# Affine plane of order 4?

I cannot seem to construct an affine plane of order 4. I have the construction for order 3- but cannot seem to come up with or find the construction for 4 anywhere. Could someone show me a picture of one, preferably with parallel lines indicated?

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An example is given here, but without any motivation. You could probably try looking at $F\times F$, where $F$ is the field of 4 elements.