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This paper presents a number of theoretical and numerical results for two norms of optimal correlation matrices in relation to correlation control in Monte Carlo type sampling and the designs of experiments. The optimal correlation matrices are constructed for cases when the number of simulations (experiments) N sim is less than or equal to the stochastic dimension, i.e. the number of random variables (factors) N var . In such cases the estimated correlation matrix can not be positive definitedoi:10.1016/j.probengmech.2012.06.003 fatcat:zr3d3lzeujbgnkpsypssvt7cay