Information on Result #1856328
There is no (1, m, 57)-net in base 27 for arbitrarily large m, because m-reduction would yield (1, 55, 57)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2755, 57, S27, 54), but
- the (dual) Plotkin bound shows that M ≥ 430 023359 390034 222082 732011 948356 798311 147247 214997 695270 038813 781532 497547 421283 / 55 > 2755 [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 (1, 56)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (1, 1+k, 57)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (1, m, 57)-net in base 27 with unbounded m | [i] | ||