Information on Result #1849572
There is no (53, m, 62)-net in base 2 for arbitrarily large m, because m-reduction would yield (53, 426, 62)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2426, 62, S2, 7, 373), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 33618 620041 214880 172388 271982 734889 904166 799538 931775 973942 064914 952283 357143 210679 359689 674012 692384 430868 432907 018308 426311 663616 / 187 > 2426 [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, 61)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (53, 53+k, 62)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (53, m, 62)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (53, 53+k, 62)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (53, m, 62)-net over F2 with unbounded m | [i] | ||