Information on Result #1857420
There is no (6, 58)-sequence in base 8, because net from sequence would yield (6, m, 59)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (6, 115, 59)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8115, 59, S8, 2, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5447 059212 976419 840075 699626 342456 484391 841849 274667 668876 773493 543941 830710 151419 166294 063636 548505 567232 / 55 > 8115 [i]
- extracting embedded OOA [i] would yield OOA(8115, 59, S8, 2, 109), 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 (6, 58)-sequence in base 8 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (6, m, 58)-net in base 8 with m > ∞ | [i] | ||