Largest induced subgraphs of the n-cube that contain no. 4-cycles
Journal of Combinatorial Theory Series B
Finite fields
The AETG System: An Approach to Testing Based on Combinatorial Design
IEEE Transactions on Software Engineering
Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes
Designs, Codes and Cryptography
Constructions of difference covering arrays
Journal of Combinatorial Theory Series A
Designs, Codes and Cryptography
Cyclic Difference Packing and Covering Arrays
Designs, Codes and Cryptography
Roux-type constructions for covering arrays of strengths three and four
Designs, Codes and Cryptography
Covering and radius-covering arrays: Constructions and classification
Discrete Applied Mathematics
Constructions of covering arrays of strength five
Designs, Codes and Cryptography
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A covering array CA(N; t, k, v) is an N 脳 k array with entries from a set X of v symbols such that every N 脳 t sub-array contains all t-tuples over X at least once, where t is the strength of the array. The minimum size N for which a CA(N; t, k, v) exists is called the covering array number and denoted by CAN(t, k, v). Covering arrays are used in experiments to screen for interactions among t-subsets of k components. One of the main problems on covering arrays is to construct a CA(N; t, k, v) for given parameters (t, k, v) so that N is as small as possible. In this paper, we present some constructions of covering arrays of strengths 3 and 4 via holey difference matrices with prescribed properties. As a consequence, some of known bounds on covering array number are improved. In particular, it is proved that (1) CAN(3, 5, 2v) 驴 2v 2(4v + 1) for any odd positive integer v with gcd(v, 9) 驴 3; (2) CAN(3, 6, 6p) 驴 216p 3 + 42p 2 for any prime p 5; and (3) CAN(4, 6, 2p) 驴 16p 4 + 5p 3 for any prime p 驴 1 (mod 4) greater than 5.