Information on Result #1852032
There is no (20, m, 140)-net in base 7 for arbitrarily large m, because m-reduction would yield (20, 277, 140)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7277, 140, S7, 2, 257), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 60 583333 217025 632376 642604 420619 134235 784911 500367 919816 861378 984868 836145 835314 342631 038967 488518 752345 301455 492138 386110 468381 706218 346895 180334 602780 948018 896953 700242 297751 922134 903126 648843 532419 724463 548591 136214 559711 378810 081143 / 43 > 7277 [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 (20, 139)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (20, 20+k, 140)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (20, m, 140)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (20, 20+k, 140)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (20, m, 140)-net over F7 with unbounded m | [i] | ||