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.
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Emami, M. and Naserian, O. (2014). On the number of mutually disjoint cyclic designs. Transactions on Combinatorics, 3(1), 7-13. doi: 10.22108/toc.2014.3820
MLA
Emami, M. , and Naserian, O. . "On the number of mutually disjoint cyclic designs", Transactions on Combinatorics, 3, 1, 2014, 7-13. doi: 10.22108/toc.2014.3820
HARVARD
Emami, M., Naserian, O. (2014). 'On the number of mutually disjoint cyclic designs', Transactions on Combinatorics, 3(1), pp. 7-13. doi: 10.22108/toc.2014.3820
CHICAGO
M. Emami and O. Naserian, "On the number of mutually disjoint cyclic designs," Transactions on Combinatorics, 3 1 (2014): 7-13, doi: 10.22108/toc.2014.3820
VANCOUVER
Emami, M., Naserian, O. On the number of mutually disjoint cyclic designs. Transactions on Combinatorics, 2014; 3(1): 7-13. doi: 10.22108/toc.2014.3820