On blocking sets in a design

In this paper we give a bound for the cardinality of an intersection set of a 2-(v,k,λ) design D. We give a new proof of Drakeʹs inequality for the cardinality of a blocking set of D. Our proof will enable us to characterize the case of equality. We investigate the existence of the blocking sets of type (1,s) in a design. We prove some non-existence theorems and give some bounds for the parameters of a design containing such a blocking set.