On this page I have collected all non-isomorphic (n,k,t) double covering designs.
The designs were generated using integer programming, mainly using glpk, and isomorphism
reduction was done using Brendan McKay's
Nauty. The generation program
is complete so unless there has been an undetected computer error this list should be
complete.
Definition
An (n,k,t) double covering design is a family F of k-subsets of 1...n
such that every t-subset of 1...n is a subset of at least two members of F.
The size of F is the number of sets in F.
We say that F is an optimum (n,k,t)-covering design if no
other (n,k,t)-covering design has smaller size.
We say that two designs F and H are isomorphic if F can be mapped to
H by a permutation of 1...n
The designs
The format for the files is as follows.
A file named "covdes-2-n=x-k=y-t=z" contains all
non-isomorphic covering designs with the given parameters.
Every design consists of a sequence of lines, each representing
a block in the design, followed by a line with "---" marking the
end of the design.
Each block is described as a sequence of integers separated by
a space, each integer represents an element of the block.
13/05/14 Added (20,17,2), (20,17,9), (20,15,2) and additional examples of (19,14,3) and (12,3,2).
13/01/17 Corrected typos in the tables and added many new designs.
13/01/04 Added all double covering designs on at most 10 points, and many for larger n.
08/09/13 Added the first double covering designs. More on the way.
The size and number of non-isomorphic double covering designs
A table entry of the form "S, N" means that an optimal
covering design with the given parameters has size S and there exists N
non-isomorphic such designs.