Information on Result #546242
There is no linear OA(2147, 169, F2, 72) (dual of [169, 22, 73]-code), because residual code would yield OA(275, 96, S2, 36), but
- the linear programming bound shows that M ≥ 22708 462595 641194 417680 809984 / 528333 > 275 [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(2148, 170, F2, 73) (dual of [170, 22, 74]-code) | [i] | Truncation | |
| 2 | No linear OOA(2148, 169, F2, 2, 73) (dual of [(169, 2), 190, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2147, 169, F2, 2, 72) (dual of [(169, 2), 191, 73]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2147, 169, F2, 3, 72) (dual of [(169, 3), 360, 73]-NRT-code) | [i] | ||
| 5 | No linear OOA(2147, 169, F2, 4, 72) (dual of [(169, 4), 529, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2147, 169, F2, 5, 72) (dual of [(169, 5), 698, 73]-NRT-code) | [i] | ||
| 7 | No linear OOA(2147, 169, F2, 6, 72) (dual of [(169, 6), 867, 73]-NRT-code) | [i] | ||
| 8 | No linear OOA(2147, 169, F2, 7, 72) (dual of [(169, 7), 1036, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(2147, 169, F2, 8, 72) (dual of [(169, 8), 1205, 73]-NRT-code) | [i] | ||
| 10 | No digital (75, 147, 169)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |