We use a Jastrow-Slater wave function with an elliptical Fermi sea to describe the nematic state of the two-dimensional electron gas in a magnetic field and the Monte Carlo method to calculate a variational energy upper bound. These energy upper boun
ds are compared with other upper bounds describing stripe-ordered ground states which are obtained from optimized Hartree-Fock calculations and with those which correspond to an isotropic ground state. Our findings support the conclusions drawn in our previous study where the Fermi-hypernetted chain approximation was used instead of the Monte Carlo method. Namely, the nematic state becomes energetically favorable relative to the stripe-ordered Wigner crystal phase for the second excited Landau level and below a critical value of the layer ``thickness parameter which is very close to its value in the actual materials.
