Information on Result #1856182
There is no (12, m, 19)-net in base 2 for arbitrarily large m, because m-reduction would yield (12, 89, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9284 550294 640352 061743 431680 / 13 > 289 [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 (12, 18)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (12, 12+k, 19)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (12, m, 19)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (12, 12+k, 19)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (12, m, 19)-net over F2 with unbounded m | [i] | ||