Information on Result #1856271
There is no (10, m, 54)-net in base 5 for arbitrarily large m, because m-reduction would yield (10, 105, 54)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5105, 54, S5, 2, 95), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 123 259516 440783 094595 582588 325435 348386 438505 485784 844495 356082 916259 765625 / 4 > 5105 [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 (10, 53)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (10, 10+k, 54)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (10, m, 54)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (10, 10+k, 54)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (10, m, 54)-net over F5 with unbounded m | [i] | ||