Further results on large sets plus of partitioned incomplete Latin squares

Abstract

In this paper, we continue to study the existence of large sets plus of partitioned incomplete Latin squares of type $g^n{\left(ug\right)}^1$, denoted by LSPILS${}^{+}\left(g^n{\left(ug\right)}^1\right)$. We almost solve the existence of an LSPILS${}^{+}\left(g^n{\left(ug\right)}^1\right)$ for any integer $g\ge 1$ and $u=3,4$ with some possible exceptions.