A static dictionary is a data structure storing subsets of a finite univers
e U, answering membership queries. We show that on a unit cost RAM with wor
d size Theta (log |U|), a static dictionary for n-element sets with constan
t worst case query time can be obtained using B+O ( log log |U|) + o(n) bit
s of storage, where B = inverted right perpendicular log(2)((|U|)(n))invert
ed left perpendicular is the minimum number of bits needed to represent all
n-element subsets of U.