Information on Result #1856387
There is no (48, 56)-sequence in base 2, because net from sequence would yield (48, m, 57)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (48, 391, 57)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2391, 57, S2, 7, 343), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 250911 975458 640043 623792 927357 714532 710747 779674 323964 381494 732398 236756 240894 237173 486047 511107 142800 656607 042273 804288 / 43 > 2391 [i]
- extracting embedded OOA [i] would yield OOA(2391, 57, S2, 7, 343), but
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 (48, 56)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (48, m, 56)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (48, 56)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (48, m, 56)-net over F2 with m > ∞ | [i] | ||