Information on Result #547205
There is no linear OA(4179, 237, F4, 132) (dual of [237, 58, 133]-code), because residual code would yield OA(447, 104, S4, 33), but
- the linear programming bound shows that M ≥ 1174 046639 191630 223681 185273 503735 047219 518200 396804 079380 889257 898555 970298 959666 030187 642880 / 54879 229485 183725 296974 155563 481145 282045 055361 543282 990010 805653 > 447 [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(4180, 238, F4, 133) (dual of [238, 58, 134]-code) | [i] | Truncation | |
| 2 | No linear OA(4181, 239, F4, 134) (dual of [239, 58, 135]-code) | [i] | ||
| 3 | No linear OA(4182, 240, F4, 135) (dual of [240, 58, 136]-code) | [i] | ||
| 4 | No linear OOA(4180, 237, F4, 2, 133) (dual of [(237, 2), 294, 134]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4181, 237, F4, 2, 134) (dual of [(237, 2), 293, 135]-NRT-code) | [i] | ||
| 6 | No linear OOA(4182, 237, F4, 2, 135) (dual of [(237, 2), 292, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(4179, 237, F4, 2, 132) (dual of [(237, 2), 295, 133]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4179, 237, F4, 3, 132) (dual of [(237, 3), 532, 133]-NRT-code) | [i] | ||
| 9 | No digital (47, 179, 237)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |