On the Number of Frequency Hypercubes F$ {}^{n}(4;2,2) $

A frequency $ n -cube F {}^{n}(4;2,2) is an -dimensional 4 -by-…-by- array filled by 0 s and 1 such that each line contains exactly two s. We classify the -cubes {}^{4}(4;2,2) , find a testing set of size 25 for {}^{3}(4;2,2) derive upper bound on number . Additionally, every greater than 2 we construct cannot be refined to Latin hypercube, while its sub-F {}^{n-1}(4;2,2) can.