Information on Result #1849578
There is no (55, m, 65)-net in base 2 for arbitrarily large m, because m-reduction would yield (55, 381, 65)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2381, 65, S2, 6, 326), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 827 442130 124284 063457 859842 103015 889906 674524 679774 380026 914161 489160 157201 441422 839699 591352 583228 456939 187796 443136 / 109 > 2381 [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 (55, 64)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (55, 55+k, 65)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (55, m, 65)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (55, 55+k, 65)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (55, m, 65)-net over F2 with unbounded m | [i] | ||