A family of translation planes of order \(q^ 3\)
Let \(q\) be an odd prime power such that \(q\notin\{3,7\}\). The author constructs translation planes of order \(q^ 3\) whose translation complement has an orbit of length \(q^ 3-1\) on the line at infinity. Considering additional orbit lengths occuring these planes are shown to be different from planes with the same property constructed by \textit{J. André} [Math. Z. 60, 156-186 (1954; Zbl 0056.385)], \textit{Y. Hiramine} [Osaka J. Math. 23, 563-575 (1986; Zbl 0609.51002)], and the author [Osaka J. Math. 22, 773-786 (1985; Zbl 0574.51005)].
scientific article; zbMATH DE number 98738