On the order of a minimal additive basis

Let A be a set of non-negative integers. IF every sufficiently large integer is the sum of h not necessarily distinct elements of A, then A is called an asymptotic basis of order ii. An asymptotic basis A of order h is called minimal if no proper subset of A is an asymptotic basis of order h. It is proved that for every integer h greater than or equal to 3, no set A is simultaneously a minimal asymptotic basis of orders it and 2h. For h = 2, the problem had already been solved. (C) 1998 Academic Press.