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ABSTRACT
Let denote the maximum cardinality of a set
of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q,
, such that any two different subspaces
have a distance
of at least d. Lower bounds on
can be obtained by explicitly constructing corresponding sets
. When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of
. With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on
and
for 8 ⩽ n ⩽ 11 are obtained.