This reposytorium contains programs, which were intented to verify a conjecture about a specific property of small weak epsilon-nets.
Clone this repositorium and install or-tools for Python. Make sure Python3 is installed on Your computer.
git clone git@github.com:erheron/grid-conjecture.git && cd grid-conjecture
python3 -m venv ortools
source ortools/bin/activate
python3 -m pip install ortools
Run gen4.cpp which (for nets for size 4) generates the set G of inclusion-minimal sets of rectangles, which cannot be hit by any net.
cd grid-conjecture
g++ -O4 gen4.cpp -o gen4
./gen4 > input.txt &
Next, run LP solver, which will take a few hours. You can pass --terminate option, and in that case the program will end after it finds first counterexample.
python3 lp-solver.py [--terminate] input.txt 4 > examples.out &
In examples.out there will be all counterexamples for k=4.