Abstract
Using basis reduction, we settle the existence problem for 4-(21,5,lambda) designs with lambda is-an-element-of {3,5,6,8). These designs each have as an automorphism group the Frobenius group G of order 171 fixing two points. We also show that a 4-(21, 5, 1) design cannot have the subgroup of order 57 of G as an automorphism group.