Information on Result #547127
There is no linear OA(4138, 226, F4, 100) (dual of [226, 88, 101]-code), because residual code would yield OA(438, 125, S4, 25), but
- the linear programming bound shows that M ≥ 389 567034 474678 876680 715278 147118 516148 790886 400000 / 5089 117647 497197 040645 830161 > 438 [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(4139, 227, F4, 101) (dual of [227, 88, 102]-code) | [i] | Truncation | |
| 2 | No linear OOA(4139, 226, F4, 2, 101) (dual of [(226, 2), 313, 102]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(4138, 226, F4, 2, 100) (dual of [(226, 2), 314, 101]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(4138, 226, F4, 3, 100) (dual of [(226, 3), 540, 101]-NRT-code) | [i] | ||
| 5 | No digital (38, 138, 226)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(4100, 238, F4, 70) (dual of [238, 138, 71]-code) | [i] | Construction Y1 (Bound) | |