On The Set $J_o(v)$ for Steiner Quadruple Systems

Abstract

We prove that for every $v\equiv 4,8(\mathrm{mod}12)$ with $v\ge 16$, there exists a pair of $S(3,4,v)$s having exactly $k\in \{0,1,\dots ,\lfloor \frac{v}{4}\rfloor \}$ pairwise disjoint blocks in common.