Information on Result #1850274
There is no (53, m, 118)-net in base 3 for arbitrarily large m, because m-reduction would yield (53, 584, 118)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3584, 118, S3, 5, 531), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 60074 732088 444453 280705 277157 101490 553823 338281 143501 150748 127312 257853 807628 492485 274420 351708 699444 017276 510796 645059 964300 976644 665433 396175 753735 044015 118064 909490 174363 739469 303649 952987 723372 252353 039260 288489 185987 352767 177915 338072 721616 793074 230635 871095 614636 978433 163978 / 133 > 3584 [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 (53, 117)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (53, 53+k, 118)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (53, m, 118)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (53, 53+k, 118)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (53, m, 118)-net over F3 with unbounded m | [i] | ||