Information on Result #1851591
There is no (17, m, 83)-net in base 5 for arbitrarily large m, because m-reduction would yield (17, 245, 83)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5245, 83, S5, 3, 228), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 645570 871830 419924 636880 574448 055468 740063 259242 340906 093291 881802 042574 469997 747437 486128 899560 489511 854031 317062 579653 202577 636473 581679 243949 338342 645205 557346 343994 140625 / 229 > 5245 [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 (17, 82)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (17, 17+k, 83)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (17, m, 83)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (17, 17+k, 83)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (17, m, 83)-net over F5 with unbounded m | [i] | ||