Abstract
Let r(k) be the smallest upper bound for the radius of k congruent balls in the 3-dimensional cubical flat torus. It will be proved that $$r(1)={1/2}$$ , $$r(2)={\sqrt{3}/4}$$ , $$r(3)={\sqrt{2}/4}$$ and $$r(4)={\sqrt{2}/4}.$$
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