  Entangled states with a positive partial transpose (PPTES) have interest both
in quantum information and in the theory of positive maps. In $3\otimes 3$
there is a conjecture by Sanpera, Bru{\ss} and Lewenstein [PRA, 63, 050301]
that all PPTES have Schmidt number two (or equivalently that every 2-positive
map between $3\times 3$ matrices is decomposable). In order to prove or
disprove the conjecture it is sufficient to look at edge PPTES. Here the rank m
of the PPTES and the rank n of its partial transpose seem to play an important
role. Until recently all known examples of edge PPTES had ranks (4,4) or (6,7).
In a recent paper Ha and Kye [quant-ph/0509079] managed to find edge PPTES for
all ranks except (5,5) and (6,6). Here we complement their work and present
edge PPTES with those ranks.
