University of IsfahanTransactions on Combinatorics2251-86573120140301On the number of mutually disjoint cyclic designs713382010.22108/toc.2014.3820ENMojgan EmamiDepartment of Mathematics, University of ZanjanOzra NaserianDepartment of Mathematics, University of ZanjanJournal Article20121216We 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 $N(2,29,4,3)$ 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.http://toc.ui.ac.ir/article_3820_cf20d0b9a831a25a6c55e7bf6461ca78.pdf