Abstract: Global sensitivity indices play important roles in global sensitivity analysis based on ANOVA high-dimensional representation, Wang et al. (2012) showed that orthogonal arrays are A-optimality designs for the estimation of parameter , the definition of which can be seen in Section 2. This paper presented several other optimal properties of orthogonal arrays under ANOVA high-dimensional representation, including E-optimality for the estimation of and universal optimality for the estimation of , where is the independent parameters of . Simulation study showed that randomized orthogonal arrays have less biased and more precise in estimating the confidence intervals comparing with other methods.