Constructions of Bh sets in various dimensions (2021)
Let A ⊂ Z+ and h be positive integer.We say that A is a Bh set if any integern can be written in at most one-ways as the sum of h elements of A, The fundamental problem is to determine the cardinal maximum of a set Bh contained in the integer interval [1, n] := {1, 2, 3, . . . , n}. Not many constructions of integer sets Bh are known, among them are Singer [13], Bose-Chowla [3] and Gómez-Trujillo [7]. The Bh set concept can be extended to arbitrary groups. In this article, the generalized constructions on the groups that come from a field are presented and new construction of a set Bh+s in h + 1 dimensions is obtained.