Pairwise balanced designs with block sizes \(6t+1\) (Q1112034)
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scientific article; zbMATH DE number 4077221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pairwise balanced designs with block sizes \(6t+1\) |
scientific article; zbMATH DE number 4077221 |
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Pairwise balanced designs with block sizes \(6t+1\) (English)
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1987
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In this paper we construct pairwise balanced designs (PBDs) having block sizes which are prime powers congruent to 1 modulo 6. Such a PBD contains \(n=6r+1\) points, for some positive integer r. We show that this condition is sufficient for \(n\geq 1927\), with at most 31 possible exceptions below this value. As an immediate corollary, we prove that there exists a pair of orthogonal Steiner triple systems of order n, for the same values of n.
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pairwise balanced designs
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block sizes
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orthogonal Steiner triple systems
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