Information on Result #1849653
There is no (80, m, 90)-net in base 2 for arbitrarily large m, because m-reduction would yield (80, 621, 90)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2621, 90, S2, 7, 541), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2889 118738 270890 832116 830774 483674 468735 793808 758777 421860 297996 411436 759020 387444 152761 561121 687516 644495 481068 484007 314965 534148 209849 196281 211010 261106 701850 246871 733871 390204 456771 518464 / 271 > 2621 [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 (80, 89)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (80, 80+k, 90)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (80, m, 90)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (80, 80+k, 90)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (80, m, 90)-net over F2 with unbounded m | [i] | ||