Information on Result #1849749
There is no (112, m, 123)-net in base 2 for arbitrarily large m, because m-reduction would yield (112, 851, 123)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2851, 123, S2, 7, 739), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 993998 952924 100522 344655 894010 924650 217856 103768 335881 512642 475885 719991 313431 268628 022225 644736 294611 430738 206263 306113 405191 434472 793415 257097 202332 429545 141134 722818 360171 143086 282141 025359 354229 236532 324197 114103 740371 772216 307448 774588 011465 958351 699968 / 185 > 2851 [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 (112, 122)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (112, 112+k, 123)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (112, m, 123)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (112, 112+k, 123)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (112, m, 123)-net over F2 with unbounded m | [i] | ||