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 , where each item has a unique label, or partially labeled ) and different lattice dimensions.