On t-fold blocking sets in affine spaces and the sharpness of Bruenʼs bound

In this note we investigate the sharpness of Bruenʼs bound on the size of a t-fold blocking set in AG(n,q) with respect to the hyperplanes. We give a construction for t-fold blocking sets meeting Bruenʼs bound with t=q−n+2. This construction is used further to find the minimal size of a t-fold affine blocking set with t=q−n+1.