Finding Longest Paths in Hypercubes: 11 New Lower Bounds for Snakes, Coils, and Symmetrical Coils

New Bounds for the Snake-in-the-Box Problem

“…-For n = 9, Wynn [20] proved that the length of a longest snake and coil is at least 190 and 188, respectively. -For n = 10, Kinny [10] showed that a longest snake has length at least 370 and Meyerson et al [12] showed that a longest coil has length at least 362.…”

“…-For 11 ≤ n ≤ 12, the results of Meyerson et al [12] from 2015 are known to give the best lower bounds for the lengths of a longest snake and coil. -For n = 13, Meyerson et al [12] showed that a longest snake has length at least 2520 and Abbott and Katchalski [1] showed that a longest coil has length at least 2468. -For 14 ≤ n ≤ 20, the results of Abbott and Katchalski [1] from 1991 are still unbeaten.…”