(A preprint is available online.)

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

We use Magma to perform a number of calculations outlined in the paper. Our Magma programs can be found in two files:

We also require a list of the isomorphism classes of unimodular quaternary Hermitian forms over the quadratic rings with discriminant -19 and -20; such lists are available from the Hermitian lattices web site maintained by Rainer Schulze-Pillot-Zieman. Copies of the relevant files, copied from the math.uni-sb.de server in March 2012, are available locally here: