A construction for 2-chromatic Steiner quadruple systems

In 1971, Doyen and Vandensavel gave a special doubling construction that gives a direct construction of 2-chromatic SQS(v) for all v≡4v≡4 or 8(mod12). In this paper, we introduce the concept of a 2-chromatic candelabra quadruple system, and use it to provide a construction for 2-chromatic SQS. It is proved that a 2-chromatic SQS(v) exists if v≡10v≡10 or 26(mod48), or if v≡2v≡2 or 34(mod96) with the possible exception v=98v=98.