2019/12/10 by Tuvi Etzion, Etzion, Tuvi, Junling Zhou +1
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Limits and Structures in Graph Theory #Algorithms and Data Compression
paper · pdf · doi:10.48550/arxiv.1912.04489
Let D(n) be the number of pairwise disjoint Steiner quadruple systems. A simple counting argument shows that D(n) ≤ n-3 and a set of n-3 such systems is called a large set. No nontrivial large set was constructed yet, although it is known that they exist if n ≡ 2 or 4~(mod~6) is large enough. When n ≥ 7 and n ≡ 1 or 5~(mod~6), we present a recursive construction and prove a recursive formula on D(4n), as follows: D(4n) ≥ 2n + min \D(2n) ,2n-7\. The related construction has a few advantages over some of the previously known constructions for pairwise disjoint Steiner quadruple systems.