Existence conditions for balanced fractional 3m factorial designs of resolution R({00,10,01,20,11})

We consider a fractional 3(m) factorial design derived from a simple array (SA) such that the non negligible factorial effects are the general mean, the linear and the quadratic components of the main effect, and the linear-by-linear and the linear-by-quadratic components of the two-factor interaction. If these effects are estimable, then a design is said to be of resolution R({00, 10, 01, 20, 11}). In this paper, we give a necessary and sufficient condition for an SA to be a balanced fractional 3(m) factorial design of resolution R({00, 10, 01, 20, 11}). Such a design is concretely characterized by the suffixes of the indices of an SA.