Print Email Facebook Twitter On The Cap Set Problem Title On The Cap Set Problem: upper bounds on maximal cardinalities of caps in dimensions seven to ten Author Versluis, Nina (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics) Contributor Gijswijt, Dion (mentor) van Elderen, Emiel (graduation committee) de Groot, Joost (graduation committee) Degree granting institution Delft University of Technology Date 2017-07 Abstract This thesis concerns the cap set problem in affine geometry. The problem is illustrated by the card game SET and its geometrical interpretation in ternary affine space. The maximal cardinality of a cap is known for the dimension one to six. For the four lowest dimensions, a maximal cap is constructed and the optimality of its size proven. From there, two recursive methods are described and applied to obtain upper bounds for the maximal size of caps in dimensions seven to ten. The best found upper bounds are 291, 771, 2070 and 5619, respectively. Subject Affine capsAffine geometryOptimization To reference this document use: http://resolver.tudelft.nl/uuid:6818b21f-038d-4700-afcd-e6dac79e7e82 Part of collection Student theses Document type bachelor thesis Rights © 2017 Nina Versluis Files PDF Bachelor_Thesis_Nina_D_Versluis.pdf 1.04 MB Close viewer /islandora/object/uuid:6818b21f-038d-4700-afcd-e6dac79e7e82/datastream/OBJ/view