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| Paper IPM / M / 739 |
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| Abstract: | |||||
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A large set of t-(v,k,λ) designs of size N, denoted by
LS[N](t,k,v), is a partition of all k-subsets of a
v-set 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 t-designs 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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