Cover starters for covering arrays of strength two

A cover starter is a single vector that yields a covering array under the actions of groups on both the columns and the symbols of the starter. The existence of this compact representation of covering arrays facilitates effective exhaustive and heuristic search. When the group action on symbols fixes a small number f of symbols, such cover starters lead to covering arrays that embed covering arrays on fewer symbols. Lower bounds on the length of cover starters over specified groups are established, and extensive computational results are developed to improve upper bounds for numerous covering array numbers.