A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems
Journal of Combinatorial Theory Series A
Further results on large sets of disjoint group-divisible designs
Discrete Mathematics
The fundamental construction for 3-designs
Proceedings of the first Malta conference on Graphs and combinatorics
Some new 2-resolvable Steiner quadruple systems
Designs, Codes and Cryptography
Constructions for Steiner quadruple systems with a spanning block design
Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
A new existence proof for large sets of disjoint Steiner triple systems
Journal of Combinatorial Theory Series A
A construction for large sets of disjoint Kirkman triple systems
Designs, Codes and Cryptography
Constructions for large sets of L-intersecting Steiner triple systems
Designs, Codes and Cryptography
Large sets of Kirkman triple systems and related designs
Journal of Combinatorial Theory Series A
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A (2, 3)-packing on X is a pair (X, A), where A is a set of 3-subsets (called blocks) of X, such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph (X, E) such that E consists of all the pairs which do not appear in any block of A. For a (6k + 5)-set X a large set of maximum packing. denoted by LMP(6k + 5), is a set of 6k + 1 disjoint (2, 3)-packings on X with a cycle of length four as their common leave. Schellenberg and Stinson (J. Combin. Math. Combin. Comput. 5 (1989) 143) first introduced such a large set problem and used it to construct perfect threshold schemes. In this paper, we show that an LMP(6k + 5) exists for any positive integer k. This complete solution is based on the known existence result of S(3, 4, v)s by Hanani and that of 1-fan S(3, 4, v)s and S(3, {4, 5, 6}, v)s by the second author. Partitionable candelabra system also plays an important role together with two special known LMP(6k + 5)s for k = 1, 2.