Information on Result #1850886
There is no (31, m, 107)-net in base 4 for arbitrarily large m, because m-reduction would yield (31, 423, 107)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4423, 107, S4, 4, 392), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 84459 564324 052877 587175 524074 479139 689757 295427 431914 787626 368146 079605 079466 356714 408364 734028 728034 546232 715827 936454 465805 269995 900236 694816 435199 698933 050446 927879 147653 995037 068936 252885 888599 772389 076404 544236 216314 252701 942591 726906 231445 473743 339520 / 131 > 4423 [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 (31, 106)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (31, 31+k, 107)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (31, m, 107)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (31, 31+k, 107)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (31, m, 107)-net over F4 with unbounded m | [i] | ||