D-optimal asymmetric orthogonal array plus p run designs

In a recent paper, Chatzopoulos et al. (2011) identified some sufficient conditions to describe a set of p runs which, when adjoined to a symmetric orthogonal array, would result in a Type 1 optimal orthogonal array plus p run design. In this paper we find conditions for sets of p runs which, when adjoined to an asymmetric orthogonal array, result in a D-optimal orthogonal array plus p run design.