The Existence Of LHHTS(m~v) And R-LMTS(v)

The problem of large sets is an important topic of design theory,which has some valuable applications to experimental design,coding theory and so on.In this paper,we will mainly consider the existence problems of LHHTS(m~v)and r-LMTS(v).An LHHTS(m~v)is a collection of {(X,g,Br)r?R},such that every(X,g,Br)is an HHTS(m~v),and for each cyclic and transitive triple B of X with |G?B|?1 for all G?g,there is exactly one r?R such that B? Br.In this paper,by using the idea of large sets with holes,combining with the methods of direct and recursive constructions,we get the spectrm of LHHTS(m~v)to be v(v-1)m2 ? 0(mod 3)and(m,v)?(1,3).A r-LMTS(v)is an LOD(v),{(X,Ai):1?i?v-2},which satisfies the following conditions:(1)for 1 ? i ? r,each(X,Ai)corresponds to an MTS(v);(2)for r+ 1?i ? v-2,(X,Ai)s are OD(v)s with character(Q).By using some auxiliary designs:r-LMTS(v;h),**POCS(gn:s)r etc.,we demonstrate some recursive constructions about r-LMTS(v).At the same time,we display a tripling construction from r-LMTS(v)to(2v+r)-LMTS(3v).Combining the results of r-LMTS(v)with v ? 1,3,5(mod 6)and v a power of prime number,we give some results of r-LMTS(v).