Information on Result #1857423
There is no (9, 80)-sequence in base 8, because net from sequence would yield (9, m, 81)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (9, 159, 81)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8159, 81, S8, 2, 150), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 78 043713 757899 805784 539930 744829 157643 714953 566624 278771 478923 990634 293470 494140 503007 652576 587299 278995 673278 035165 572386 199391 982207 132657 254400 / 151 > 8159 [i]
- extracting embedded OOA [i] would yield OOA(8159, 81, S8, 2, 150), 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 (9, 80)-sequence in base 8 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (9, m, 80)-net in base 8 with m > ∞ | [i] | ||