Information on Result #548023
There is no linear OA(951, 86, F9, 45) (dual of [86, 35, 46]-code), because construction Y1 would yield
- linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
- construction Y1 [i] would yield
- OA(949, 51, S9, 45), but
- the (dual) Plotkin bound shows that M ≥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 949 [i]
- OA(95, 55, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 4), but
- OA(949, 51, S9, 45), but
- construction Y1 [i] would yield
- OA(935, 86, S9, 31), but
- discarding factors would yield OA(935, 85, S9, 31), but
- the linear programming bound shows that M ≥ 112620 123087 737061 231244 499443 215625 747636 066957 184847 246285 / 44 721454 781644 057928 595589 > 935 [i]
- discarding factors would yield OA(935, 85, S9, 31), 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(952, 87, F9, 46) (dual of [87, 35, 47]-code) | [i] | Truncation | |
| 2 | No linear OA(953, 88, F9, 47) (dual of [88, 35, 48]-code) | [i] | ||
| 3 | No linear OOA(952, 86, F9, 2, 46) (dual of [(86, 2), 120, 47]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(953, 86, F9, 2, 47) (dual of [(86, 2), 119, 48]-NRT-code) | [i] | ||
| 5 | No linear OOA(951, 86, F9, 2, 45) (dual of [(86, 2), 121, 46]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(951, 86, F9, 3, 45) (dual of [(86, 3), 207, 46]-NRT-code) | [i] | ||
| 7 | No digital (6, 51, 86)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |