A covering array t-CAðn; k; gÞ is a k n array on a set of g symbols with the property that in each t n subarray, every t 1 column appears at least once. This paper improves many of the best known upper bounds on n for covering arrays, 2-CAðn; k; gÞ with gþ 1 k 2g, for g 1⁄4 3 12 by a construction which in many of these cases produces a 2-CAðn; k; gÞ with n 1⁄4 kðg 1Þ þ 1. The construction is an...

‎in [u‎. ‎dempwolff‎, ‎on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$‎, ‎textit{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎, ‎textbf{48} (1972)‎, ‎359‎ - ‎364.] dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the‎ ‎elementary abelian group $2^{5}$ by the general linear group‎ ‎$gl(5,2)$)‎. ‎this group is the second l...

Let V be a finite set of order v. A (v,k,A.) covering design of index A. and block size k is a collection of k-element subsets, called blocks, such that every 2-subset of V occurs in at least '}.. blocks. The covering problem is to determine the minimum number of blocks, a (v, k, A.), in a covering design. It is well known that a(v,k''}..)Lr~~=~'}..ll=(v,k,A.), where rxl is the smallest integer

A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). It is easy to see that a covering must contain at least (v t )

We compute the minimal cardinalities of coverings and irredundant coverings of a vector space over an arbitrary field by proper linear subspaces. Analogues for affine linear subspaces are also given. Notation: The cardinality of a set S will be denoted by #S. For a vector space V over a field K , we denote its dimension by dim K . 1. LINEAR COVERINGS. Let V be a vector space over a field K . A ...

A covering array CA(N ; t, k, v) is anN×k array on v symbols such that everyN×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). In this work we prove that if exists CA(N ; t+ 1, k + 1, v) it can be obtained from the juxtaposition of v ...