More mutually disjoint Steiner systems S(5,8,24)

Kramer and Magliveras constructed simple 5-(24,8,λ) designs for λ⩽9. Betten et al. constructed simple 5-(24,8,λ) designs for λ=16,17,…,484. In this paper, we construct 15 mutually disjoint Steiner systems S(5,8,24) and thus we construct simple 5-(24,8,λ) design for λ=10,11,12,13,14 and 15. As a consequence there exists a simple 5-(24,8,λ) design for any positive integer λ⩽λmax=969.