Information on Result #520265
There is no (31, 67, 72)-net in base 2, because extracting embedded orthogonal array would yield OA(267, 72, S2, 36), but
- adding a parity check bit [i] would yield OA(268, 73, S2, 37), but
- the (dual) Plotkin bound shows that M ≥ 7083 549724 304467 820544 / 19 > 268 [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 (31, 68, 72)-net in base 2 | [i] | m-Reduction | |
| 2 | No (31, 69, 72)-net in base 2 | [i] | ||
| 3 | No (31, 70, 72)-net in base 2 | [i] | ||