Transitive latin bitrades
  In this note we give two results. First, if a latin bitrade $(T_1, T_2)$ is primary, thin, separated, and the autotopism group of $T_1$ acts regularly on $T_1$, then $(T_1, T_2)$ may be derived from a group-based construction. Second, if a latin bitrade $(T_1, T_2)$ has genus 0 then the disjoint mate $T_2$ is unique and the autotopism group of $T_1$ is equal to the autotopism group of $T_2$. 
Carlo Hamalainen, Nicholas J. Cavenagh