  A Kochen-Specker (KS) set is a specific set of projectors and measurement
contexts that prove the Bell-Kochen-Specker contextuality theorem. The simplest
known KS sets in Hilbert space dimensions $d=3,4,5,6,8$ are reproduced, and
several methods by which a new KS set can be constructed using one or more
known KS sets in lower dimensions are reviewed and improved. These KS sets and
improved methods enable the construction of explicitly critical new KS sets in
all dimensions, where critical refers to the irreducibility of the set of
contexts. The simplest known critical KS sets are derived in all even
dimensions $d\geq10$ with at most 9 contexts and 30 projectors, and in all odd
dimensions $d\geq 7$ with at most 13 contexts and 39 projectors. These results
show that neither the number of contexts nor the number of projectors in a
minimal KS set scales with dimension $d$.
