The spectrum of lambda-times repeated blocks for TS(upsilon, lambda)

Abstract A triple system TS(υ,λ) is a collection of 3-element subsets (=blocks) of a v -element set X such that each pair x , y ϵ X is contained in precisely λ blocks. We determine the spectrum of λ-times repeated blocks in a TS(υ,λ), leaving only one value in doubt for each v ≡2( mod 12).