Information on Result #1849623
There is no (70, m, 80)-net in base 2 for arbitrarily large m, because m-reduction would yield (70, 472, 80)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2472, 80, S2, 6, 402), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 463059 963052 986404 917795 152138 041035 060046 749663 699514 003524 679344 400542 934589 835210 535680 361110 949529 697129 462461 590067 033957 438754 499286 007808 / 403 > 2472 [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 (70, 79)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (70, 70+k, 80)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (70, m, 80)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (70, 70+k, 80)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (70, m, 80)-net over F2 with unbounded m | [i] | ||