Tables of curves with many points

These tables record results on curves with many points over finite fields. For relatively small genus (0 ≤ g ≤ 50) and q a small power of 2 or 3 we give in two tables the best presently known bounds for Nq(g), the maximum number of rational points on a smooth absolutely irreducible projective curve of genus g over a field Fq of cardinality q. In additional tables we list for a given pair (g, q) the type of construction of the best curve so far and we give a reference to the literature where such a curve can be found. Updated Version 28 November 2006 [Next update: July 2007]