Fixed block configuration group divisible designs with block size six

Abstract: We present constructions and results about GDDs with two groups and block size 6. We study those GDDs in which each block has configuration (s,t), that is in which each block has exactly s points from one of the two groups and t points from the other. We show the necessary conditions are sufficient for the existence of GDD(n,2,6;{\lambda}1,{\lambda}2)s with fixed block configuration (3,3). For configuration (1,5), we give minimal or near-minimal index examples for all group sizes n \geq 5 except n = 10, 15, 160, or 190. For configuration (2,4), we provide constructions for several families of GDD(n,2,6;{\lambda}1,{\lambda}2)s.