“School of Mathematics”
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Paper IPM / M / 8067  


Abstract:  
A direct method for constructing large sets of tdesigns is
based on the concept of assembling orbits of a permutation group
G on ksubsets of a vset into block sets of tdesigns so
that these designs form a large set. If G is thomogeneous,
then any orbit is a tdesign and therefore we obtain a large set
by partitioning the set of orbits into parts consisting of the
same number of ksubsets. 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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