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Paper IPM / M / 739  


Abstract:  
A large set of t(v,k,λ) designs of size N, denoted by
LS[N](t,k,v), is a partition of all ksubsets of a
vset into N disjoint t(v,k,λ) designs, where
N=((v−t)  (k−t))/λ. A set of trivial necessary conditions for
the existence of an LS[N](t,k,v) is N ((v−i)  (k−i)) for i=0,...,t.
In this paper we extend some of the recursive methods for
constructing large sets of tdesigns of prime sizes. By utilizing these
methods we show that for the construction of all possible large
sets with the given N, t, and k, it suffices to construct a
finite number of large sets which we call root cases. As a
result, we show that the trivial necessary conditions for the
existence of LS[3](2,k,v) are sufficient for k ≤ 80.
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