Information on Result #520184
There is no (22, 48, 53)-net in base 2, because extracting embedded orthogonal array would yield OA(248, 53, S2, 26), but
- adding a parity check bit [i] would yield OA(249, 54, S2, 27), but
- the (dual) Plotkin bound shows that M ≥ 4503 599627 370496 / 7 > 249 [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 (22, 49, 53)-net in base 2 | [i] | m-Reduction | |
| 2 | No (22, 50, 53)-net in base 2 | [i] | ||
| 3 | No (22, 51, 53)-net in base 2 | [i] | ||