The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). The main idea is to embed the covariance matrix in a larger nested block circulant matrix, whose factorization can be rapidly computed thanks to the fast FFT algorithm. The CEM requires that the extended matrix is at least positive semidefinite which is proved to be the case if the enclosing domain is sufficiently large. In this paper, we study the Matérn family of covariances and we propose algorithms for this family of covariances based on fitting functions to compute good estimates of the required enclosing domain size for the CEM algorithm to work. The fitting functions are inspired by the theoretical work from [Graham et al, SIAM Journal on Numerical Analysis, 2018] and the function parameters estimations are done with numerical simulations. Several numerical tests are performed to show the efficiency of the proposed algorithms.