Subdesigns in Steiner quadruple systems
Journal of Combinatorial Theory Series A
A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems
Journal of Combinatorial Theory Series A
Partitions of triples into optimal packings
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
Large sets of disjoint packings on 6k + 5 points
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
Combinatorial constructions of fault-tolerant routings with levelled minimum optical indices
Discrete Applied Mathematics
Large sets of Kirkman triple systems and related designs
Journal of Combinatorial Theory Series A
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A Steiner triple system of order v (briefly STS(v)) consists of a v-element set X and a collection of 3-element subsets of X, called blocks, such that every pair of distinct points in X is contained in a unique block. A large set of disjoint STS(v) (briefly LSTS(v)) is a partition of all 3-subsets (triples) of X into v - 2 STS(v). In 1983-1984, Lu Jiaxi first proved that there exists an LSTS(v) for any v ≡ 1 or 3 (mod 6) with six possible exceptions and a definite exception v = 7. In 1989, Teirlinck solved the existence of LSTS(v) for the remaining six orders. Since their proof is very complicated, it is much desired to find a simple proof. For this purpose, we give a new proof which is mainly based on the 3-wise balanced designs and partitionable candelabra systems.