The Ramsey multiplicity c(t) is the limit as n tends to infinity of the smallest possible number of monochromatic t-cliques in a red/blue edge-coloring of the complete graph Kn, normalized by (n choose t). Disproving a conjecture by Erdős (1962), Thomason (1989) showed that c(4) is smaller than 1/32, the value obtained from a random graph G(n,1/2), but the exact value remains unknown. A recent work by Parczyk et al. (2024) has used local search heuristics on Cayley graphs, and with considerable computational effort has given the so-far best known upper bound on c(4), and also on c(5). Introducing new methods and ideas, we provide randomized constructions that improve these bounds, showing c(4) < 0.030139 and c(5) < 0.001652. Our constructions are more structured, symmetric, and human-friendly than the previous ones, paving the way for potential further progress on this longstanding problem and related questions. MSc advisor: Chaim Even Zohar