Information on Result #547206
There is no linear OA(4180, 251, F4, 132) (dual of [251, 71, 133]-code), because residual code would yield OA(448, 118, S4, 33), but
- the linear programming bound shows that M ≥ 11741 391231 673162 520784 823169 575929 136281 422846 471752 288804 624247 186167 273881 600000 / 141904 351037 772816 847773 975434 784371 947508 137187 747933 > 448 [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(4181, 252, F4, 133) (dual of [252, 71, 134]-code) | [i] | Truncation | |
| 2 | No linear OA(4182, 253, F4, 134) (dual of [253, 71, 135]-code) | [i] | ||
| 3 | No linear OA(4183, 254, F4, 135) (dual of [254, 71, 136]-code) | [i] | ||
| 4 | No linear OOA(4181, 251, F4, 2, 133) (dual of [(251, 2), 321, 134]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4182, 251, F4, 2, 134) (dual of [(251, 2), 320, 135]-NRT-code) | [i] | ||
| 6 | No linear OOA(4183, 251, F4, 2, 135) (dual of [(251, 2), 319, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(4180, 251, F4, 2, 132) (dual of [(251, 2), 322, 133]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4180, 251, F4, 3, 132) (dual of [(251, 3), 573, 133]-NRT-code) | [i] | ||
| 9 | No digital (48, 180, 251)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |