  Optical orthogonal signature pattern codes (OOSPCs) have attracted wide
attention as signature patterns of spatial optical code division multiple
access networks. In this paper, an improved upper bound on the size of an
$(m,n,3,\lambda_a,1)$-OOSPC with $\lambda_a=2,3$ is established. The exact
number of codewords of an optimal $(m,n,3,\lambda_a,1)$-OOSPC is determined for
any positive integers $m,n\equiv2\ ({\rm mod }\ 4)$ and $\lambda_a\in\{2,3\}$.
