Information on Result #1856310
There is no (12, m, 114)-net in base 9 for arbitrarily large m, because m-reduction would yield (12, 99, 114)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(999, 114, S9, 87), but
- the linear programming bound shows that M ≥ 183 712452 224151 496359 730756 773016 045194 033482 014231 382801 426138 213217 418543 740185 901581 517780 371424 905718 474237 / 4987 502939 947913 > 999 [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, 113)-sequence in base 9 | [i] | Net from Sequence | |
| 2 | No (12, 12+k, 114)-net in base 9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (12, m, 114)-net in base 9 with unbounded m | [i] | ||
| 4 | No digital (12, 12+k, 114)-net over F9 for arbitrarily large k | [i] | ||
| 5 | No digital (12, m, 114)-net over F9 with unbounded m | [i] | ||