Information on Result #1856649
There is no (49, 109)-sequence in base 3, because net from sequence would yield (49, m, 110)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (49, 544, 110)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3544, 110, S3, 5, 495), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5048 724587 122425 577275 101757 319130 788548 515367 006696 429671 931108 972073 453425 248775 181485 336665 367346 275384 392035 748694 002292 597541 117361 799478 623513 230660 068926 845938 192778 244867 811520 875056 405598 755215 259235 017197 921517 391945 748112 361990 710921 906430 979595 646221 / 124 > 3544 [i]
- extracting embedded OOA [i] would yield OOA(3544, 110, S3, 5, 495), 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 (49, 109)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (49, m, 109)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (49, 109)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (49, m, 109)-net over F3 with m > ∞ | [i] | ||