On the arithmetic of one del Pezzo surface over the field with three   elements
  We discuss the problem of existence of rational curves on a certain del Pezzo surface from a computational point of view and suggest a computer algorithm implementing search. In particular, our computations reveal that the surface contains 920 rational curves with parametrizations of degree 8 and does not contain rational curves for a smaller degree. 
Nikita Kozin, Deepak Majeti
math.NT