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The existence of balanced \((v,\{3,6\},\lambda)\) difference families with \(v\) a prime power. (English) Zbl 1294.05035

Summary: A \((v,K,\lambda)\) difference family can be used to construct a \((v,K,\lambda)\)-PBD. It is proved that for each prime power \(v\equiv 1\pmod{36}\) and \(v\geq 37\), there exists a balanced \((v,\{3,6\},1)\) difference family. In this paper, it is proved that necessary conditions for the existence of balanced \((v,\{3,6\},\lambda)\) difference families are also sufficient when \(v\) is a prime power.

MSC:

05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
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