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 ≡ 4 or 8 ( mod 12 ) . 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 ≡ 10 or 26 ( mod 48 ) , or if v ≡ 2 or 34 ( mod 96 ) with the possible exception v = 98 .