Information on Result #1856873
There is no (22, 78)-sequence in base 4, because net from sequence would yield (22, m, 79)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (22, 233, 79)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4233, 79, S4, 3, 211), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11241 648221 963106 790253 554477 404590 578562 456690 504962 030071 427039 666560 827048 716527 532840 581100 221331 691271 297373 229415 944301 181950 562062 565376 / 53 > 4233 [i]
- extracting embedded OOA [i] would yield OOA(4233, 79, S4, 3, 211), 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 (22, 78)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (22, m, 78)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (22, 78)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (22, m, 78)-net over F4 with m > ∞ | [i] | ||