On The Cap Set Problem

upper bounds on maximal cardinalities of caps in dimensions seven to ten

Bachelor thesis (2017)

Authors

N.D. Versluis Electrical Engineering, Mathematics and Computer Science

Contributors

Dion Gijswijt (mentor)
E.M. van Elderen (graduation committee member)
J.A.M. de Groot (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2017 Nina Versluis
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Published Date

2017-7

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

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.