Information on Result #547182
There is no linear OA(4169, 237, F4, 124) (dual of [237, 68, 125]-code), because residual code would yield OA(445, 112, S4, 31), but
- the linear programming bound shows that M ≥ 30 703316 954186 650166 302103 088413 940385 262854 668690 715040 548493 721600 / 24108 147423 127287 645158 347013 987588 540153 > 445 [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(4170, 238, F4, 125) (dual of [238, 68, 126]-code) | [i] | Truncation | |
| 2 | No linear OA(4171, 239, F4, 126) (dual of [239, 68, 127]-code) | [i] | ||
| 3 | No linear OA(4172, 240, F4, 127) (dual of [240, 68, 128]-code) | [i] | ||
| 4 | No linear OOA(4170, 237, F4, 2, 125) (dual of [(237, 2), 304, 126]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4171, 237, F4, 2, 126) (dual of [(237, 2), 303, 127]-NRT-code) | [i] | ||
| 6 | No linear OOA(4172, 237, F4, 2, 127) (dual of [(237, 2), 302, 128]-NRT-code) | [i] | ||
| 7 | No linear OOA(4169, 237, F4, 2, 124) (dual of [(237, 2), 305, 125]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4169, 237, F4, 3, 124) (dual of [(237, 3), 542, 125]-NRT-code) | [i] | ||
| 9 | No digital (45, 169, 237)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |