The existence of symmetric cyclic Steiner quadruple systems

A Steiner quadruple system of order $v$, denoted by $\operatorname{SQS}(v)$, is called cyclic if it admits $\mathbb Z_v$ as a group of automorphisms acting regularly on its point set. A cyclic system is called symmetric cyclic, or S-cyclic, if the multiplier $-1$ preserves each block orbit individua