On several new projective curves over F/sub 2/ of genus 3, 4, and 5

Using known techniques of desingularization for singular plane projective curves over finite fields F/sub q/, q=2/sup m/, we found several new binary plane projective curves of genus 3, 4, and 5 with the maximal number of F/sub q/-rational points (q=2/sup m/, m=3, 4, 5, 6, 7, 8, and 9) on their smooth projective models, which are close to or meet Serre's upper bound.