A new upper bound for finite additive h-bases

Let h≥2h≥2 be a fixed integer. For a positive integer N  , a set A⊂[0,N]∩ZA⊂[0,N]∩Z is called an h-basis for N   if every integer n∈[0,N]n∈[0,N] can be represented as n=a1+a2+⋯+ahn=a1+a2+⋯+ah, where aj∈Aaj∈A, j=1,2,…,hj=1,2,…,h. In this paper, we improve the existing lower bound estimates for the cardinality of an additive h-basis for N  , as N→∞N→∞.