Degree of Unirationality for del Pezzo Surfaces over Finite Fields

We address the question of the degree of unirational parameterizations of degree four and degree three del Pezzo surfaces. Specifically we show that degree four del Pezzo surfaces over finite fields admit degree two parameterizations and minimal cubic surfaces admit parameterizations of degree 6. It is an open question whether or not minimal cubic surfaces over finite fields can admit degree 3 or 4 parameterizations.