Covering Designs Contributors

Many people have contributed coverings. Thanks go to Rade Belic, Riccardo Bertolo, John Cock, Michael Dambmann, Jan de Heer, Alessandro Jurcovich, Felix Rodriguez Martin, Michael Morley, Adolf Muehl, Steve Muir, Uenal Mutlu, Floyd Oats, Andrei Ochmat, Dietmar Pree, Guenther Schlegl, D. T. Todorov, John van Rees and Jose Milan Vega.

Kari Nurmela and Patric Ostergard wrote a simulated annealing program was used to quickly construct many of the coverings.

Another program that generates good coverings is Ininuga, which produced many coverings in the tables.

Alex Sidorenko has contributed many coverings and several general methods based on his work in Turan theory.

Greg Kuperberg noticed that complements of linear [v,t] codes give variable block-size (v,*,t)-coverings, which led to a number of improvements.

Lower Bounds

There has also been some progress on lower bounds, starting with Sidorenko's work in the 1990s.

More recently, in 2002 David Applegate, Eric Rains, and Neil Sloane showed that C(10,5,4)=51; C(11,6,5)>=96; C(11,7,6)=84; C(12,7,6)>=165; C(12,8,7)=126; C(13,9,8)=185.

Also in 2002, John Bate, Ben Li, and John van Rees showed that C(19,6,2)=15, and Li and van Rees showed C(17,10,3)=11.

In 2004, Malcolm Greig, Li, and van Rees showed that C(28,9,2)=C(41,13,2)=14.

In 2007, Klas Marström gave many new lower bounds, and found all non-isomorphic coverings for many parameters.

These bounds, with other improvements that result from them, are given here.

This page last updated 9 January 2006