Information on Result #1856651
There is no (51, 113)-sequence in base 3, because net from sequence would yield (51, m, 114)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (51, 564, 114)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3564, 114, S3, 5, 513), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 34 833079 033725 498407 483846 277852 064926 643632 588192 760492 289168 367295 159322 738941 334952 889116 558263 158580 492438 381019 102044 859491 978828 181077 461020 406303 337996 253130 726598 583112 772843 556884 183546 562314 759813 759534 292706 198110 579942 398950 756516 636054 075810 107747 093052 299399 / 257 > 3564 [i]
- extracting embedded OOA [i] would yield OOA(3564, 114, S3, 5, 513), 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 (51, 113)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (51, m, 113)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (51, 113)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (51, m, 113)-net over F3 with m > ∞ | [i] | ||