Information on Result #547691
There is no linear OA(2133, 160, F2, 64) (dual of [160, 27, 65]-code), because construction Y1 would yield
- OA(2132, 150, S2, 64), but
- the linear programming bound shows that M ≥ 7654 730789 395636 393332 135297 086550 086927 777792 / 1 285141 > 2132 [i]
- OA(227, 160, S2, 10), but
- discarding factors would yield OA(227, 111, S2, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 134 381744 > 227 [i]
- discarding factors would yield OA(227, 111, S2, 10), 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(2134, 161, F2, 65) (dual of [161, 27, 66]-code) | [i] | Truncation | |
| 2 | No linear OOA(2134, 160, F2, 2, 65) (dual of [(160, 2), 186, 66]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2133, 160, F2, 2, 64) (dual of [(160, 2), 187, 65]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2133, 160, F2, 3, 64) (dual of [(160, 3), 347, 65]-NRT-code) | [i] | ||
| 5 | No linear OOA(2133, 160, F2, 4, 64) (dual of [(160, 4), 507, 65]-NRT-code) | [i] | ||
| 6 | No linear OOA(2133, 160, F2, 5, 64) (dual of [(160, 5), 667, 65]-NRT-code) | [i] | ||
| 7 | No linear OOA(2133, 160, F2, 6, 64) (dual of [(160, 6), 827, 65]-NRT-code) | [i] | ||
| 8 | No linear OOA(2133, 160, F2, 7, 64) (dual of [(160, 7), 987, 65]-NRT-code) | [i] | ||
| 9 | No linear OOA(2133, 160, F2, 8, 64) (dual of [(160, 8), 1147, 65]-NRT-code) | [i] | ||
| 10 | No digital (69, 133, 160)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |