Information on Result #1856178
There is no (8, m, 15)-net in base 2 for arbitrarily large m, because m-reduction would yield (8, 40, 15)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(240, 15, S2, 3, 32), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13 194139 533312 / 11 > 240 [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 (8, 14)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (8, 8+k, 15)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (8, m, 15)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (8, 8+k, 15)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (8, m, 15)-net over F2 with unbounded m | [i] | ||