On designs related to coherent configurations of type $\text{(}{}^2{}^2{}_4\text{)}$

Abstract

Coherent configurations of type $\text{(}{}^2{}^2{}_4\text{)}$ correspond to certain complementary pairs of 2-designs with two or three intersection sizes, which are investigated in this paper. We establish relations on the parameters of such designs, and use them to show the Witt design $\text{L}$(5, 8, 24) is determined by the association scheme on its blocks, and to characterize the family of designs based on systems of linked symmetric designs.