In this paper, we investigate the existence of large sets of symmetric partitioned incomplete latin squares of type g^u (LSSPILSs) which can be viewed as a generalization of the well‐known golf designs. Constructions for LSSPILSs are presented from some other large sets, such as golf designs, large sets of group divisible designs, and large sets of Room frames. We prove that there exists an LSSPILS(g^u) if and only if u ≥ 3, g(u − 1) ≡ 0 (mod 2), and (g, u) ≠ (1, 5).

中文翻译：

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对称划分的不完整拉丁方的大集合的存在

在本文中，我们研究了存在大量类型为g ^u（LSSPILSs）的对称分区的不完整拉丁方，这可以看作是众所周知的高尔夫设计的概括。LSSPILS的构造来自其他一些大型集合，例如高尔夫球场设计，大型组可分割设计和大型房间框架。我们证明了存在一个LSSPILS（克^û）当且仅当ü  ≥3，克（Ú  - 1）≡0（模2），和（克，  Û）≠（1,5）。