Information on Result #1850880
There is no (29, m, 101)-net in base 4 for arbitrarily large m, because m-reduction would yield (29, 299, 101)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4299, 101, S4, 3, 270), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 302 914636 528312 485971 405774 049454 764023 908574 953697 893699 682985 067417 655233 142294 687178 614573 138576 983038 445722 624957 610314 846028 505059 597475 741862 890319 349155 466271 648310 195229 032448 / 271 > 4299 [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 (29, 100)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (29, 29+k, 101)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (29, m, 101)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (29, 29+k, 101)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (29, m, 101)-net over F4 with unbounded m | [i] | ||