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Bastia were left frustrated after just five minutes had been played, when Yannick Cahuzac saw his speculative effort from range cannon back off the crossbar.
Nantes had to wait for the best part of 30 minutes to create a meaningful chance, and Kolbeinn Sigthorsson might have done better as he skewed his shot wide of the target from inside the area.
Yacine Bammou might have put Nantes into the lead after half time, but he was unable to keep his header down despite climbing highest in the box.
Both sides pushed for the winner late on, but neither team was able to prove clinical enough as the game finished goalless.