of [(223, 2), 271, 131]-NRT-code) | [i] | ||
| 6 | No linear OOA(4176, 223, F4, 2, 131) (dual of [(223, 2), 270, 132]-NRT-code) | [i] | ||
| 7 | No linear OOA(4173, 223, F4, 2, 128) (dual of [(223, 2), 273, 129]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4173, 223, F4, 3, 128) (dual of [(223, 3), 496, 129]-NRT-code) | [i] | ||
| 9 | No digital (45, 173, 223)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |