Information on Result #546388
There is no linear OA(2188, 233, F2, 90) (dual of [233, 45, 91]-code), because residual code would yield OA(298, 142, S2, 45), but
- 1 times truncation [i] would yield OA(297, 141, S2, 44), but
- the linear programming bound shows that M ≥ 33406 063517 297373 977917 219831 876457 216369 229824 / 189199 322419 332537 > 297 [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(2189, 234, F2, 91) (dual of [234, 45, 92]-code) | [i] | Truncation | |
| 2 | No linear OOA(2189, 233, F2, 2, 91) (dual of [(233, 2), 277, 92]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2188, 233, F2, 2, 90) (dual of [(233, 2), 278, 91]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2188, 233, F2, 3, 90) (dual of [(233, 3), 511, 91]-NRT-code) | [i] | ||
| 5 | No linear OOA(2188, 233, F2, 4, 90) (dual of [(233, 4), 744, 91]-NRT-code) | [i] | ||
| 6 | No linear OOA(2188, 233, F2, 5, 90) (dual of [(233, 5), 977, 91]-NRT-code) | [i] | ||
| 7 | No linear OOA(2188, 233, F2, 6, 90) (dual of [(233, 6), 1210, 91]-NRT-code) | [i] | ||
| 8 | No linear OOA(2188, 233, F2, 7, 90) (dual of [(233, 7), 1443, 91]-NRT-code) | [i] | ||
| 9 | No linear OOA(2188, 233, F2, 8, 90) (dual of [(233, 8), 1676, 91]-NRT-code) | [i] | ||
| 10 | No digital (98, 188, 233)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |