Abstract
The aim of this paper is to a geometric construction of Surface Complete (k, r)-cap in PG(3,7). We found that the maximum complete (k, 2)-cap which is called an ovaloid, exists in PG (3, 7) when k = 23. Moreover the complete (k, 3)-caps, (k, 4)-caps and (k, 5)-caps,(k,6)-caps, (k,7)-caps, (k,8)-caps, and we obtain a new example for theorem(2.8 ).
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