An "n-overlap" is a word of the form xxx', where x is a nonempty word of length at least n, and x' is a prefix of x of length n. Thus, for example, abcdabcdab is a 2-overlap. A split occurrence of a pattern p is a word of the form xyz where xz matches the pattern.
For n = 0,1,2,3 the lexicographically least words achieving the bound are:
n = 0: 01
n = 1: 0011
n = 2: 000110100111
n = 3: 00111010100001010011101000011111000011010001110