New infinite classes of 2‐chromatic Steiner quadruple systems

Abstract

In 1971, Doyen and Vandensavel gave a special doubling construction that gives a direct construction of 2‐chromatic Steiner quadruple system of order v $v$ (SQS ( v ) $(v)$ ) for all v ≡ 4 $v\equiv 4$ or 8 ( mod 12 ) $8\,(\mathrm{mod}\,12)$ . The first author presented a construction for 2‐chromatic SQSs based on 2‐chromatic candelabra quadruple systems and s $s$ ‐fan designs. In this paper, it is proved that a 2‐chromatic SQS ( v ) $(v)$ also exists if v ≡ 10 ( mod 12 ) $v\equiv 10\,(\mathrm{mod}\,12)$ , or if v ≡ 2 ( mod 24 ) $v\equiv 2\,(\mathrm{mod}\,24)$ .