Unital designs with blocking sets

A unital 2-(28, 4, 1) design has 28 points, each block has size 4 and every pair of points is on exactly one block. A blocking set in a design is a subset of the point set with the property that every block intersects the blocking set nontrivially but no block is contained in the blocking set. In this work, we classify the unital 2-(28, 4, 1) designs with blocking sets. We find 68,806 unitals with a blocking set. Of these, 68,484 have a trivial automorphism group.