On the number of mutually disjoint cyclic designs

We denote by LS[N](t; k; v) a large set of t-(v; k; lambda ) designs of size N, which is a partition of all k-subsets of a v-set into N disjoint t-(v; k;lambda )designs and $N={v-t choose k-t}/lambda$. We use the notation N(t; v; k; lambda) as the maximum possible number of mutually disjoint cyclic t-(v; k; lambda)designs. In this paper we give some new bounds for N(2;; 4; 3) and N(2; 31; 4; 2). Within these bounds we present the new large sets LS[9](2; 4;; 29); LS[13](2; 4; 29) and LS[7](2; 4; 31), where their existences were proved before.