Information on Result #547180
There is no linear OA(4167, 209, F4, 124) (dual of [209, 42, 125]-code), because residual code would yield OA(443, 84, S4, 31), but
- the linear programming bound shows that M ≥ 743 432824 923585 138466 079893 608385 692163 936496 473876 252564 706270 846821 427655 153621 009913 103585 162421 132960 451704 728431 099904 / 9 052373 288486 345160 206941 767894 606217 335850 613093 145925 916389 354432 331859 732314 014078 839167 611385 > 443 [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(4168, 210, F4, 125) (dual of [210, 42, 126]-code) | [i] | Truncation | |
| 2 | No linear OA(4169, 211, F4, 126) (dual of [211, 42, 127]-code) | [i] | ||
| 3 | No linear OA(4170, 212, F4, 127) (dual of [212, 42, 128]-code) | [i] | ||
| 4 | No linear OOA(4168, 209, F4, 2, 125) (dual of [(209, 2), 250, 126]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4169, 209, F4, 2, 126) (dual of [(209, 2), 249, 127]-NRT-code) | [i] | ||
| 6 | No linear OOA(4170, 209, F4, 2, 127) (dual of [(209, 2), 248, 128]-NRT-code) | [i] | ||
| 7 | No linear OOA(4167, 209, F4, 2, 124) (dual of [(209, 2), 251, 125]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4167, 209, F4, 3, 124) (dual of [(209, 3), 460, 125]-NRT-code) | [i] | ||
| 9 | No digital (43, 167, 209)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |