We consider problem of constructing search designs for 3m factorial designs. By using projection properties of some three-level orthogonal arrays, some search designs are obtained for 3 ≤ m ≤ 11. The new obtained orthogonal search designs are capable to search and identify up to four 2-factor interactions and estimate them along with the general mean and main effects. The resulted designs have very high searching probabilities; it means that besides of the well-known orthogonal structure, they have high ability in searching the true effects.
