Modified group divisible designs with block size 5 and even index
The existence of \((5,\lambda)\)-modified group-divisible designs (MGDDs) is studied when \(\lambda\) is even. The necessary conditions for a \((5,\lambda)\)-MGDD of type \(m^n\) to exist (i.e. \(m \geq 5\); \(n \geq 5\); \(\lambda(nm+1-m-n) \equiv 0 \pmod{4}\); and \(\lambda n m (nm+1-n-m) \equiv 0 \pmod{20}\)) are shown to be sufficient when \(\lambda \geq 4\) is even. When \(\lambda = 2\), sufficiency is established with 13 possible exceptions.
scientific article; zbMATH DE number 5300620
scientific article