Information on Result #1856220
There is no (11, m, 32)-net in base 3 for arbitrarily large m, because m-reduction would yield (11, 90, 32)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(390, 32, S3, 3, 79), but
- the LP bound with quadratic polynomials shows that M ≥ 177 468592 551116 819326 458415 416026 789247 509463 / 20 > 390 [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, 31)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (11, 11+k, 32)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (11, m, 32)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (11, 11+k, 32)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (11, m, 32)-net over F3 with unbounded m | [i] | ||