Information on Result #1856208
There is no (38, m, 47)-net in base 2 for arbitrarily large m, because m-reduction would yield (38, 228, 47)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2228, 47, S2, 5, 190), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 84546 392748 184406 396075 759312 893561 792526 084909 087235 300740 921741 541376 / 191 > 2228 [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 (38, 46)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (38, 38+k, 47)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (38, m, 47)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (38, 38+k, 47)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (38, m, 47)-net over F2 with unbounded m | [i] | ||