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A direct method for constructing large sets of $t$-designs is
based on the concept of assembling orbits of a permutation group
$G$ on $k$-subsets of a $v$-set into block sets of $t$-designs so
that these designs form a large set. If $G$ is $t$-homogeneous,
then any orbit is a $t$-design and therefore we obtain a large set
by partitioning the set of orbits into parts consisting of the
same number of $k$-subsets. In general, it is hard to find such
partitions. We solve this problem when orbit sizes are limited to
two values. We then use its corollaries to obtain some results in
a special case in which a simple divisibility condition holds and
no knowledge about orbit sizes is assumed.
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