Information on Result #1849719
There is no (102, m, 112)-net in base 2 for arbitrarily large m, because m-reduction would yield (102, 887, 112)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2887, 112, S2, 8, 785), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 412730 102449 738473 712765 456966 028598 842849 473465 719939 162469 303927 088986 372441 296464 388481 162232 178042 714371 088482 131780 376834 030861 473075 976983 576924 171544 459677 096874 222722 006821 498184 708157 072675 181959 539990 940740 647103 712157 608467 497577 161747 247257 452016 326357 811200 / 393 > 2887 [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 (102, 111)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (102, 102+k, 112)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (102, m, 112)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (102, 102+k, 112)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (102, m, 112)-net over F2 with unbounded m | [i] | ||