New bounds on the maximum number of points on genus-4 curves over small   finite fields
  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. 
Everett W. Howe
math.AG math.NT