On group-divisible designs with block size four and group-type 6um1

We investigate the spectrum for {4}-GDDs of type gum1. Wedetermine, for each even g, all values of m for which a {4}-GDD of typegum1 exists, for every ‘fourth’ value of u. We similarlydetermine, for each odd g ≠ 11 or 17, all values of m for which a {4}-GDD of typegum1 exists, for every ‘third’ value of u. Finally, weestablish, up to a finite number of values of u, the spectrum for {4}-GDDs of typegum1 where gu is even, g ∉ {11, 17}.

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