In the P.Q. Nguyen and I.E. Shparlinski, The Insecurity of the Digital Signature Algorithm with Partially Known Nonces, Journal of Cryptology, vol. 15, no. 3, pp. 151–176, Springer, 2002 on the page 157 the author says:
This is done by considering the (d + 1)-dimensional lattice $L(q, \ell, t_1,..., t_d)$ spanned by the rows of the following matrix:
$\begin{pmatrix} q & 0 & \dots & 0 & 0 \\ 0 & q & \ddots & \vdots & \vdots \\ \vdots & \ddots & \ddots & 0 & \vdots \\ 0 & \dots & 0 & q & 0 \\ t_1 & \dots & \dots & t_d & 1/2^{\ell+1} \end{pmatrix}$
How $L(q, \ell, t_1,..., t_d)$ might be (d+1) dimensional? (It has d+2 dimensions: q, $\ell$ and d numbers of t)
How lattice can be spanned by the rows of the matrix? What does it means? Maybe that means that we need to multiply the matrix by the basis (in vector-column representation) of the lattice?
(Please give the answer or point the to literature)
For the first question, I understand, that $q, \ell, t_1,..., t_d$ is the parameters not a dimension.