Information on Result #546389
There is no linear OA(2189, 239, F2, 90) (dual of [239, 50, 91]-code), because residual code would yield OA(299, 148, S2, 45), but
- 1 times truncation [i] would yield OA(298, 147, S2, 44), but
- the linear programming bound shows that M ≥ 386 271048 917458 443577 540946 323578 953396 125696 / 1194 549431 128209 > 298 [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(2190, 240, F2, 91) (dual of [240, 50, 92]-code) | [i] | Truncation | |
| 2 | No linear OOA(2190, 239, F2, 2, 91) (dual of [(239, 2), 288, 92]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2189, 239, F2, 2, 90) (dual of [(239, 2), 289, 91]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2189, 239, F2, 3, 90) (dual of [(239, 3), 528, 91]-NRT-code) | [i] | ||
| 5 | No linear OOA(2189, 239, F2, 4, 90) (dual of [(239, 4), 767, 91]-NRT-code) | [i] | ||
| 6 | No linear OOA(2189, 239, F2, 5, 90) (dual of [(239, 5), 1006, 91]-NRT-code) | [i] | ||
| 7 | No linear OOA(2189, 239, F2, 6, 90) (dual of [(239, 6), 1245, 91]-NRT-code) | [i] | ||
| 8 | No linear OOA(2189, 239, F2, 7, 90) (dual of [(239, 7), 1484, 91]-NRT-code) | [i] | ||
| 9 | No linear OOA(2189, 239, F2, 8, 90) (dual of [(239, 8), 1723, 91]-NRT-code) | [i] | ||
| 10 | No digital (99, 189, 239)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2190, 269, F2, 90) (dual of [269, 79, 91]-code) | [i] | Construction Y1 (Bound) | |