Projective embedding of [0, m]-spaces

A [0, m]-space is a linear space with the following property: For any point-line pair (x, G) there are at most m lines through x which are coplanar with G and which have no point in common with G. For every [0, m]-space (M, M) we define an order ord M in a natural way. For dim M ⩾ 3 and ord M ⩾ 3m + 2, every [0, m]-space (M, M) can be embedded in a projective space (P, L) with dim P = dim M and ord P = ord M.