New bounds on the maximum number of points on genus-4 curves over small finite fields (1108.5393v4)

Abstract: For prime powers q<100, we compute new upper and lower bounds on N_q(4), the maximal number of points on a genus-4 curve over a finite field with q elements. We determine the exact value of N_q(4) for 17 prime powers q for which the value was previously unknown.