🚀 go-pugleaf

Does anyone know the status on the following problem ?

Let S(n) be the set of all permutations of the integers 1..n
Let T(n) be the set of all transpositions (i.e. swapping
two numbers).

For which n can one find a set B(n) such that for all p in S(n)
either p is in B(n), or p differs by exactly one transposition
from an element of B(n), and such that no two elements from B(n)
differ by exactly one transposition ?

If such a B(n) exists, then it is of size n!/[1+n(n-1)/2] since
each element from B(n) differs by exactly one transposition from
n(n-1)/2 elements from S(n), thus we can rule out n=3,4,5. It is
trivially possible for n=2, and in 1974 (!) no other affirmative
solution was known.