SERIES OF MAIN EFFECT PLUS ONE OR TWO PLANS FOR 2^m FACTORIALS WHEN THREE-FACTOR AND HIGHER ORDER INTERACTIONS ARE NEGLIGIBLE

Abstract

This paper constructs a series of main effect plus k (=1, 2) plans for 2^m factorials in the absence of three-factor and higher order interactions. These plans are derived from balanced arrays of strength 4. In particular, the nonisomorphic simple graphs with 4 vertices are useful in obtaining plans for k=2. It is shown that the plans obtained for each m≥4 when k=1 and for each m≥5 when k=2, are of the minimum values of treatments among plans derived from balanced arrays of strength 4.