CONICET | Buscador de Institutos y Recursos Humanos

Abstract. We study a construction published by Donald Knuth in 1965yielding a completely uniformly distributed sequence of real numbers. Knuth?swork is based on de Bruijn sequences of increasing orders and alphabetsizes, which grow exponentially in each of the successive segments composingthe generated sequence. In this work we present a similar albeit simplerconstruction using linearly increasing alphabet sizes, and give an elementaryproof showing that the sequence it yields is also completely uniformlydistributed. In addition, we present an alternative proof of the same resultbased on Weyl?s criterion.