Information on Result #547181
There is no linear OA(4168, 223, F4, 124) (dual of [223, 55, 125]-code), because residual code would yield OA(444, 98, S4, 31), but
- the linear programming bound shows that M ≥ 3414 029206 960280 274418 067767 340182 249392 781167 507062 000069 867201 406582 128640 000000 / 10 918790 901850 294268 885174 154273 677983 317839 404573 351291 > 444 [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(4169, 224, F4, 125) (dual of [224, 55, 126]-code) | [i] | Truncation | |
| 2 | No linear OA(4170, 225, F4, 126) (dual of [225, 55, 127]-code) | [i] | ||
| 3 | No linear OA(4171, 226, F4, 127) (dual of [226, 55, 128]-code) | [i] | ||
| 4 | No linear OOA(4169, 223, F4, 2, 125) (dual of [(223, 2), 277, 126]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4170, 223, F4, 2, 126) (dual of [(223, 2), 276, 127]-NRT-code) | [i] | ||
| 6 | No linear OOA(4171, 223, F4, 2, 127) (dual of [(223, 2), 275, 128]-NRT-code) | [i] | ||
| 7 | No linear OOA(4168, 223, F4, 2, 124) (dual of [(223, 2), 278, 125]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4168, 223, F4, 3, 124) (dual of [(223, 3), 501, 125]-NRT-code) | [i] | ||
| 9 | No digital (44, 168, 223)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |