Information on Result #547161
There is no linear OA(4158, 223, F4, 116) (dual of [223, 65, 117]-code), because residual code would yield OA(442, 106, S4, 29), but
- the linear programming bound shows that M ≥ 11 515430 185021 615009 307015 123093 343331 130678 608727 482845 042118 230016 / 573326 282922 594402 886717 422034 435890 047071 > 442 [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(4159, 224, F4, 117) (dual of [224, 65, 118]-code) | [i] | Truncation | |
| 2 | No linear OA(4160, 225, F4, 118) (dual of [225, 65, 119]-code) | [i] | ||
| 3 | No linear OA(4161, 226, F4, 119) (dual of [226, 65, 120]-code) | [i] | ||
| 4 | No linear OOA(4159, 223, F4, 2, 117) (dual of [(223, 2), 287, 118]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4160, 223, F4, 2, 118) (dual of [(223, 2), 286, 119]-NRT-code) | [i] | ||
| 6 | No linear OOA(4161, 223, F4, 2, 119) (dual of [(223, 2), 285, 120]-NRT-code) | [i] | ||
| 7 | No linear OOA(4158, 223, F4, 2, 116) (dual of [(223, 2), 288, 117]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4158, 223, F4, 3, 116) (dual of [(223, 3), 511, 117]-NRT-code) | [i] | ||
| 9 | No digital (42, 158, 223)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |