Partial geometric designs with block sizes three and four

Abstract

In this paper, we focus on partial geometric designs with block sizes three and four. First, we show that a partial geometric design with block size three is a 2‐design, or a transversal design, or each line of a generalized quadrangle that is repeated λ times. Second, we introduce the concept of type of partial geometric designs with block size four and characterize partial geometric designs of type [λ,1,1] for some integer λ≥1.