The classification of the smallest nontrivial blocking sets in

We determine the smallest nontrivial blocking sets with respect to t-spaces in PG ( n , 2 ) , n ⩾ 3 . For t = n − 1 , they are skeletons of solids in PG ( n , 2 ) ; for 1 ⩽ t < n − 1 , they are cones with vertex an ( n − t − 3 ) -space π n − t − 3 and base the set of points on the edges of a tetrahedron in a solid skew to π n − t − 3 .