Construction of two \((15, 3,1)\) block designs
It is known that there are 80 distinct 2--(15,3,1) designs, of which the classical one is the points and lines of \(PG (3,2)\). Here, two non-isomorphic designs are constructed from the \(10_3\) configuration whose points are the vertices of a tetrahedron \(T\) and the midpoints of its edges in an affine space over a field of characteristic not 2 or 3. Adding the centroids of the faces and the centroid of \(T\) completes the 15 points. The two designs are constructed from these 15 points, and one is \(PG (3,2)\).
scientific article; zbMATH DE number 878374