Pairwise balanced designs with block sizes 8, 9, and 10 (Q1352866)

The authors determine the spectrum of pairwise balanced designs with block sizes 8, 9, and 10 with few exceptions. They use results about the structure of Denniston arcs in projective planes to deduce properties of certain transversal designs and in turn use these to get the pairwise balanced designs. They utilize many other PBD techniques also and give several interesting constructions for four level thwarts.