New infinite classes of 2‐chromatic Steiner quadruple systems.

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(mod12) $8\,(\mathrm{mod}\,12)$. 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(mod12) $v\equiv 10\,(\mathrm{mod}\,12)$, or if v≡2(mod24) $v\equiv 2\,(\mathrm{mod}\,24)$. [ABSTRACT FROM AUTHOR]