Mirror symmetric orthogonal Latin hypercubes (MSOLHs) are efficient designs for computer experiments as they enjoy both high-order orthogonality and one-dimensional maximum stratification. The construction of MSOLHs is limited and challenging. In this talk, we propose a construction method for MSOLHs using orthogonal arrays from Reed-Solomon codes. Theoretical results guarantee that the resulting MSOLHs enjoy attractive orthogonality and low-dimensional space-filling properties. Moreover, some of them are optimal under the maximin distance criterion. Simulation comparisons are also provided to demonstrate the superiority of the proposed MSOLHs over existing designs.