Information on Result #1856329
There is no (2, m, 78)-net in base 27 for arbitrarily large m, because m-reduction would yield (2, 74, 78)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2774, 78, S27, 72), but
- the linear programming bound shows that M ≥ 981 000392 047679 793224 589514 892092 100547 285178 849241 756604 164607 128464 559760 391182 392033 793658 959804 539641 190037 / 106799 > 2774 [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 (2, 77)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (2, 2+k, 78)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (2, m, 78)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (2, 2+k, 78)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (2, m, 78)-net over F27 with unbounded m | [i] | ||