Note on sunflowers

A sunflower with p petals consists of sets whose pairwise intersections are identical. The goal the problem is to find smallest r=r(p,k) such that any family rk distinct k-element contains a petals. Building upon breakthrough Alweiss, Lovett, Wu and Zhang from 2019, Rao proved r=O(plog(pk)) suffices; this bound was reproved by Tao in 2020. In short note we record r=O(plogk) suffices, using minor variant probabilistic part these recent proofs.