Bi-Cayley normal uniform multiplicative designs

A study of normal uniform multiplicative designs admitting groups of automorphisms which act semiregularly on points and blocks and with two orbits is made. We call these designs Bi-Cayley normal uniform multiplicative designs (BCNUMD). It is also determined when the incidence matrices of such designs have maximum determinant. An infinite family of BCNUMDs is constructed which gives rise to symmetric designs.