Sufficient conditions for STS(3^k) of 3-rank \≤ 3^k-r to be\n resolvable

2019/06/03 by Yaqi Lu, Lu, Yaqi, Minjia Shi +1
Engineering · #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1906.00620

openalex publication_date 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the structure of non-full-3-rank STS(3^k) and the orthogonal\nLatin squares, we mainly give sufficient conditions for STS(3^k) of 3-rank\n\≤ 3^k-r to be resolvable in the present paper. Under the conditions, the\nblock set of STS(3^k) can be partitioned into \(3^k-1)/(2) parallel\nclasses, i.e., \(3^k-1)/(2) 1-(v,3,1) designs. Finally, we prove that\nSTS(3^k) of 3-rank \≤ 3^k-r is resolvable under the sufficient\nconditions.\n

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