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 .