Information on Result #547679
There is no linear OA(2106, 171, F2, 48) (dual of [171, 65, 49]-code), because construction Y1 would yield
- OA(2105, 145, S2, 48), but
- the linear programming bound shows that M ≥ 727 070369 678229 731686 401086 929362 121333 407744 / 17 521374 765895 > 2105 [i]
- OA(265, 171, S2, 26), but
- discarding factors would yield OA(265, 170, S2, 26), but
- the linear programming bound shows that M ≥ 15890 939443 762705 189763 180081 227518 381108 756480 / 413 412834 411090 648392 969149 > 265 [i]
- discarding factors would yield OA(265, 170, S2, 26), 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(2107, 172, F2, 49) (dual of [172, 65, 50]-code) | [i] | Truncation | |
| 2 | No linear OOA(2107, 171, F2, 2, 49) (dual of [(171, 2), 235, 50]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2106, 171, F2, 2, 48) (dual of [(171, 2), 236, 49]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2106, 171, F2, 3, 48) (dual of [(171, 3), 407, 49]-NRT-code) | [i] | ||
| 5 | No linear OOA(2106, 171, F2, 4, 48) (dual of [(171, 4), 578, 49]-NRT-code) | [i] | ||
| 6 | No linear OOA(2106, 171, F2, 5, 48) (dual of [(171, 5), 749, 49]-NRT-code) | [i] | ||
| 7 | No linear OOA(2106, 171, F2, 6, 48) (dual of [(171, 6), 920, 49]-NRT-code) | [i] | ||
| 8 | No linear OOA(2106, 171, F2, 7, 48) (dual of [(171, 7), 1091, 49]-NRT-code) | [i] | ||
| 9 | No linear OOA(2106, 171, F2, 8, 48) (dual of [(171, 8), 1262, 49]-NRT-code) | [i] | ||
| 10 | No digital (58, 106, 171)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |