Information on Result #1849716
There is no (101, m, 111)-net in base 2 for arbitrarily large m, because m-reduction would yield (101, 879, 111)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2879, 111, S2, 8, 778), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3232 515060 202053 280445 682582 878466 174530 910915 229564 367268 558415 522708 662799 784372 699605 096602 638738 186102 789189 088571 170529 500905 770521 552085 359655 206890 416568 955387 628189 678217 488686 954452 558323 100546 206553 444672 597646 261495 609394 442705 633630 090745 121840 987243 544576 / 779 > 2879 [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 (101, 110)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (101, 101+k, 111)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (101, m, 111)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (101, 101+k, 111)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (101, m, 111)-net over F2 with unbounded m | [i] | ||