Information on Result #1850265
There is no (50, m, 112)-net in base 3 for arbitrarily large m, because m-reduction would yield (50, 554, 112)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3554, 112, S3, 5, 504), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1186 145528 364117 535737 037647 785197 557137 685959 372186 469530 968081 490221 223844 563942 363921 609990 826865 796813 560521 588061 834264 622037 072704 491910 984592 526076 703801 733360 115161 336227 325282 271920 754570 543993 276437 453515 047928 856365 953996 034966 307116 714278 332445 634035 374809 / 505 > 3554 [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 (50, 111)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (50, 50+k, 112)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (50, m, 112)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (50, 50+k, 112)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (50, m, 112)-net over F3 with unbounded m | [i] | ||