(Received January 11, 1990; revised July 30, 1990)
Abstract. In the absence of four-factor and higher order interactions, we present a series of search designs for 2m factorials (m > 6) which allow the search of at most k (= 1,2) nonnegligible three-factor interactions, and the estimation of them along with the general mean, main effects and two-factor interactions. These designs are derived from balanced arrays of strength 6. In particular, the nonisomorphic weighted graphs with 4 vertices in which two distinct vertices are assigned with integer weight omega (1 < omega < 3), are useful in obtaining search designs for k = 2. Furthermore, it is shown that a search design obtained for each m > 6 is of the minimum number of treatments among balanced arrays of strength 6. By modifying the results for m > 6, we also present a search design for m =5 and k = 2.
Key words and phrases: Search design, minimum treatment, balanced array, strength 6, weighted graph, isomorphic graph.