Abstract
A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection \(\{(X, \mathcal {B}_i) : 1 \leq i \leq v - 2\}\), where every \((X, \mathcal {B}_i)\) is a KTS(v) and all \(\mathcal {B}_i\) form a partition of all triples on X. In this article, we give a new construction for LKTS(6v + 3) via OLKTS(2v + 1) with a special property and obtain new results for LKTS, that is there exists an LKTS(3v) for \(v = \prod_{i=1}^{p}(2q_i^{r_i}+1)\prod_{j=1}^{q}(4^{s_j}-1)\), where p, q ≥ 0, r i , s j ≥ 1, q i is a prime power and \(q_i \equiv 7\) mod 12.
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Communicated by J. D. Key.
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Yuan, L., Kang, Q. Another construction for large sets of Kirkman triple systems. Des. Codes Cryptogr. 48, 35–42 (2008). https://doi.org/10.1007/s10623-008-9168-8
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DOI: https://doi.org/10.1007/s10623-008-9168-8