A Difference Set in $$\left( {\mathbb{Z}/4\mathbb{Z}} \right)^3 \times \mathbb{Z}/5\mathbb{Z} $$.

We present a (320, 88, 24)-difference set in $$\left( {\mathbb{Z}/4\mathbb{Z}} \right)^3 \times \mathbb{Z}/5\mathbb{Z} $$ , the existence of which was previously open. This new difference set improves a theorem of Davis-Jedwab with the removal of the “exceptional” case. It also enables us to state a theorem of Schmidt on Davis-Jedwab difference sets more neatly. [ABSTRACT FROM AUTHOR]