A Census of Orthogonal Steiner Triple Systems of Order 15

Abstract

A Steiner triple system (STS) of order ν (STS(ν)) is a (ν,3,1)-balanced incomplete block design (BIBD). An STS (ν) is often represented by the pair ( V,B ) where V is the set of elements and B is the collection of blocks, or triples. Orthogonal STS's and the purpose of constructing Room squares are described in this chapter. The chapter presents the pairs of orthogonal STS's of orders 7, 13, and 19, conjecturing that such pairs exist for all orders. A brief survey of known results on orthogonal STS's is reviewed in the chapter. There exists only one pair of orthogonal STS (13)'s. The chapter describes the existence of exactly 19 nonequivalent pairs of orthogonal STS (15)'s involving 24 nonisomorphic systems.