An octagon quadrangle [] is the graph consisting of an 8-cycle with the two additional edges and . An octagon quadrangle system of order and index [ or ] is a pair , where is a finite set of vertices and is a collection of edge disjoint (blocks) which partition the edge set of defined on . In this paper (i) -perfect , (ii) -perfect and (iii) strongly perfect are studied for , that is the smallest index for which the spectrum of the admissible values of is the largest possible. This paper is the continuation of Berardi et al. (2010) [1], where the spectrum is determined for , that is the index for which the spectrum of the admissible values of is the minimum possible.