A strengthened inequality of Alon-Babai-Suzuki's conjecture on set systems with restricted intersections modulo p

In this paper, we will prove that if n≥2s−2r+1 or n≥s+max1≤i≤rki, then |A|≤n−1s+n−1s−1+⋯+n−1s−2r+1.This result strengthens both the upper bound of Alon-Babai-Suzuki's conjecture and Qian and Ray-Chaudhuri's result, when n≥2s−2.