Abstract We investigate the sharp endpoint extension inequality for the moment curve in finite fields. We determine the optimal constant and characterize the maximizers in two complementary regimes: (i) low dimensions d 20 and (ii) large field cardinality q d (d-1) 2 6 + (2d-1) 3. Our proof strategy relies on an intriguing interplay between analysis, algebra, and combinatorics.
Biswas et al. (Fri,) studied this question.