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A large set of disjoint $S(\lambda;t, k, v)$ designs, denoted by
$LS(\lambda; t, k, v)$, is a partition of $k$-subsets of $v$-set
into $S(\lambda;t , k, v)$ designs. In this paper, we develop some
recursive methods to construct large sets of $t$-designs. As a
consequence, we show that a conjecture of Hartman on halving
complete designs is true for $t=2$ and $3\leq k \leq 15$.
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