On the number of frequency hypercubes Fn(4;2,2)
Abstract
A frequency n-cube Fn(4;2,2) is an n-dimensional 4-by-...-by-4 array filled by 0s and 1s such that each line contains exactly two 1s. We classify the frequency 4-cubes F4(4;2,2), find a testing set of size 25 for F3(4;2,2), and derive an upper bound on the number of Fn(4;2,2). Additionally, for any n greater than 2, we construct an Fn(4;2,2) that cannot be refined to a latin hypercube, while each of its sub-Fn-1(4;2,2) can. Keywords: frequency hypercube, frequency square, latin hypercube, testing set, MDS code
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