Information on Result #1851996
There is no (8, m, 64)-net in base 7 for arbitrarily large m, because m-reduction 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]
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 | [i] | Net from Sequence | |
| 2 | No (8, 8+k, 64)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (8, m, 64)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (8, 8+k, 64)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (8, m, 64)-net over F7 with unbounded m | [i] | ||