"Codes that are similar are located closer together than codes that are different." I dug hoping to find out how they handle boundary effects, and gave up. Th

"Codes that are similar are located closer together than codes that are different." I dug hoping to find out how they handle boundary effects, and gave up. The numbers 0.999999 and 1.000000 are far apart in Hamming distance but close in position. What bounds are achievable for the maximum Hamming distance between two nearby locations, in any such system? Do they approach the theoretical limit here, or is "that are similar" a crock that only sometimes holds? For example, for a base 12 location code one could overlay a dodecahedron onto the earth, then rotate it by a low-discrepancy sequence of quaternions for successive digits. This would have very nice bounds for the maximum Hamming distance between nearby locations, at the expensive of efficiency: each successive digit subdivides the location by far less than a factor of 12. As locations approach each other, vanishingly few rotations will distinguish them. One can imagine easy fixes for this scheme, but what is the theory? Do they have a theory? Do they implement it?