Information on Result #1856322
There is no (7, m, 120)-net in base 16 for arbitrarily large m, because m-reduction would yield (7, 111, 120)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16111, 120, S16, 104), but
- the linear programming bound shows that M ≥ 92086 954283 537596 660104 192126 770459 664696 363604 028357 116797 528075 544556 954927 352946 662893 970276 794850 999821 883009 523266 007059 187150 407449 182208 / 1974 452051 > 16111 [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 (7, 119)-sequence in base 16 | [i] | Net from Sequence | |
| 2 | No (7, 7+k, 120)-net in base 16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (7, m, 120)-net in base 16 with unbounded m | [i] | ||
| 4 | No digital (7, 7+k, 120)-net over F16 for arbitrarily large k | [i] | ||
| 5 | No digital (7, m, 120)-net over F16 with unbounded m | [i] | ||