On the Incompleteness of (k, n)-arcs in Desarguesian Planes of Order q Where n Divides q |
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Authors: | Simeon Ball Aart Blokhuis |
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Institution: | (1) Technische Universiteit Eindhoven, Postbox 513, 5600 MB Eindhoven, The Netherlands |
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Abstract: | We investigate the completeness of an ( nq – q + n – , n)-arc in the Desarguesian plane of order q where n divides q. It is shown that such arcs are incomplete for 0< n/2 if q/n3. For q = 2n they are incomplete for 0 < < 0.381n and for q = 3n they are incomplete for 0 < < 0.476n. For q odd it is known that such arcs do not exist for = 0 and, hence, we improve the upper bound on the maximum size of such a ( k, n)-arc. |
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Keywords: | maximal arcs arcs finite Desarguesian planes |
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