Information on Result #1849599
There is no (62, m, 72)-net in base 2 for arbitrarily large m, because m-reduction would yield (62, 423, 72)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2423, 72, S2, 6, 361), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4852 171964 711426 004262 224822 250396 481013 764881 907679 006548 339266 075587 288659 844840 319955 210682 244261 670434 619182 456250 700704 776192 / 181 > 2423 [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 (62, 71)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (62, 62+k, 72)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (62, m, 72)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (62, 62+k, 72)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (62, m, 72)-net over F2 with unbounded m | [i] | ||