Information on Result #520201
There is no (24, 52, 57)-net in base 2, because extracting embedded orthogonal array would yield OA(252, 57, S2, 28), but
- adding a parity check bit [i] would yield OA(253, 58, S2, 29), but
- the (dual) Plotkin bound shows that M ≥ 144115 188075 855872 / 15 > 253 [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 (24, 53, 57)-net in base 2 | [i] | m-Reduction | |
| 2 | No (24, 54, 57)-net in base 2 | [i] | ||
| 3 | No (24, 55, 57)-net in base 2 | [i] | ||