New results on large sets of Kirkman triple systems

Authors:
Junling Zhou;Yanxun Chang
Affiliations:
Institute of Mathematics, Beijing Jiaotong University, Beijing, China 100044;Institute of Mathematics, Beijing Jiaotong University, Beijing, China 100044
Venue:
Designs, Codes and Cryptography
Year:
2010

Citing 6
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Abstract

The existence problem on the large sets of Kirkman triple systems (LKTS) was posed by Sylvester in 1850's as an extension of Kirkman's 15 schoolgirls problem. An LKTS(15) was constructed by Denniston in 1974. However, up to now the smallest unknown order for the existence of LKTS is still 21. In this paper we construct the two smallest unknown LKTS(v)s with v = 21 and v = 39 by using multiplier automorphism groups. Applying known recursive constructions, we show the existence of more infinite classes of large sets of Kirkman triple systems.