The author considers the connection between the rate of growth of an entire function and the rate of the best polynomial approximation to this function. Let \(K\) be a compact subset on the complex plane. If \(u_1, \dots, u_n \in K\), \(n \in \mathbb{N}\), then set \[ V(u_1, \dots, u_n) = \prod_{1 \leq k < l \leq n} (u_k - u_l), \quad V_n = \max_{u_1, \dots, u_n \in K} \bigl |V(u_1, \dots, u_n) \bigr |. \] If \(f\) is a continuous function on \(K\), then \(E_n (f,K)\) denotes the best uniform approximation of \(f\) on \(K\) by polynomials of degree at most \(n\). For an arbitrary infinite compact set \(K \subset \mathbb{C}\) the explicit formulas of the order and the type of an entire function \(f\) in terms of asymptotic behavior of the sequence \(E_n (f,K) V_{n + 1} (V_{n + 2})^{-1}\), \(n \in \mathbb{N}\), are obtained.