Grease and flour bottoms of two 9 x 1 1/2-inch round cake pans. In a medium bowl, stir flour, cocoa, baking soda and baking powder; set aside. In a large bowl with mixer at high speed, beat eggs, sugar and vanilla, scraping bowl occasionally, 3 minutes or until light and fluffy. Reduce speed to low; beat in mayonnaise until blended. Add flour mixture in 4 additions alternately with water, beginning and ending with flour. Pour into prepared pans. Bake as 350 degrees for 30 to 35 minutes or until cake tester inserted in center comes out clean. Cool in pans on wire racks 10 minutes. Remove; cool completely on racks. Frost as desired.