Information on Result #520463
There is no (50, 106, 111)-net in base 2, because extracting embedded orthogonal array would yield OA(2106, 111, S2, 56), but
- adding a parity check bit [i] would yield OA(2107, 112, S2, 57), but
- the (dual) Plotkin bound shows that M ≥ 5192 296858 534827 628530 496329 220096 / 29 > 2107 [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 (50, 107, 111)-net in base 2 | [i] | m-Reduction | |
| 2 | No (50, 108, 111)-net in base 2 | [i] | ||
| 3 | No (50, 109, 111)-net in base 2 | [i] | ||
| 4 | No (50, 110, 111)-net in base 2 | [i] | ||
| 5 | No (50, 111, 111)-net in base 2 | [i] | ||
| 6 | No (50, 112, 111)-net in base 2 | [i] | ||
| 7 | No (50, 113, 111)-net in base 2 | [i] | ||