Mahou shoujo lyrical nanoha innocents manga

Mahou Shoujo Lyrical Nanoha Innocents summary:

Set in a world parallel to other continuities. Summer 2010. A strange researcher from a suburban city developed a total-immersion virtual reality game that would sweep the world. The game is called "Brave Duel," a motion-sensing simulation card game with team battles. This is a story of a girl whose fate leads her to meet many rivals, compete with them and grow from the experience. Their summer is about to start!