Determine the exact asymptotic constant for ternary-cube covers

Determine the exact value of the constant C_3 governing the asymptotic relation f(n)=(C_3+o(1))(3/2)^n for the minimum number f(n) of binary subcubes required to cover the ternary cube Z_3^n.

Background

The paper defines f(n) as the minimum number of sets of the form A_1×⋯×A_n, with each A_i a two-element subset of Z_3, whose union covers Z_3^n. It proves the lower bound f(n)≥(3/2)^n and the upper bound f(n)≤2(3/2)^n−1.

The normalized sequence f(n)/(3/2)^n is shown to be nondecreasing and to converge to a constant C_3 satisfying 1.62227<C_3≤2. The exact value of this limiting constant remains unresolved; the authors explicitly state that they do not optimize the upper bound in the paper.