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IPM
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“School of Mathematics”

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Paper   IPM / M / 8067
School of Mathematics
  Title:   Large sets of t-designs from t-homogeneous groups
  Author(s): 
1.  G. R. Omidi
2.  B. Tayfeh-Rezaie (Joint with R. Laue)
  Status:   Published
  Journal: Ars Combin.
  Vol.:  97
  Year:  2010
  Pages:   333-342
  Supported by:  IPM
  Abstract:
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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