  A brief review is given of the sign problem in finite density lattice QCD and
various attempts to overcome it. To date there is still no solution to this
problem which would work for realistic QCD. The main focus then is on the
deconfined phase, where QCD can be described by a dimensionally reduced
effective action. After summarizing derivation and validity of the effective
theory, it is demonstrated that it can be simulated efficiently in the presence
of a chemical potential for quarks $\mu/T\lsim 4$. Direct comparison of
simulations with imaginary and real $\mu$ suggests that equilibrium plasma
properties could be analytically continued from 4d QCD simulations at imaginary
$\mu$.
