In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper [13] by Kötter and Kschischang were they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue [7] which they used for the construction of designs over finite fields to do the construction of space codes. Using this approach we found many new constant dimension spaces codes with a larger number of codewords than previously known codes. We will finally give a table of the best found constant dimension space codes. network coding, q-analogue of Steiner systems, subspace codes

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We construct new (n, r)-arcs in P G(2, q) by prescribing a group of automorphisms and solving the resulting Diophantine linear system with lattice point enumeration. We can improve the known lower bounds for q = 11, 13, 16, 17, 19 and give the first example of a double blocking set of size n in P G(2, p) with n < 3p and p prime.

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