Information on Result #1850259
There is no (48, m, 108)-net in base 3 for arbitrarily large m, because m-reduction would yield (48, 534, 108)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3534, 108, S3, 5, 486), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 343821 538392 794744 971988 367444 317149 888019 219654 310042 978368 480701 286267 732702 345837 301631 075869 708080 900589 987744 222222 378349 655973 124873 248600 186718 565415 389661 554907 134496 046023 218886 509206 619300 572111 944324 007291 155879 944548 899070 269532 503024 107801 974623 / 487 > 3534 [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 (48, 107)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (48, 48+k, 108)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (48, m, 108)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (48, 48+k, 108)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (48, m, 108)-net over F3 with unbounded m | [i] | ||