A Serre-type integrality argument applied to the Weil-Oesterlé hierarchy gives an explicit strengthening of Ihara's bound on N_q(g), improving known records for several (q,g) pairs.
Howe, New bounds on the maximum number of points on genus-4 curves over small finite fields, Arithmetic, geometry, cryptography and coding theory, Contemp
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Refinements on higher order Weil-Oesterl\'e bounds via a Serre type argument
A Serre-type integrality argument applied to the Weil-Oesterlé hierarchy gives an explicit strengthening of Ihara's bound on N_q(g), improving known records for several (q,g) pairs.