Design theory
Frames for Kirkman triple systems
Discrete Mathematics
A survey of Kirkman triple systems and related designs
Discrete Mathematics
The fundamental construction for 3-designs
Proceedings of the first Malta conference on Graphs and combinatorics
An improved product construction for large sets of Kirkman triple systems
Discrete Mathematics
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
New results on large sets of Kirkman 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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In this paper, we introduce LR(u) designs and use these designs together with large sets of Kirkman triple systems (LKTS) and transitive KTS (TKTS) of order υ to construct an LKTS(uυ). Our main result is that there exists an LKTS(υ) for υ ∈ {3nm(2 . 13k + 1)t; n ≥ 1, k ≥ 1, t = 0,1, m ∈ {1, 5, 11, 17, 25, 35, 43}}.