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{\bf Artem A. Zhuravlev, Melissa S. Keranen and Donald L. Kreher}
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{\bf Small Group Divisible Steiner Quadruple Systems}
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A {\it group divisible Steiner quadruple system},
is a triple $(X, {\cal H}, {\cal B})$ where $X$ is a
$v$-element set of {\it points}, ${\cal H} = \{H_1,H_2,\ldots,H_r\}$
is a partition of $X$ into {\it holes} and ${\cal B}$ is a collection of
$4$-element subsets of $X$  called {\it blocks}
such that every  $3$-element subset is either in a block or a hole
but not both.  In this article we investigate the existence 
and non-existence of these designs. We settle all parameter
situations on at most 24 points, with 6 exceptions.
A {\it uniform} group divisible Steiner quadruple system is
a system in which all the holes have equal size. These
were called by Mills {\it G-design}s and their
existence is completely settled in this article.



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