Abstract
AbstractA triple system is a collection of b blocks, each of size three, on a set of v points. It is j‐balanced when every two j‐sets of points appear in numbers of blocks that are as nearly equal as possible, and well balanced when it is j‐balanced for each . Well‐balanced systems arise in the minimization of variance in file availability in distributed file systems. It is shown that when a triple system that is 2‐balanced and 3‐balanced exists, so does one that is well balanced. Using known and new results on variants of group divisible designs, constructions for well‐balanced triple systems are developed. Using these, the spectrum of pairs for which such a well‐balanced triple system exists is determined completely.
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