  An unextendible product basis (UPB) is a set of orthogonal product states
which span a subspace of a given Hilbert space while the complementary subspace
contains no product state. These product bases are useful to produce bound
entangled (BE) states. In this work we consider reducible and irreducible UPBs
of maximum size, which can produce BE states of minimum rank. From a reducible
UPB, it is possible to eliminate one or more states locally, keeping the
post-measurement states orthogonal. On the other hand, for an irreducible UPB,
the above is not possible. Particularly, the UPBs of the present size are
important as they might be useful to produce BE states, having ranks of the
widest variety, which satisfy the range criterion. Here we talk about such BE
states. We also provide other types of BE states and analyze certain properties
of the states. Some of the present BE states are associated with the tile
structures. Furthermore, we provide different UPBs corresponding to the present
BE states of minimum rank and discuss important properties of the UPBs.
