Information on Result #1850229
There is no (38, m, 88)-net in base 3 for arbitrarily large m, because m-reduction would yield (38, 346, 88)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3346, 88, S3, 4, 308), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 134671 938588 441224 113431 736827 290363 245597 051186 402233 094311 094053 748600 754444 196567 509079 338081 106678 435003 151014 332077 567079 051883 911111 653043 899025 362948 629563 002119 / 103 > 3346 [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 (38, 87)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (38, 38+k, 88)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (38, m, 88)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (38, 38+k, 88)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (38, m, 88)-net over F3 with unbounded m | [i] | ||