A frequency n-cube Fn(q;l0,...,lm−1) is an n-dimensional q-by-...-by-q array, where q=l0+...+lm−1, filled by numbers 0,...,m−1 with the property that each line contains exactly li cells with symbol i, i=0,...,m−1 (a line consists of q cells of the array differing in one coordinate). The trivial upper bound on the number of frequency n-cubes is m(q−1)n. We improve that lower bound for n>2, replacing q−1 by a smaller value s, by constructing a testing set of size sn for frequency n-cubes (a testing set is a collection of cells of an array the values in which uniquely determine the array with given parameters). We also construct new testing sets for generalized frequency n-cubes, which are essentially correlation-immune functions in n q-valued arguments; the cardinalities of new testing sets are smaller than for testing sets known before.