Information on Result #1849530
There is no (39, m, 48)-net in base 2 for arbitrarily large m, because m-reduction would yield (39, 280, 48)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2280, 48, S2, 6, 241), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 310 827022 756116 651347 113905 091763 025062 785094 248342 323400 289985 558224 685632 833359 708160 / 121 > 2280 [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 (39, 47)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (39, 39+k, 48)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (39, m, 48)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (39, 39+k, 48)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (39, m, 48)-net over F2 with unbounded m | [i] | ||