  We study the distinguishability of a particular type of maximally entangled
states -- the "lattice states" using a new approach of semidefinite program.
With this, we successfully construct all sets of four ququad-ququad orthogonal
maximally entangled states that are locally indistinguishable and find some
curious sets of six states having interesting property of distinguishability.
Also, some of the problems arose from \cite{CosentinoR14} about the
PPT-distinguishability of "lattice" maximally entangled states can be answered.
