Resolvable balanced incomplete block designs with block size 5

Abstract

Abstract 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≡5 mod 10 . 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.