The paper gives tighter exponential bounds on the Rado covering constant F(Q^d) for cubes and F(B^d) for balls in high dimensions d, with the ball upper bound obtained via the Kabatiansky-Levenshtein sphere packing bound.
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Rado's covering problem for cubes and balls: a semi-survey
The paper gives tighter exponential bounds on the Rado covering constant F(Q^d) for cubes and F(B^d) for balls in high dimensions d, with the ball upper bound obtained via the Kabatiansky-Levenshtein sphere packing bound.