Information on Result #546222
There is no linear OA(2144, 195, F2, 68) (dual of [195, 51, 69]-code), because residual code would yield OA(276, 126, S2, 34), but
- the linear programming bound shows that M ≥ 38 459620 016436 403553 321591 630765 416829 509898 862592 / 484 232223 153801 738635 105625 > 276 [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(2145, 196, F2, 69) (dual of [196, 51, 70]-code) | [i] | Truncation | |
| 2 | No linear OOA(2145, 195, F2, 2, 69) (dual of [(195, 2), 245, 70]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2144, 195, F2, 2, 68) (dual of [(195, 2), 246, 69]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2144, 195, F2, 3, 68) (dual of [(195, 3), 441, 69]-NRT-code) | [i] | ||
| 5 | No linear OOA(2144, 195, F2, 4, 68) (dual of [(195, 4), 636, 69]-NRT-code) | [i] | ||
| 6 | No linear OOA(2144, 195, F2, 5, 68) (dual of [(195, 5), 831, 69]-NRT-code) | [i] | ||
| 7 | No linear OOA(2144, 195, F2, 6, 68) (dual of [(195, 6), 1026, 69]-NRT-code) | [i] | ||
| 8 | No linear OOA(2144, 195, F2, 7, 68) (dual of [(195, 7), 1221, 69]-NRT-code) | [i] | ||
| 9 | No linear OOA(2144, 195, F2, 8, 68) (dual of [(195, 8), 1416, 69]-NRT-code) | [i] | ||
| 10 | No digital (76, 144, 195)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |