Information on Result #1856255
There is no (19, m, 70)-net in base 4 for arbitrarily large m, because m-reduction would yield (19, 206, 70)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4206, 70, S4, 3, 187), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 655767 521039 926610 160299 985568 508871 509777 445500 566969 530371 604912 210544 906420 855058 587696 756197 562568 810482 328823 171437 821952 / 47 > 4206 [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 (19, 69)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (19, 19+k, 70)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (19, m, 70)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (19, 19+k, 70)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (19, m, 70)-net over F4 with unbounded m | [i] | ||