Journal of Geometry 0047-2468/92/020053-0451.50+0.20/0 Vol. 43 (1992) (c) 1992 Birkhguser Verlag, Basel A NOTE ON THE BOERNER-LANTZ SEMIFIELD PLANES Minerva Cordero We determine the number of nonisomorphic semifMd plmaes of order p4 associated to the Boerner-Lantz semifields. 1. INTRODUCTION In [1] Boerner-Lantz constructed a class of semifield planes of order q4. In [2] we showed that the constructed planes of order p4 belong to the class of planes called p-primitive semifield planes which are studied in articles[2], [3] and [4]. In this note we determine the number of nonisomorphic Boerner-Lantz semifield planes of order pd. 2. THE SEMIFIELD PLANES OF BOERNER-LANTZ The construction of the Boerner-Lantz semifield planes is as follows: (i) for p ----3 Let S = {~ +/3x]~,/3 E GF(9)} and x (/GF(9). Define addition on S to be the usual vector addition. If multiplication on S is defined by ((~ +/3x) 9 (7 + 5x) = o~ 7 +/3(53a ,1) + (~* +/3~3)x where ~ = ~1 + *2a.a ~CF(3).a ~ = 2a + 1 and '1.'2 ~ at(3), then (S, +, ") is a semifield of order 81.