Information on Result #1850295
There is no (60, m, 133)-net in base 3 for arbitrarily large m, because m-reduction would yield (60, 526, 133)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3526, 133, S3, 4, 466), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 45 749376 695876 574596 544178 102538 190422 581384 179693 504822 412055 940395 131223 460005 421772 207849 589406 242393 199955 789579 652324 605064 265082 190889 099392 682399 599960 399439 496719 183057 488035 454230 521296 021782 069992 567481 246842 388517 406099 652987 529213 428861 572855 / 467 > 3526 [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 (60, 132)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (60, 60+k, 133)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (60, m, 133)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (60, 60+k, 133)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (60, m, 133)-net over F3 with unbounded m | [i] | ||