Information on Result #1858346
There is no (3, 200)-sequence in base 49, because net from sequence would yield (3, m, 201)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (3, 199, 201)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49199, 201, S49, 196), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 547 250302 168056 542712 127228 243331 087649 877436 679853 093167 709703 757719 531581 746045 010739 284234 843576 403699 976867 641269 307762 478550 853513 188644 458604 264341 923552 200333 719864 313805 849803 317895 396455 294394 665441 374378 490890 124885 441116 981991 327777 984582 367683 962185 673163 698596 949848 453152 616585 565558 638415 979099 195017 460030 489973 646561 200005 / 197 > 49199 [i]
- extracting embedded OOA [i] would yield OA(49199, 201, S49, 196), but
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 (3, 200)-sequence in base 49 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (3, m, 200)-net in base 49 with m > ∞ | [i] | ||
| 3 | No digital (3, 200)-sequence over F49 (for arbitrarily large k) | [i] | ||
| 4 | No digital (3, m, 200)-net over F49 with m > ∞ | [i] | ||