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 v=2(3n)+1 with no almost parallel class; that is, with no set of v-13 disjoint triples. In fact, we construct families of (v,k,λ)-designs with an analogous property. The only previously known examples of Steiner triple systems of order congruent to 1 (mod 6) without almost parallel classes were the projective triple systems of order 2n - 1 with n odd, and 2 of the 11,084,874,829 Steiner triple systems of order 19