Title: Covering and uncovering on structures

Abstract: 

A covering design is a generalisation of a block design: it is a set of 
blocks of size k chosen from {1,...,n} where each t-set must be contained 
in at least one block.  An uncovering is closely related: we want a set of 
blocks which avoid any t-set at least once.

We consider the situation when the blocks of our uncovering have some 
structure, such as being the basis for a vector space, a base for a 
permutation group, or a spanning tree for a graph.