论文标题
关于频率超管的数量$ f^n（4; 2,2）$
On the number of frequency hypercubes $F^n(4;2,2)$
论文作者
论文摘要
频率$ n $ -cube $ f^n（4; 2,2）$是$ n $ dimensional $ 4 $ -by -...- by-4 $ 4 $ 4 $ 4 $阵列，填充$ 0 $ s和$ 1 $ s，使每条线完全包含两个$ 1 $ s。我们对频率$ 4 $ -ICUBES $ f^4（4; 2,2）$进行分类，找到$ f^3（4; 2,2）$的尺寸$ 25 $的测试集，并在$ f^n（4; 2,2）$的上方限制了上限。此外，对于任何大于$ 2 $的$ n $，我们构建了无法将其构建的$ f^n（4; 2,2）$，而无法将其完善到拉丁语HyperCube，而其每个子$ f^{n-1}（4; 2,2）$ can can。 关键字：频率超越立方体，频率平方，拉丁超立方体，测试集，MDS代码
A frequency $n$-cube $F^n(4;2,2)$ is an $n$-dimensional $4$-by-...-by-$4$ array filled by $0$s and $1$s such that each line contains exactly two $1$s. We classify the frequency $4$-cubes $F^4(4;2,2)$, find a testing set of size $25$ for $F^3(4;2,2)$, and derive an upper bound on the number of $F^n(4;2,2)$. Additionally, for any $n$ greater than $2$, we construct an $F^n(4;2,2)$ that cannot be refined to a latin hypercube, while each of its sub-$F^{n-1}(4;2,2)$ can. Keywords: frequency hypercube, frequency square, latin hypercube, testing set, MDS code
