Partial geometric designs from group actions

Jerod Michel, Qi Wang

Abstract: In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $$1\frac{1}{2}$$ 1 1 2 -designs). Using this new method, we construct several infinite families of partial geometric designs by investigating the actions of various linear groups of degree two on certain subsets of $${\mathbb {F}}_{q}^{2}$$ F q 2 . Moreover, by computing the stabilizers of such subsets in various linear groups of degree two, we are also able to construct a new infinite family of balanced incomplete block designs.