Information on Result #1851594
There is no (18, m, 87)-net in base 5 for arbitrarily large m, because m-reduction would yield (18, 257, 87)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5257, 87, S5, 3, 239), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 295425 283264 166693 807952 779420 059935 667400 054665 442207 753555 520525 288770 474364 058695 726125 520843 233984 082094 091922 449539 549264 842024 792004 047950 566558 711216 202937 066555 023193 359375 / 2 > 5257 [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 (18, 86)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (18, 18+k, 87)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (18, m, 87)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (18, 18+k, 87)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (18, m, 87)-net over F5 with unbounded m | [i] | ||