Group Divisible Designs with Block Size Four and Group Type for |
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| Authors: | Hengjia Wei Gennian Ge |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou, P. R. China;2. School of Mathematical Sciences, Capital Normal University, Beijing, P. R. China |
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| Abstract: | Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in the constructions for other types of designs. In this paper, we investigate the existence problem of  ‐GDDs of type  for  . First, we determine completely the spectrum of  ‐GDDs of types  and  . Furthermore, for general cases, we show that for each  and  , a  ‐GDD of type  exists if and only if  ,  and  , except possibly for  ,  and  . |
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| Keywords: | group divisible designs double group divisible designs incomplete group divisible designs AMS subject classifications: Primary 05B05 |
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