For every fixed $k\ge3$, we construct an explicit total Boolean function in the $k$-player number-on-forehead model with public-coin randomized communication complexity $O_k(1)$ and nondeterministic communication complexity $\Omega_k(n)$, where $n$ is the number of bits on each forehead. This extends the explicit three-player separations of Kelley, Lovett, and Meka (STOC 2024) and Kelley and Lyu (FOCS 2025) to every fixed number of players, and as a side product improves the three-player nondeterministic lower bound from $\Omega(n^{1/2})$ to the optimal $\Omega(n)$. Our construction is based on algebraic geometry codes.