known; the best lengths found so far for dimensions nine through thirteen are 190, 370, 712, 1373, 2687. For cycles (the coil-in-the-box problem), a cycle cannot exist in a hypercube of dimension less than two. The maximum lengths of the longest possible cycles are 0, 4, 6, 8, 14, 26, 48, 96 . Beyond that length, the exact length of the longest cycle is not known; the best lengths found so far for dimensions nine through thirteen are 188, 366, 692, 1344, 2594. Doubled coils are a special case: cycles whose second half repeats the structure of their first half, also known as symmetric coils. For dimensions two through seven the lengths of the longest possible doubled coils are 4, 6, 8, 14, 26, 46. Beyond that, the best lengths found so far for dimensions eight through thirteen are 94, 186, 362, 662, 1222, 2354. For both the snake and the coil in the box problems, it is known that the maximum length is proportional to 2n for an n-dimensional box, asymptotically as n grows large, and bounded above by 2n − 1. However the constant of proportionality is not known, but is observed to be in the range 0.3 - 0.4 for current best known values. Notes References External links Error detection and correction Computational problems in graph theory