Information on Result #1856879
There is no (28, 97)-sequence in base 4, because net from sequence would yield (28, m, 98)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (28, 290, 98)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4290, 98, S4, 3, 262), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1171 356781 376623 073310 539939 549049 092006 382069 343339 273833 002633 655961 258104 534922 918618 475426 047061 070734 571873 612435 911168 064802 476773 730406 298590 562566 043253 049672 896239 108096 / 263 > 4290 [i]
- extracting embedded OOA [i] would yield OOA(4290, 98, S4, 3, 262), 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 (28, 97)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (28, m, 97)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (28, 97)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (28, m, 97)-net over F4 with m > ∞ | [i] | ||