Information on Result #1856253
There is no (17, m, 63)-net in base 4 for arbitrarily large m, because m-reduction would yield (17, 185, 63)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4185, 63, S4, 3, 168), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 413644 108018 789698 761718 438551 312351 957624 215974 124562 187933 744234 024911 175385 755930 374377 187512 542127 608643 452928 / 169 > 4185 [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 (17, 62)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (17, 17+k, 63)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (17, m, 63)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (17, 17+k, 63)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (17, m, 63)-net over F4 with unbounded m | [i] | ||