Information on Result #546255
There is no linear OA(2150, 172, F2, 74) (dual of [172, 22, 75]-code), because residual code would yield OA(276, 97, S2, 37), but
- 1 times truncation [i] 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(2151, 173, F2, 75) (dual of [173, 22, 76]-code) | [i] | Truncation | |
| 2 | No linear OOA(2151, 172, F2, 2, 75) (dual of [(172, 2), 193, 76]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2150, 172, F2, 2, 74) (dual of [(172, 2), 194, 75]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2150, 172, F2, 3, 74) (dual of [(172, 3), 366, 75]-NRT-code) | [i] | ||
| 5 | No linear OOA(2150, 172, F2, 4, 74) (dual of [(172, 4), 538, 75]-NRT-code) | [i] | ||
| 6 | No linear OOA(2150, 172, F2, 5, 74) (dual of [(172, 5), 710, 75]-NRT-code) | [i] | ||
| 7 | No linear OOA(2150, 172, F2, 6, 74) (dual of [(172, 6), 882, 75]-NRT-code) | [i] | ||
| 8 | No linear OOA(2150, 172, F2, 7, 74) (dual of [(172, 7), 1054, 75]-NRT-code) | [i] | ||
| 9 | No linear OOA(2150, 172, F2, 8, 74) (dual of [(172, 8), 1226, 75]-NRT-code) | [i] | ||
| 10 | No digital (76, 150, 172)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |