The maximum number of SETs for 12 cards

SET is a card game that is played with a deck of 81 cards. The shape(s) shown on each card have four qualities: quantity, shading, colour, and shape. Each of the qualities can have one of three possible values: the quantity can be one, two, or three; the shading can be open, striped/shaded, or solid; the colour can be red, green, or purple; and the shap…