The card game SET can be modeled by four-dimensional vectors over Z3. These vectors correspond to points in the affine four-space of order three (AG(4,3)), where lines correspond to SETs, and in the affine plane of order nine (AG(2,9)). SETless collections and other aspects of the game of SET will be explored through caps in AG(4,3) and conics in AG(2,9).
"Geometric Models of the Card Game SET,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8:
1, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss1/10