Abstract Let φ( n, w, λ) be the largest possible size of an ( n, w, λ) optical orthogonal code. What is the exact value of ø( n, w, λ? This is an open problem! F. Chung, J. Salehi and V. Wei found in 1988 that φ( n, 3, 1) =⌊( n − 1)⧸6⌊ (for n ≠ 2 mod 6, where x⌊ means the integral part of the real number x). In this paper we will further show the exact values of φ( n, 3, 2) and φ( n, w, w − 1) in general.