Information on Result #1851585
There is no (15, m, 74)-net in base 5 for arbitrarily large m, because m-reduction would yield (15, 218, 74)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5218, 74, S5, 3, 203), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13056 405650 419723 277775 708120 647691 087053 828021 227424 328634 697487 389886 317136 615343 670538 531185 693700 127912 995358 724079 775214 477194 822393 357753 753662 109375 / 51 > 5218 [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 (15, 73)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (15, 15+k, 74)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (15, m, 74)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (15, 15+k, 74)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (15, m, 74)-net over F5 with unbounded m | [i] | ||