Information on Result #546224
There is no linear OA(2146, 214, F2, 68) (dual of [214, 68, 69]-code), because residual code would yield OA(278, 145, S2, 34), but
- the linear programming bound shows that M ≥ 6 452658 897421 925882 991923 762933 214377 859980 440698 591468 415644 336128 / 20 712793 240469 221474 764436 259197 787149 263939 > 278 [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(2147, 215, F2, 69) (dual of [215, 68, 70]-code) | [i] | Truncation | |
| 2 | No linear OOA(2147, 214, F2, 2, 69) (dual of [(214, 2), 281, 70]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2146, 214, F2, 2, 68) (dual of [(214, 2), 282, 69]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2146, 214, F2, 3, 68) (dual of [(214, 3), 496, 69]-NRT-code) | [i] | ||
| 5 | No linear OOA(2146, 214, F2, 4, 68) (dual of [(214, 4), 710, 69]-NRT-code) | [i] | ||
| 6 | No linear OOA(2146, 214, F2, 5, 68) (dual of [(214, 5), 924, 69]-NRT-code) | [i] | ||
| 7 | No linear OOA(2146, 214, F2, 6, 68) (dual of [(214, 6), 1138, 69]-NRT-code) | [i] | ||
| 8 | No linear OOA(2146, 214, F2, 7, 68) (dual of [(214, 7), 1352, 69]-NRT-code) | [i] | ||
| 9 | No linear OOA(2146, 214, F2, 8, 68) (dual of [(214, 8), 1566, 69]-NRT-code) | [i] | ||
| 10 | No digital (78, 146, 214)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |