Nuclei of point sets of sizeq+1 contained in the union of two lines inPG(2,q)

Abstract

We give a complete classification for pairs ( $$\mathcal{N}$$ (ℬ),ℬ) where $$\mathcal{N}$$ (ℬ) is the set of all nuclei of a set ℬ ofq+1 not collinear points contained in the union of two lines in a desarguesian planePG(2,q) of orderq. We also obtain some new results concerning blocking sets of Redei type and certain point-sets of type [0,1,m,n] inPG(2, q).