Information on Result #1849611
There is no (66, m, 76)-net in base 2 for arbitrarily large m, because m-reduction would yield (66, 447, 76)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2447, 76, S2, 6, 381), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 75591 227326 743116 617129 676020 352471 572778 701511 481078 269274 980714 786485 963793 384025 923869 274231 410818 319302 247051 682505 087598 569375 924224 / 191 > 2447 [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 (66, 75)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (66, 66+k, 76)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (66, m, 76)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (66, 66+k, 76)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (66, m, 76)-net over F2 with unbounded m | [i] | ||