Information on Result #547140
There is no linear OA(4146, 196, F4, 108) (dual of [196, 50, 109]-code), because residual code would yield OA(438, 87, S4, 27), but
- the linear programming bound shows that M ≥ 750676 473656 767244 506582 044594 315077 520225 769567 027200 / 9 306912 430727 497773 727968 244619 > 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(4147, 197, F4, 109) (dual of [197, 50, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(4148, 198, F4, 110) (dual of [198, 50, 111]-code) | [i] | ||
| 3 | No linear OA(4149, 199, F4, 111) (dual of [199, 50, 112]-code) | [i] | ||
| 4 | No linear OOA(4147, 196, F4, 2, 109) (dual of [(196, 2), 245, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4148, 196, F4, 2, 110) (dual of [(196, 2), 244, 111]-NRT-code) | [i] | ||
| 6 | No linear OOA(4149, 196, F4, 2, 111) (dual of [(196, 2), 243, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(4146, 196, F4, 2, 108) (dual of [(196, 2), 246, 109]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4146, 196, F4, 3, 108) (dual of [(196, 3), 442, 109]-NRT-code) | [i] | ||
| 9 | No digital (38, 146, 196)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |