Information on Result #1857271
There is no (8, 63)-sequence in base 7, because net from sequence would yield (8, m, 64)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (8, 125, 64)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7125, 64, S7, 2, 117), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 333999 431003 545482 755376 316309 265495 380733 140585 771192 834356 762366 331846 319516 550942 904758 800305 436017 702139 / 59 > 7125 [i]
- extracting embedded OOA [i] would yield OOA(7125, 64, S7, 2, 117), 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 (8, 63)-sequence in base 7 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (8, m, 63)-net in base 7 with m > ∞ | [i] | ||
| 3 | No digital (8, 63)-sequence over F7 (for arbitrarily large k) | [i] | ||
| 4 | No digital (8, m, 63)-net over F7 with m > ∞ | [i] | ||