q-analogs of group divisible designs

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Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
Bayreuth , 2018 . - 17 S.

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Abstract

A well known class of objects in combinatorial design theory are group divisible designs.Here, we introduce the q-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces, q-Steiner systems, design packings and $q^r$-divisible projective sets. We give necessary conditions for the existence of q-analogs of group divisible designs, construct an infinite series of examples, and provide further existence results with the help of a computer search. One example is a (6,3,2,2)_2 group divisible design over GF(2) which is a design packing consisting of 180 blocks that such every 2-dimensional subspace in GF(2)^6 is covered at most twice.