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A necessary condition for the existence of a resolvable balanced incomplete block design on v points with λ=2 and k=5, is that v=5mod10. This condition is shown to be sufficient for v>395, with at most 13 exceptions below this value. Also given are a new (185,5,1) RBIBD, (v,5,4) RBIBDs for v=110 and 140, and (45,5,λ) RBIBDs for λ>=3.
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