Information on Result #599025
There is no digital (49, 140, 182)-net over F3, because extracting embedded orthogonal array would yield linear OA(3140, 182, F3, 91) (dual of [182, 42, 92]-code), but
- construction Y1 [i] would yield
- linear OA(3139, 160, F3, 91) (dual of [160, 21, 92]-code), but
- construction Y1 [i] would yield
- OA(3138, 150, S3, 91), but
- the linear programming bound shows that M ≥ 13 106423 371120 876472 986931 421169 566720 811359 868949 528224 695915 065174 686944 / 17 599301 > 3138 [i]
- OA(321, 160, S3, 10), but
- discarding factors would yield OA(321, 133, S3, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 10487 287539 > 321 [i]
- discarding factors would yield OA(321, 133, S3, 10), but
- OA(3138, 150, S3, 91), but
- construction Y1 [i] would yield
- OA(342, 182, S3, 22), but
- discarding factors would yield OA(342, 168, S3, 22), but
- the Rao or (dual) Hamming bound shows that M ≥ 114 464714 711551 910433 > 342 [i]
- discarding factors would yield OA(342, 168, S3, 22), but
- linear OA(3139, 160, F3, 91) (dual of [160, 21, 92]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (49, 141, 182)-net over F3 | [i] | m-Reduction | |