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Jan 5, 2021 at 15:00 comment added Max Alekseyev It may be worth to try solvers like Gurobi or CPLEX (possibly from SageMath).
Jan 5, 2021 at 14:10 comment added Matthias Künzer Thanks! That worked efficiently for a 12-dimensional subspace of a 64-dimensional space. We have used Magma's MinimalIntegerSolution. Trying to push the boundary then, for a 20-dimensional subspace of a 144-dimensional space, it produced an overflow.
Jan 5, 2021 at 14:01 vote accept Matthias Künzer
Jan 4, 2021 at 3:34 history bounty ended Louis Deaett
Jan 3, 2021 at 18:22 history edited Max Alekseyev CC BY-SA 4.0
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Jan 3, 2021 at 18:11 history answered Max Alekseyev CC BY-SA 4.0