Information on Result #1856307
There is no (9, m, 90)-net in base 9 for arbitrarily large m, because m-reduction would yield (9, 80, 90)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(980, 90, S9, 71), but
- the linear programming bound shows that M ≥ 825617 125614 748653 438025 314237 742758 149006 797066 212440 636337 770986 951542 029890 113291 / 30 000971 > 980 [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 (9, 89)-sequence in base 9 | [i] | Net from Sequence | |
| 2 | No (9, 9+k, 90)-net in base 9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (9, m, 90)-net in base 9 with unbounded m | [i] | ||
| 4 | No digital (9, 9+k, 90)-net over F9 for arbitrarily large k | [i] | ||
| 5 | No digital (9, m, 90)-net over F9 with unbounded m | [i] | ||