Information on Result #1856272
There is no (11, m, 58)-net in base 5 for arbitrarily large m, because m-reduction would yield (11, 113, 58)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5113, 58, S5, 2, 102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1107 409718 022660 615507 187316 986333 208159 408447 723848 212262 964807 450771 331787 109375 / 103 > 5113 [i]
Mode: Bound.
Optimality
Show details for fixed 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 (11, 57)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (11, 11+k, 58)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (11, m, 58)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (11, 11+k, 58)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (11, m, 58)-net over F5 with unbounded m | [i] | ||