The limit for coverings is v<100, k<=25, and t<=8 just to draw the line somewhere. Only coverings with at most 100000 blocks are given, except for some which were grandfathered in. Some Steiner systems (coverings in which every tset is covered exactly once) which are too big for the database will be included in the link below.
LJCR Tables 

Recent Improvements  Top Contributors 
Steiner Systems  Lower bounds 
Coverings with Sage  
Acknowledgements and Links  
Contribute a cover 
Maintained by Dan Gordon