We denote by LS[N ](t, k, v) a large set of t-(v, k, λ) designs of size N , which is a partition of all k-subsets of a v-set into N disjoint t-(v, k, λ) designs and N = ( v−t k−t ) /λ. We use the notation N(t, v, k, λ) as the maximum possible number of mutually disjoint cyclic t-(v, k, λ)designs. In this paper we give some new bounds for N(2, 29, 4, 3) and N(2, 31, 4, 2). Consequently we presen...