Information on Result #1849587
There is no (58, m, 68)-net in base 2 for arbitrarily large m, because m-reduction would yield (58, 399, 68)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2399, 68, S2, 6, 341), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 103 289995 123476 343586 236766 880120 474973 188231 713168 940513 226374 261625 904880 673647 785185 814131 205513 257436 126878 909899 735040 / 57 > 2399 [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 (58, 67)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (58, 58+k, 68)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (58, m, 68)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (58, 58+k, 68)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (58, m, 68)-net over F2 with unbounded m | [i] | ||