A short proof of the nonexistence of a 2-resolvable balanced incomplete block design with parameters (v,b,r,k,λ)=(10,15,6,4,2)

The nonexistence of a 2-resolvable balanced incomplete block design with parameters (v,b,r,k,λ)=(10,15,6,4,2) was established by Kadowaki in 2001 using a computer search and by Kadowaki and Kageyama in 2008 by a lengthy case-by-case analysis. We give a short proof based on properties of the row sum vectors of submatrices in an incidence matrix.