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We denote the complete design $D$ (or the so-called trivial design) by $S({v-t\choose k-t};t,k,v)$. A conjecture of Hartman states that one can partition $D$ into two $S({v-t \choose k-t}/2;t,k,v)$ designs if and only if ${v-i\choose k-i}$ is even for $i=0,\ldots , t$. In this paper, some progress in support of the conjecture is reported.
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