On the graph of a function in many variables over a finite field

Some improved bounds on the number of directions not determined by a point set in the affine space AG(k, q) are presented. More precisely, if there are more than pe (q -1) directions not determined by a set of qk-1 points S then every hyperplane meets S in 0 modulo pe+1 points. This bound is shown to be tight in the case pe = qs and when q = pes sets of qk-1 points that do not meet every hyperplane in 0 modulo pe+1 points and have a little less than pe (q - 1) non-determined directions are constructed.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Simeon Ball
• Keywords: Case Pe, Computer Graphics, DCC 2008, Modulo Pe+1 Points, Qk-1 Points