Information on Result #1856248
There is no (12, m, 48)-net in base 4 for arbitrarily large m, because m-reduction would yield (12, 140, 48)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4140, 48, S4, 3, 128), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 124 330809 102446 660538 845562 036705 210025 114037 699336 929360 115994 223289 874253 133343 883264 / 43 > 4140 [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 (12, 47)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (12, 12+k, 48)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (12, m, 48)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (12, 12+k, 48)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (12, m, 48)-net over F4 with unbounded m | [i] | ||