Chapter

Packing Arrays

DOI: 10.1007/3-540-45995-2_28
Source: DBLP

ABSTRACT A packing array is a b×k array of values from a g-ary alphabet such that given any two columns, i and j, and for all ordered pairs of elements from the g-ary alphabet, (g1, g2), there is at most one row, r, such that ar,i = g1 and ar,j = g2. Further, there is a set of at least n rows that pairwise differ in each column: they are disjoint. A central question is to determine, for given g and k, the maximum possible b. We developg eneral direct and recursive constructions and upper bounds on the sizes of packing arrays. We also show the
equivalence of the problem to a matching problem on graphs and a class of resolvable pairwise balanced designs. We provide
tables of the best known upper and lower bounds.

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