Information on Result #1856247
There is no (11, m, 45)-net in base 4 for arbitrarily large m, because m-reduction would yield (11, 131, 45)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4131, 45, S4, 3, 120), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1452 495967 392894 355393 274435 948981 116111 418687 645795 235310 955933 795262 298203 357184 / 121 > 4131 [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 (11, 44)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (11, 11+k, 45)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (11, m, 45)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (11, 11+k, 45)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (11, m, 45)-net over F4 with unbounded m | [i] | ||