Explicit brill-noether-petri general curves

Let p1;⋯; pg be the points in A2.(ℚ ⊂ ℙ2.(ℚ) with coordinates (equation Presented) respectively. We prove that, for any genus g, a plane curve of degree 3g having a g-tuple point at p1;⋯; p8, and a (g - 1)-tuple point at pg, and no other singularities, exists and that the general plane curve of that degree and with those singularities is a Brill-Noether-Petri general curve of genus g