Information on Result #1856869
There is no (18, 66)-sequence in base 4, because net from sequence would yield (18, m, 67)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (18, 197, 67)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4197, 67, S4, 3, 179), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 282433 580415 755626 993616 159437 829423 754811 571090 696321 715853 367121 633333 658092 005662 617460 515015 075313 301909 434519 257088 / 5 > 4197 [i]
- extracting embedded OOA [i] would yield OOA(4197, 67, S4, 3, 179), 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 (18, 66)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (18, m, 66)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (18, 66)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (18, m, 66)-net over F4 with m > ∞ | [i] | ||