Information on Result #520168
There is no (20, 44, 49)-net in base 2, because extracting embedded orthogonal array would yield OA(244, 49, S2, 24), but
- adding a parity check bit [i] would yield OA(245, 50, S2, 25), but
- the (dual) Plotkin bound shows that M ≥ 562 949953 421312 / 13 > 245 [i]
Mode: Bound.
Optimality
Show details for fixed k and m, k and s, k and t, 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 (20, 45, 49)-net in base 2 | [i] | m-Reduction | |
| 2 | No (20, 46, 49)-net in base 2 | [i] | ||
| 3 | No (20, 47, 49)-net in base 2 | [i] | ||