Information on Result #1856198
There is no (28, m, 36)-net in base 2 for arbitrarily large m, because m-reduction would yield (28, 209, 36)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2209, 36, S2, 6, 181), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 75693 209636 775477 939128 582397 638123 229205 849819 144673 714036 015104 / 91 > 2209 [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 (28, 35)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (28, 28+k, 36)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (28, m, 36)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (28, 28+k, 36)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (28, m, 36)-net over F2 with unbounded m | [i] | ||