Before revision:  We systematically analyze the intrinsic optimality structure, which is fairly rich and intriguing, under different levels of item distinguishability (fully labeled  or partially labeled  ) and different lattice dimensions.
After revision:  We systematically analyze the intrinsic optimality structure, which is fairly rich and intriguing, under different levels of item distinguishability (fully labeled or partially labeled , where multiple items may be of the same type ) and different lattice dimensions.