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An accurate numerical calculation of the ground-state entropy associated to two-dimensional ±J Ising lattices is presented. The method is based on the use of the thermodynamic integration method. Total energy is calculated by means of the Monte Carlo method. Then the entropy (or degeneracy) of a state of interest is obtained by using thermodynamic integration starting at a known reference state. Results for small sizes are compared to exact values obtained by exhaustive scanning of the entire ground-state manifold, which serves as a test for the reliability of the simulation model developed here. The close agreement between simulated and exact results for energy and remnant entropy supports the validity of the technique used for describing the properties of ±J Ising lattices at the fundamental level. Finally, the results are extrapolated in order to estimate tendencies for larger systems.