Information on Result #599023
There is no digital (49, 136, 198)-net over F3, because extracting embedded orthogonal array would yield linear OA(3136, 198, F3, 87) (dual of [198, 62, 88]-code), but
- construction Y1 [i] would yield
- linear OA(3135, 164, F3, 87) (dual of [164, 29, 88]-code), but
- construction Y1 [i] would yield
- OA(3134, 150, S3, 87), but
- the linear programming bound shows that M ≥ 1998 191076 053927 805178 143382 564872 985089 052204 487349 698881 740338 723055 870219 / 227413 116931 > 3134 [i]
- OA(329, 164, S3, 14), but
- discarding factors would yield OA(329, 163, S3, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 69 685080 318363 > 329 [i]
- discarding factors would yield OA(329, 163, S3, 14), but
- OA(3134, 150, S3, 87), but
- construction Y1 [i] would yield
- OA(362, 198, S3, 34), but
- discarding factors would yield OA(362, 187, S3, 34), but
- the linear programming bound shows that M ≥ 86 582238 519540 759403 959995 312746 663126 603948 166833 519820 296875 / 223 323463 041708 430754 736757 380607 > 362 [i]
- discarding factors would yield OA(362, 187, S3, 34), but
- linear OA(3135, 164, F3, 87) (dual of [164, 29, 88]-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, 137, 198)-net over F3 | [i] | m-Reduction | |