  In 1993, Shub and Smale posed the problem of finding a sequence of univariate
polynomials of degree $N$ with condition number bounded above by $N$. In a
previous paper by C. Belt\'an, U. Etayo, J. Marzo and J. Ortega-Cerd\`a, it was
proved that the optimal value of the condition number is of the form
$O(\sqrt{N})$, and the sequence demanded by Shub and Smale was described by a
closed formula (for large enough $N\geqslant N_0$ with $N_0$ unknown) and by a
search algorithm for the rest of the cases. In this paper we find concrete
estimates for the constant hidden in the $O(\sqrt{N})$ term and we describe a
simple formula for a sequence of polynomials whose condition number is at most
$N$, valid for all $N=4M^2$, with $M$ a positive integer.
