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