New covering array numbers

Abstract A covering array CA( N ; t, k, v ) is an N  ×  k array on v symbols such that each N  ×  t subarray contains as a row each t -tuple over the v symbols at least once. The minimum N for which a CA( N ; t, k, v ) exists is called the covering array number of t, k , and v , and it is denoted by CAN( t, k, v ). We prove that CA ( N ; t + 1 , k + 1 , v ) can be obtained from the juxtaposition of v covering arrays CA( N 0 ; t, k, v ), … , CA ( N v − 1 ; t , k , v ) , where N = ∑ i = 0 v − 1 N i . Given this, we developed an algorithm that constructs all possible juxtapositions and determines the nonexistence of certain covering arrays which allow us to establish the new covering array numbers CAN ( 4 , 13 , 2 ) = 32 , CAN ( 5 , 8 , 2 ) = 52 , CAN ( 5 , 9 , 2 ) = 54 , CAN ( 5 , 14 , 2 ) = 64 , CAN(6, 15, 2) = 128, and CAN ( 7 , 16 , 2 ) = 256 . Additionally, the computational results are the improvement of the lower bounds of 13 covering array numbers.