The existence of simple 6-(14,7,4) designs
Journal of Combinatorial Theory Series A
Non-trivial t-designs without repeated blocks exist for all t
Discrete Mathematics
Partitioning sets of quadruples into designs I
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems
Journal of Combinatorial Theory Series A
More on halving the complete designs
Discrete Mathematics
Extending large sets of t-designs
Journal of Combinatorial Theory Series A
All block designs with b= v k /2 exist
Discrete Mathematics
Some infinite families of large sets of t-designs
Journal of Combinatorial Theory Series A
On the Existence of Large Sets of t-designs of Prime Sizes
Designs, Codes and Cryptography
Vertex-transitive self-complementary uniform hypergraphs
European Journal of Combinatorics
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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-t/k-t 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.