Simple 8-(40, 11, 1440) designs (Q1302150)

A simple \(t\)-\((v,k,\lambda)\) design \(D= (V,B)\) is a set \(B\) of \(k\)-subsets of a \(v\)-set \(V\) such that each \(t\)-subset of \(V\) appears exactly \(\lambda\) times in \(B\). This short note deals with the existence of simple 8-(40, 11, 1440) designs with automorphism group A-PSL(4,3). The construction of these designs (numbering more than 100,000; of which the authors are not able to construct all) is carried out by applying the method of Kramer and Mesner [see \textit{E. S. Kramer} and \textit{D. M. Mesner}, Discrete Math. 15, 263-296 (1976; Zbl 0362.05049)] and using the software package DISCRETA.