Information on Result #548331
There is no linear OA(2146, 165, F2, 72) (dual of [165, 19, 73]-code), because residual code would yield linear OA(274, 92, F2, 36) (dual of [92, 18, 37]-code), but
- adding a parity check bit [i] would yield linear OA(275, 93, F2, 37) (dual of [93, 18, 38]-code), but
- “Bro†bound on codes from Brouwer’s database [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, 166, F2, 73) (dual of [166, 19, 74]-code) | [i] | Truncation | |
| 2 | No linear OOA(2147, 165, F2, 2, 73) (dual of [(165, 2), 183, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2146, 165, F2, 2, 72) (dual of [(165, 2), 184, 73]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2146, 165, F2, 3, 72) (dual of [(165, 3), 349, 73]-NRT-code) | [i] | ||
| 5 | No linear OOA(2146, 165, F2, 4, 72) (dual of [(165, 4), 514, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2146, 165, F2, 5, 72) (dual of [(165, 5), 679, 73]-NRT-code) | [i] | ||
| 7 | No linear OOA(2146, 165, F2, 6, 72) (dual of [(165, 6), 844, 73]-NRT-code) | [i] | ||
| 8 | No linear OOA(2146, 165, F2, 7, 72) (dual of [(165, 7), 1009, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(2146, 165, F2, 8, 72) (dual of [(165, 8), 1174, 73]-NRT-code) | [i] | ||
| 10 | No digital (74, 146, 165)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |