A two-distance set in E^d is a point set X inthe d-dimensional
Euclidean spacesuch that the distances between distinct points in
Xassume only two different non-zero values. Based on results from
classical distance geometry, we developan algorithm to classify,
for a given dimension, all maximal (largest possible)two-distance
sets in E^d.Using this algorithm we have completed the full
classificationfor all dimensions less than or equal to 7, andwe
have found one set in E^8 whosemaximality follows from Blokhuis'
upper bound on sizes of s-distance sets.While in the dimensions
less than or equal to 6 our classifications confirmthe maximality
of previously known sets, the results in E^7 and E^8are new. Their
counterpart in dimension larger than 10is a set of unit vectors
with only two values of inner products in the Lorentz space
R^{d,1}.The maximality of this set again follows from a bound due
to Blokhuis.

Number of pages | 20 |
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Publication status | Published - 1996 |
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