More on halving the complete designs

Abstract A large set of disjoint S (λ; t , k , v ) designs, denoted by LS (λ; t , k , v ), is a partition of k -subsets of v -set into S (λ; t , k , v ) designs. In this paper, we develop some recursive methods to construct large sets ot t -designs. As a consequence, we show that a conjecture of Hartman on halving complete designs is true for t = 2 and 3 ⩽ k ⩽ 15.