3-Group Divisible Designs with 3 Groups and Block Size 5

JOURNAL OF MATHEMATICS(2023)

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摘要
A 3-GDD (n, 2, k, lambda 1, lambda 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, mu 1, mu 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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