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In this paper, we further investigate the constructions on three-dimensional$(u\times v\times w,k,1)$ optical orthogonal codes with the at most one opticalpulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\timesv\times w,k,1)$-OOCs) by way of the corresponding designs. Several newauxiliary designs such as incomplete holey group divisible designs andincomplete group divisible packings are introduced and therefore newconstructions are presented. As a consequence, the exact number of codewords ofan optimal AM-OPP $3$-D $(u\times v\times w,3,1)$-OOC is finally determined forany positive integers $v,w$ and $u\geq3$.

Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction