Information on Result #547162
There is no linear OA(4159, 239, F4, 116) (dual of [239, 80, 117]-code), because residual code would yield OA(443, 122, S4, 29), but
- the linear programming bound shows that M ≥ 14974 882928 795402 502879 363014 902325 642932 640714 588160 / 186 039615 985017 664535 163073 > 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(4160, 240, F4, 117) (dual of [240, 80, 118]-code) | [i] | Truncation | |
| 2 | No linear OA(4161, 241, F4, 118) (dual of [241, 80, 119]-code) | [i] | ||
| 3 | No linear OA(4162, 242, F4, 119) (dual of [242, 80, 120]-code) | [i] | ||
| 4 | No linear OOA(4160, 239, F4, 2, 117) (dual of [(239, 2), 318, 118]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4161, 239, F4, 2, 118) (dual of [(239, 2), 317, 119]-NRT-code) | [i] | ||
| 6 | No linear OOA(4162, 239, F4, 2, 119) (dual of [(239, 2), 316, 120]-NRT-code) | [i] | ||
| 7 | No linear OOA(4159, 239, F4, 2, 116) (dual of [(239, 2), 319, 117]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4159, 239, F4, 3, 116) (dual of [(239, 3), 558, 117]-NRT-code) | [i] | ||
| 9 | No digital (43, 159, 239)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |