Information on Result #1849614
There is no (67, m, 77)-net in base 2 for arbitrarily large m, because m-reduction would yield (67, 453, 77)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2453, 77, S2, 6, 386), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 163202 128134 481187 670657 211928 595733 507047 201711 208198 345045 346834 142181 869507 762315 583452 706299 037320 438494 030470 406366 742586 287730 982912 / 129 > 2453 [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 (67, 76)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (67, 67+k, 77)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (67, m, 77)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (67, 67+k, 77)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (67, m, 77)-net over F2 with unbounded m | [i] | ||