La Jolla Covering Repository
A (v,k,t)-covering design is
a collection of k-element subsets, called blocks, of {1,2,...,v},
such that any t-element subset is contained in at least one block.
This site contains (v,k,t)-coverings with v<=32, k<=16,
t<=8.
Each of these coverings gives an upper bound for the corresponding C(v,k,t),
the smallest possible number of blocks in such a covering design.
If it does not have a covering you're interested in,
or you know of an improvement, please send email to Dan Gordon at
gordon@ccrwest.org.
The original coverings in these tables (most of which have since been
improved)
were constructed using techniques from the 1995 paper
New Constructions for
Covering Designs, by myself, Greg Kuperberg, and Oren Patashnik.
A few errors in the tables there are listed on an
errata page.
Numerous people have contributed bounds, techniques,
and particular coverings.
Attributions are given in the individual coverings.
This page gives names of
people who have made major contributions
(including progress on the lower bounds),
and links to other covering sites.
Here is a list of
recent improvements.
All improvements made before 2008 are
here.
Links to the coverings are in the
La Jolla Covering Repository Tables
Printable versions of the tables are in:
Lower bounds table (pdf)
Upper bounds table (pdf)
The tables were last updated May 13, 2008.
I do not have any coverings beyond (32,16,8), lotto systems, or other
variants. If what you're interested in isn't here, you can try:
Go to Dan Gordon's home page