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

Positive-partial-transpose distinguishability for lattice-type maximally entangled states