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 $N(2,29,4,3)$ 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.