Information on Result #1849554
There is no (47, m, 56)-net in base 2 for arbitrarily large m, because m-reduction would yield (47, 328, 56)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2328, 56, S2, 6, 281), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26247 008697 396143 092470 026725 411456 384238 033170 718549 237109 247276 919435 990392 511078 682158 124276 645888 / 47 > 2328 [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 (47, 55)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (47, 47+k, 56)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (47, m, 56)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (47, 47+k, 56)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (47, m, 56)-net over F2 with unbounded m | [i] | ||