An application of 3-designs to construct 3-GDDs of block size 4 and 2 groups
Keywords:
t-design, 3-GDD, Steiner quadruple systemsAbstract
In [3], it was proved that necessary conditions are sufficient for existence of a 3-GDD for n=1, 7, 9 (mod 12). It was also proved that for n=3 (mod 12) necessary conditions are sufficient except when lambda1=9 (mod 12). In this paper, we give the construction of a 3-GDD for n=3 (mod 12) and not equal 3. We prove that necessary conditions for the existence of a 3-GDD are sufficient for n=3 (mod 12) and n = 15, 27. We also prove that necessary conditions for the existence of a 3-GDD are sufficient for n=10 (mod 12).
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