Dense infinite $B_h$ sequences
  For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\B$ with counting function   $$\mathcal{B}(x)= x^{\sqrt{(h-1)^2+1}-(h-1) + o(1)}.$$ This result extends a construction of I. Ruzsa for $B_2$ sequences. 
Javier Cilleruelo and Rafael Tesoro
math.NT math.CO