Information on Result #1851612
There is no (24, m, 111)-net in base 5 for arbitrarily large m, because m-reduction would yield (24, 329, 111)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5329, 111, S5, 3, 305), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5029 144521 642009 921749 447612 543500 221588 403977 220314 109346 553710 201583 597989 648060 971971 296184 756930 456405 439154 845724 221770 381994 049242 504954 586091 004181 464648 261676 454775 148437 205694 692988 915128 761817 641134 257428 348064 422607 421875 / 51 > 5329 [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 (24, 110)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (24, 24+k, 111)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (24, m, 111)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (24, 24+k, 111)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (24, m, 111)-net over F5 with unbounded m | [i] | ||