Information on Result #546249
There is no linear OA(2154, 217, F2, 72) (dual of [217, 63, 73]-code), because residual code would yield OA(282, 144, S2, 36), but
- the linear programming bound shows that M ≥ 2893 609949 429043 518839 097243 777165 200630 895720 113073 291264 / 558 874024 262522 794899 259597 123083 > 282 [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(2155, 218, F2, 73) (dual of [218, 63, 74]-code) | [i] | Truncation | |
| 2 | No linear OOA(2155, 217, F2, 2, 73) (dual of [(217, 2), 279, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2154, 217, F2, 2, 72) (dual of [(217, 2), 280, 73]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2154, 217, F2, 3, 72) (dual of [(217, 3), 497, 73]-NRT-code) | [i] | ||
| 5 | No linear OOA(2154, 217, F2, 4, 72) (dual of [(217, 4), 714, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2154, 217, F2, 5, 72) (dual of [(217, 5), 931, 73]-NRT-code) | [i] | ||
| 7 | No linear OOA(2154, 217, F2, 6, 72) (dual of [(217, 6), 1148, 73]-NRT-code) | [i] | ||
| 8 | No linear OOA(2154, 217, F2, 7, 72) (dual of [(217, 7), 1365, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(2154, 217, F2, 8, 72) (dual of [(217, 8), 1582, 73]-NRT-code) | [i] | ||
| 10 | No digital (82, 154, 217)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |