Information on Result #1850271
There is no (52, m, 116)-net in base 3 for arbitrarily large m, because m-reduction would yield (52, 574, 116)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3574, 116, S3, 5, 522), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 091600 209833 919750 115591 647196 387286 482529 830425 117722 012891 118712 647254 053292 184668 947662 871774 656252 028033 643900 510075 050301 142405 351332 494131 418115 957784 817623 188288 818826 148740 572583 161489 619110 247168 439753 193368 296065 191962 134004 236515 988234 796426 500480 497291 014699 291795 / 523 > 3574 [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 (52, 115)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (52, 52+k, 116)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (52, m, 116)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (52, 52+k, 116)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (52, m, 116)-net over F3 with unbounded m | [i] | ||