Group divisible designs with large block sizes
In this paper, the author showed that there is a \((k,\lambda_k)\)-GDD, group divisible design, of type \((q^{l+1}-q^l)^{(q^{n-l}-1)/(q-1)}\), for any prime power \(q\) and any integers \(k\), \(n\) with \(3\leq k \leq n\), where \(\lambda_k=\frac{\prod_{i=3}^{k-1}(q^n-q^{l+i-1})}{(k-2)!}\) and \(k+l\leq n+1\). The author generalized the \textit{C.-D. Lee} et al.'s method [ibid. 86, No. 6, 1281--1293 (2018; Zbl 1387.05024)] and used counting principles to construct such GDD. Moreover, the author showed that the conjecture given by C.-D. Lee at al. [loc. cit.] holds. It is a special case of the method given in this paper, for \(q=2\) and \(l=1\).
scientific article; zbMATH DE number 6933689