Information on Result #1856199
There is no (29, m, 38)-net in base 2 for arbitrarily large m, because m-reduction would yield (29, 182, 38)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2182, 38, S2, 5, 153), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 637 518145 000209 765077 072363 294528 620385 395474 828378 505216 / 77 > 2182 [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 (29, 37)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (29, 29+k, 38)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (29, m, 38)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (29, 29+k, 38)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (29, m, 38)-net over F2 with unbounded m | [i] | ||