A second infinite family of Steiner triple systems without almost parallel classes.

Abstract: For each positive integer n, we construct a Steiner triple system of order with no almost parallel class; that is, with no set of disjoint triples. In fact, we construct families of -designs with an analogous property. The only previously known examples of Steiner triple systems of order congruent to without almost parallel classes were the projective triple systems of order with n odd, and 2 of the 11,084,874,829 Steiner triple systems of order 19. [Copyright &y& Elsevier]