Existence of directed GDDs with block size five and index \(\lambda \geq 2\). (English) Zbl 0963.62073
Summary: It is shown that the necessary condition for the existence of a directed group divisible design with block size 5, type \(h^n\) and index \(\lambda\), namely, \(n\geq 5\), \(\lambda(n-1) h\equiv 0\pmod 2\) and \(\lambda n(n-1) h^2\equiv 0\pmod{10}\), is also sufficient for \(\lambda\geq 2\). This result guarantees the analogous existence result for group divisible designs of type \(h^n\) having block size 5 and index \(2\lambda\).
MSC:
| 62K10 | Statistical block designs |
References:
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