The minimum overlap problem
by Jan Kristian Haugland

Please confer my articles on this topic

"Record-holding" step functions:

Number of steps
1	0.5
2	0.444444...
3	0.4
4	0.4
5	0.391864...
6	0.388888....
7	0.386120....
8	0.385071....
9	0.382892....
10	0.382427....
11	0.382093....
15	0.381531....
17	0.381430....
19	0.381112....
29	0.380989....
35	0.380970....
49	0.380964....
51	0.380926....

The gap between the lower and the upper bound was significantly reduced in 2022 when E. P. White improved the lower bound (for lim M(n)/n) from 0.356393... (Moser, 1959) to 0.379005.