Information on Result #1857126
There is no (14, 69)-sequence in base 5, because net from sequence would yield (14, m, 70)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (14, 206, 70)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5206, 70, S5, 3, 192), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 218 777880 862305 763141 783501 890707 492833 251052 806603 532023 086130 988700 349634 056449 104123 060188 013369 346143 356664 047274 762197 048403 322696 685791 015625 / 193 > 5206 [i]
- extracting embedded OOA [i] would yield OOA(5206, 70, S5, 3, 192), but
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 (14, 69)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (14, m, 69)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (14, 69)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (14, m, 69)-net over F5 with m > ∞ | [i] | ||