Abstract
Some new families of caps in Galois affine spaces AG(N, q) of dimension N≡ 0(mod 4) and odd order q are constructed. Such caps are proven to be complete by using some new ideas depending on the concept of a regular point with respect to a complete plane arc. As a corollary, an improvement on the currently known upper bounds on the size of the smallest complete caps in AG(N, q) is obtained.
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