Information on Result #1856626
There is no (26, 62)-sequence in base 3, because net from sequence would yield (26, m, 63)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (26, 247, 63)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3247, 63, S3, 4, 221), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 317806 246861 327692 649610 852285 462512 835434 043915 247229 061739 424851 477075 056621 938593 968379 410401 484960 703396 297551 210415 / 37 > 3247 [i]
- extracting embedded OOA [i] would yield OOA(3247, 63, S3, 4, 221), 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 (26, 62)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (26, m, 62)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (26, 62)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (26, m, 62)-net over F3 with m > ∞ | [i] | ||