Information on Result #1854168
There is no (5, m, 169)-net in base 27 for arbitrarily large m, because m-reduction would yield (5, 167, 169)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27167, 169, S27, 162), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20 616285 448258 254189 632446 434101 061939 919259 309742 920263 876202 317073 200308 628068 739540 554185 109313 440135 737891 337006 986211 869313 170146 408503 076708 329690 668617 272344 297529 613836 221069 388332 816090 054458 740691 616512 138780 754856 409263 979104 870567 / 163 > 27167 [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 (5, 168)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (5, 5+k, 169)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (5, m, 169)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (5, 5+k, 169)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (5, m, 169)-net over F27 with unbounded m | [i] | ||