The nonexistence of projective planes of order 12 with a collineation group of order 8

In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. As a corollary of the result, we prove that there is no projective plane of order 12 admitting a collineation group of order 8. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 411–430, 2008