<p>Meta Gaussian distributions, also known as multivariate Gaussian copula models, are a type of statistical distribution that is particularly useful in modeling dependencies among variables. The key advantage of meta Gaussian distributions is their flexibility - they can capture a wide range of dependency structures, making them a powerful tool for statistical modeling. Discrete approximations of continuous multivariate distributions, such as meta Gaussian distributions, which are of significant importance, are widely utilized across numerous disciplines. This paper introduces a new resampling method based on mean square error representative points (<i>MSE</i>-RPs) to construct accurate approximations for meta Gaussian distributions, thereby enhancing precision in statistical analysis. We carry out a systematic examination of the structural patterns and characteristics of <i>MSE</i>-RPs of these distributions. From a theoretical perspective, we analyze the invariance properties in copula-based association measures by leveraging group theory. This allows us to identify more stable invariants that are suitable for complex dependency structures. Through a simulation study, we demonstrate that <i>MSE</i>-RPs achieve significantly higher estimation accuracy for mean vectors and correlation matrices compared to Monte Carlo (<i>MC</i>) and Quasi-Monte Carlo (<i>QMC</i>) methods. Furthermore, <i>MSE</i>-RPs offer faster computation relative to the <i>QMC</i> method based on generalized good lattice points (<i>GGLP</i>) sets. Finally, we illustrate the practical advantages of our approach through empirical analysis on real-world datasets.</p>