Information on Result #1856240
There is no (4, m, 21)-net in base 4 for arbitrarily large m, because m-reduction would yield (4, 24, 21)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(424, 21, S4, 2, 20), but
- the linear programming bound for OOAs shows that M ≥ 106960 491150 049280 / 311 > 424 [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 (4, 20)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (4, 4+k, 21)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (4, m, 21)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (4, 4+k, 21)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (4, m, 21)-net over F4 with unbounded m | [i] | ||