On the non-existence of a class of symmetric group divisible partial designs

Many non-existence theorems are known for symmetric group divisible partial designs. In the case that these partial designs are auto-dual with ₁=0, an ideal incidence structure can be defined whose elements are the equivalence-classes of non-collinear points and parallel blocks. Except for some trivial cases this incidence structure turns out to be a symmetric design, and by studying its existence we can prove much more powerful non-existence theorems.