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 October 7, 2009 [A new website is available at www.manypoints.org]

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Gerard van der Geer, Marcel van der Vlugt
• Keywords: Finite Fields, Irreducible Projective Curve, MOC 2000, Small Genus