An improved finiteness theorem for graphical \(t\)-designs (Q5939924)

This is a short note in which the author improves a result of \textit{A. Betten, M. Klin, R. Laue}, and \textit{A. Wassermann} [Graphical \(t\)-designs via polynomial Kramer-Mesner matrices, Discrete Math. 197/198, 83-109 (1999; Zbl 0936.05011)] and proves that there exist only finitely many nontrivial graphical \(t\)-\(({n\choose 2},k,\lambda)\) designs when \( k \leq 4t / 3 \). The proof uses Alltop's lemma about the degrees of polynomials in the polynomial Kramer-Mesner matrix.