A New Construction of Group Divisible Designs with Nonuniform Group Type |
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Authors: | Gennian Ge Shuxing Li Hengjia Wei |
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Institution: | 1. School of Mathematical Sciences, Capital Normal University, Beijing, China;2. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, China;3. School of Mathematical Sciences, Zhejiang University, Hangzhou, China |
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Abstract: | The construction of group divisible designs (GDDs) is a basic problem in design theory. While there have been some methods concerning the constructions of uniform GDDs, the construction of nonuniform GDDs remains a challenging problem. In this paper, we present a new approach to the construction of nonuniform GDDs with group type and block size k. We make a progress by proposing a new construction, in which generalized difference sets, a truncating technique, and a difference method are combined to construct nonuniform GDDs. Moreover, we present a variation of this new construction by employing Rees' product constructions. We obtain several infinite families of nonuniform GDDs, as well as many examples whose block sizes are relatively large. |
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Keywords: | group divisible designs generalized difference sets truncating technique α ‐parallel classes difference method Rees’ product constructions |
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