Abstract
A 3 -GDD ( n , 2 , k , λ 1 , λ 2 ) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3 -GDD ( n , 3 , 5 , μ 1 , μ 2 ). Some necessary conditions for the existence of these GDDs are developed, and several new constructions and specific instances of nonexistence are given.
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