Information on Result #547964
There is no linear OA(5135, 171, F5, 105) (dual of [171, 36, 106]-code), because construction Y1 would yield
- OA(5134, 147, S5, 105), but
- the linear programming bound shows that M ≥ 35 088836 405859 599893 783329 592875 489923 934405 996939 363274 030802 657132 976918 319400 283508 002758 026123 046875 / 7350 907663 > 5134 [i]
- OA(536, 171, S5, 24), but
- the Rao or (dual) Hamming bound shows that M ≥ 15 032494 166705 850791 777885 > 536 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(5136, 172, F5, 106) (dual of [172, 36, 107]-code) | [i] | Truncation | |
| 2 | No linear OA(5137, 173, F5, 107) (dual of [173, 36, 108]-code) | [i] | ||
| 3 | No linear OA(5138, 174, F5, 108) (dual of [174, 36, 109]-code) | [i] | ||
| 4 | No linear OOA(5136, 171, F5, 2, 106) (dual of [(171, 2), 206, 107]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(5137, 171, F5, 2, 107) (dual of [(171, 2), 205, 108]-NRT-code) | [i] | ||
| 6 | No linear OOA(5138, 171, F5, 2, 108) (dual of [(171, 2), 204, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(5135, 171, F5, 2, 105) (dual of [(171, 2), 207, 106]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(5135, 171, F5, 3, 105) (dual of [(171, 3), 378, 106]-NRT-code) | [i] | ||
| 9 | No digital (30, 135, 171)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |