Let m1(ℝn) denote the measure of the largest subset of Undefined control sequence \R not containing two points at distance one. There are essentially two methods to upper bound m1(ℝn): the earlier goes back to Frankl and Wilson intersection theorems and employs finite sets of points with 0-1 coordinates. More recently F. Oliveira and F. Vallentin have proposed a different approach based on an (infinite dimensional) linear program. While the former leads to the best known asymptotic estimate, the later has improved the known results for small dimensions. After a discussion of these two methods we will present new improvements obtained with a combination of the two approaches. In turn, new improvements on the lower bounds for the measurable chromatic number are obtained.