Additive and subtractive bases of Zₘ in average

Given a positive integer m, let Zₘ be the set of residue classes mod m. For A⊆ Zₘ and n∈ Zₘ, let σA(n) be the number of solutions to the equation $n=x+y$ with x,y∈ A. Let Hₘ be the set of subsets A⊆ Zₘ such that σA(n)≥1 for all n∈ Zₘ. Let ₘ=minA∈ Hₘ m⁻¹∑n∈ ZₘσA(n). Following a prior result of Ding and Zhao on Ruzsa's number, we know that m→∞ₘ≤ 192. Ding and Zhao then asked possible improvements on this value. In this paper, we prove m→∞ₘ≤ 144. Moreover, parallel results on subtractive bases of Zₘ were also investigated here.