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In a geometry, a maximal cap is a collection of points of largest sizecontaining no lines. In AG(4,3), maximal caps contain 20 points. The 81 pointsof AG(4,3) can be partitioned into 4 mutually disjoint maximal caps togetherwith a single point P, where every pair of points that makes a line with P liesentirely inside one of those caps. The caps in a partition can be paired up sothat both pairs are either in exactly one partition or they are both in twodifferent partitions. This difference determines the two equivalence classes ofpartitions of AG(4,3) under the action by affine transformations.

Partitions of AG(4,3) into Maximal Caps