Ovals and hyperovals in nets
In this paper, incomplete mutually orthogonal Latin squares (MOLS) were used to construct \(r\)-nets of order \(n \leq 8\) with ovals or hyperovals. To do that, several small MOLS with an oval or a hyperoval were constructed directly. As a result, now the existence of \(r\)-nets of order \(n\leq 8\) with ovals and hyperovals is reduced to a finite number of undertermined cases. The authors also investigated the existence of incomplete MOLSs of order \(n \geq 775\) with a hole of size \(8\). From that the existence of a \(9\)-net of order \(n \geq 775\) with a hyperoval is proved.
scientific article; zbMATH DE number 2182130