  We use a deterministic construction to prove the optimality of the exponent
in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem for dimension
$d=1$ and parameter range $0 < a,b \leq d$ and $b\leq 2a$. Previous
constructions by Hambrook and Laba and Chen required randomness and only
covered the range $0 < b \leq a \leq d=1$. We also resolve a question of Seeger
about the Fourier restriction inequality on the sets of well-approximable
numbers.
