  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 bounds 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.
