Geodesic
Small group divisible Steiner quadruple systems
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl EuDML
A group divisible Steiner quadruple system, is a triple $(X, {\cal H}, {\cal B})$ where $X$ is a $v$-element set of points, ${\cal H} = \{H_1,H_2,\ldots,H_r\}$ is a partition of $X$ into holes and ${\cal B}$ is a collection of $4$-element subsets of $X$ called 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 uniform group divisible Steiner quadruple system is a system in which all the holes have equal size. These were called by Mills G-designs and their existence is completely settled in this article.
DOI : 10.37236/764
Classification : 05B05, 05B07
Mots-clés : group divisible Steiner quadruple system, Mills G designs 
Artem A. Zhuravlev; Melissa S. Keranen; Donald L. Kreher. Small group divisible Steiner quadruple systems. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/764
@article{10_37236_764,
     author = {Artem A. Zhuravlev and Melissa S. Keranen and Donald L. Kreher},
     title = {Small group divisible {Steiner} quadruple systems},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/764},
     zbl = {1179.05019},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/764/}
}
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