The paper presents a novel approach to sampling projections in the uniform norm, focusing on $n$-dimensional subspaces of the space of complex-valued bounded functions on a set $D$. The authors show that there exist sampling projections with at most $2n$ samples and a norm of order $\sqrt{n}$, improving upon Auerbach's lemma. This result is derived from a specific discretization of the uniform norm, which bounds the continuous sup-norm by a discrete $\ell_2$-norm. The main theorem states that for any $n$-dimensional subspace $V_n$ of $B(D)$, there are $2n$ points $x_1, \ldots, x_{2n} \in D$ and functions $\varphi_1, \ldots, \varphi_{2n} \in V_n$ such that the projection $P$ defined by $Pf = \sum_{i=1}^{2n} f(x_i) \varphi_i$ has a norm of order $\sqrt{n}$. The paper also discusses the implications of this result for optimal recovery in $L_p$ norms and provides sharp bounds on the sampling numbers in terms of Kolmogorov widths. The authors conclude with a discussion on the sharpness of their results and related open problems.The paper presents a novel approach to sampling projections in the uniform norm, focusing on $n$-dimensional subspaces of the space of complex-valued bounded functions on a set $D$. The authors show that there exist sampling projections with at most $2n$ samples and a norm of order $\sqrt{n}$, improving upon Auerbach's lemma. This result is derived from a specific discretization of the uniform norm, which bounds the continuous sup-norm by a discrete $\ell_2$-norm. The main theorem states that for any $n$-dimensional subspace $V_n$ of $B(D)$, there are $2n$ points $x_1, \ldots, x_{2n} \in D$ and functions $\varphi_1, \ldots, \varphi_{2n} \in V_n$ such that the projection $P$ defined by $Pf = \sum_{i=1}^{2n} f(x_i) \varphi_i$ has a norm of order $\sqrt{n}$. The paper also discusses the implications of this result for optimal recovery in $L_p$ norms and provides sharp bounds on the sampling numbers in terms of Kolmogorov widths. The authors conclude with a discussion on the sharpness of their results and related open problems.