Some new large sets of geometric designs of type LS[3][2; 3; 2^8]

Let v be an n-dimensional vector space over f q. by a geometric t-[q^n; k; λ] design we mean a collection d of k-dimensional subspaces of v , called blocks, such that every t-dimensional of v appears in exactly  blocks in d: a large set, ls[n][t; k; q^n], of geometric designs, is a collection ofsubspace t n t-[qn; k; λ] designs which partitions the collection[v k] of all k-dimensional subspaces of v . prior to recent article [4] only large sets of geometric 1-designs were known to exist. however in [4] m. braun,a. kohnert, p. östergard, and a. wasserman constructed the world’s first large set of geometric 2-designs, namely an ls[3][2,3,2^8], invariant under a singer subgroup in gl8(2). in this work we construct an additional 9 distinct, large sets ls[3][2,3,2^8], with the help of lattice basis-reduction.