... find the largest certificates. The results are shown in table 3. The first column shows the Van der Waerden num-ber. In the second and third column, the used prime for power residue coloring and the number ... AppendixHere the visualizations of the certificates, improving the lower bounds for W (4, k) andW (6, k), are shown. The cycles of a zipped cyclic certificate are exact copies of each otherwhich ... overlap. For the sake of clarity, only the first cycle is visualized.Figure 9: Graphical representation of a cycle of a ZCW (4, 5, 17705) the electronic journal of combinatorics 14 (2007), #R6 14there...