ON THE NUMBER OF MUTUALLY DISJOINT CYCLIC DESIGNS.

We denote by LS[N](t, k, v) a large set of t-(v, k, λ) designs of size N, which is a partition v-t of all k-subsets of a v-set into N disjoint t-(v, k, λ) designs and N = (ktv-t)/λ. We use the notation k-t 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 present new large sets LS[9](2, 4, 29),LS[13](2, 4, 29) and LS[7](2, 4, 31), where their existences were already known. [ABSTRACT FROM AUTHOR]