A SERIES OF SEARCH DESIGNS FOR 2^{m} FACTORIAL DESIGNS OF RESOLUTION V WHICH PERMIT SEARCH OF ONE OR TWO

UNKNOWN EXTRA THREE-FACTOR INTERACTIONS

TERUHIRO SHIRAKURA^{1} AND SHINSEI TAZAWA^{2}

1Department of Mathematics, Kobe University, Nada-ku, Kobe 657, Japan 2Department of Mathematics, Kinki University, Higashi-Osaka 577, Japan

(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 2^{m} 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 ω (1 ≤ ω ≤ 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.