New Kochen–Specker sets in four dimensions

We show that all possible 388 4-dim Kochen–Specker (KS) (vector) sets (of yes–no questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component values from {−1,0,1}{−1,0,1} can be obtained by stripping vectors off a single system provided by Peres 20 years ago. In addition to them, we have found a number of other KS sets with 22 through 24 vectors. We present the algorithms we used and features we found, such as, for instance, that Peres' 24-24 KS set has altogether six critical KS subsets.