KNIGHT COVERS FOR THE 40x40 CHESSBOARD
       The 40x40 board was attempted because it seemed likely that the best possible knight cover would use Monier's pattern. The best unconstrained cover found so far is the following 232-knight cover using mainly tetrads.
       The best knight cover found using Monier's pattern is the 232-knight placement shown below it. A 230-knight cover using a newer pattern is shown below that. So it is possible that Monier's pattern never becomes the dominant pattern for large boards.

 

A 232-knight cover of a 40x40 chessboard using tetrads Found July 25, 2004 by Frank Rubin

 

A 232-knight cover of a 40x40 chessboard using Monier's pattern. The black knights show Monier's pattern. This covering can be regarded as 7 separate strands of Monier's pattern, or as one large region of a more general Monier pattern in which the strands of 1x2 blocks may be offset from each other, and may have opposing orientations. Found August 4, 2004 by Frank Rubin

 

A 230-knight cover of a 40x40 chessboard using a new pattern Found August 28, 2004 by Frank Rubin

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