The maximum length for the snake-in-the-box problem is known for dimensions one through eight; it is

1, 2, 4, 7, 13, 26, 50, 98 (sequence A099155 in the OEIS). Beyond that length, the exact length of the longest snake is not known; the best lengths found so far for dimensions nine through thirteen are

190, 370, 712, 1373, 2687.

Finding the longest snake or coil becomes notoriously difficult as the dimension number increases and the search space suffers a serious combinatorial explosion. Some techniques for determining the upper and lower bounds for the snake-in-the-box problem include proofs using discrete mathematics and graph theory, exhaustive search of the search space, and heuristic search utilizing evolutionary techniques.