Information on Result #547685
There is no linear OA(2124, 166, F2, 58) (dual of [166, 42, 59]-code), because construction Y1 would yield
- OA(2123, 150, S2, 58), but
- the linear programming bound shows that M ≥ 36000 467012 365704 432940 148948 904738 978722 217984 / 3201 323125 > 2123 [i]
- OA(242, 166, S2, 16), but
- discarding factors would yield OA(242, 146, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 467697 956730 > 242 [i]
- discarding factors would yield OA(242, 146, S2, 16), but
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(2125, 167, F2, 59) (dual of [167, 42, 60]-code) | [i] | Truncation | |
| 2 | No linear OOA(2125, 166, F2, 2, 59) (dual of [(166, 2), 207, 60]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2124, 166, F2, 2, 58) (dual of [(166, 2), 208, 59]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2124, 166, F2, 3, 58) (dual of [(166, 3), 374, 59]-NRT-code) | [i] | ||
| 5 | No linear OOA(2124, 166, F2, 4, 58) (dual of [(166, 4), 540, 59]-NRT-code) | [i] | ||
| 6 | No linear OOA(2124, 166, F2, 5, 58) (dual of [(166, 5), 706, 59]-NRT-code) | [i] | ||
| 7 | No linear OOA(2124, 166, F2, 6, 58) (dual of [(166, 6), 872, 59]-NRT-code) | [i] | ||
| 8 | No linear OOA(2124, 166, F2, 7, 58) (dual of [(166, 7), 1038, 59]-NRT-code) | [i] | ||
| 9 | No linear OOA(2124, 166, F2, 8, 58) (dual of [(166, 8), 1204, 59]-NRT-code) | [i] | ||
| 10 | No digital (66, 124, 166)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2125, 194, F2, 58) (dual of [194, 69, 59]-code) | [i] | Construction Y1 (Bound) | |