We show that a randomly chosen 3-CNF formula over n variables with clauses-tovariables
ratio at least 4.4898 is asymptotically almost surely unsatisfiable. The previous best such
bound, due to Dubois in 1999, was 4.506. The first such bound, independently discovered by many
groups of researchers since 1983, was 5.19. Several decreasing values between 5.19 and 4.506 were
published in the years between. The probabilistic techniques we use for the proof are, we believe, of
CitacióDíaz, J. [et al.]. A new upper bound for 3-SAT. A: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. "IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science". Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, 2008, p. 163-174.