Information on Result #1851600
There is no (20, m, 95)-net in base 5 for arbitrarily large m, because m-reduction would yield (20, 281, 95)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5281, 95, S5, 3, 261), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 504112 890784 525303 371583 151787 727847 532332 133580 294973 788106 761215 637819 628193 185165 565648 995788 215542 125035 645294 759063 345617 996739 121292 201506 081179 270403 296033 276063 781158 882193 267345 428466 796875 / 131 > 5281 [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 (20, 94)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (20, 20+k, 95)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (20, m, 95)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (20, 20+k, 95)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (20, m, 95)-net over F5 with unbounded m | [i] | ||