Constructing MSTD sets using bidirectional ballot sequences

A more sums than differences (MSTD) set is a finite subset S of the integers such that |S+S|>|S−S|. We construct a new dense family of MSTD subsets of {0,1,2,…,n−1}. Our construction gives Θ(n2/n) MSTD sets, improving the previous best construction with Ω(n2/n4) MSTD sets by Miller, Orosz, and Scheinerman.