Resolvable group divisible designs with block size four and index three

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type h^n and index three. The necessary conditions for the existence of such a design are n>=4 and hn=0(mod4). These necessary conditions are shown to be sufficient except for (h,n)@?{(2,4),(2,6)} and possibly excepting (h,n)=(2,54).

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