Information on Result #1856330
There is no (3, m, 103)-net in base 27 for arbitrarily large m, because m-reduction would yield (3, 97, 103)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2797, 103, S27, 94), but
- the linear programming bound shows that M ≥ 128 911025 055144 003712 512083 846133 074073 104655 021247 977332 109220 807942 928575 240457 586722 133506 291651 511625 988777 715999 325631 713723 671307 153546 411869 / 17 583797 > 2797 [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 (3, 102)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (3, 3+k, 103)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (3, m, 103)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (3, 3+k, 103)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (3, m, 103)-net over F27 with unbounded m | [i] | ||