Improve the non-asymptotic construction of zero-skip-cost CFR codes

Construct a zero-skip-cost CFR code with a better expansion factor in the non-asymptotic regime than the one provided by Construction 3.3, when efficiently finding the permutation guaranteed by Theorem 4.9 is difficult.

Background

Construction 3.3, the recursive construction, can outperform the other proposed constructions for many finite parameter values, although its asymptotic expansion factor is generally worse than that of Construction 3.2. Theorem 4.9 gives an optimal expansion factor of one for sufficiently large covering designs, but its proof is non-constructive.

The authors explicitly leave unresolved whether a construction superior to Construction 3.3 can be obtained for finite, non-asymptotic parameters if the permutation from Theorem 4.9 cannot be efficiently found. The problem therefore concerns improving practical finite-parameter performance while retaining zero skip cost.