Information on Result #599752
There is no digital (30, 135, 171)-net over F5, because extracting embedded orthogonal array would yield linear OA(5135, 171, F5, 105) (dual of [171, 36, 106]-code), but
- construction Y1 [i] 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]
- OA(5134, 147, S5, 105), 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 (30, 136, 171)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (30, 137, 171)-net over F5 | [i] | ||
| 3 | No digital (30, 138, 171)-net over F5 | [i] | ||