Here is a selection of recent papers on orthogonal Latin hypercube designs. I'm not sure these are the same as Graeco-Latin hypercubes, but surely these papers give some idea of what designs are, and are not, possible.

MR2659850 (2011k:62223)
Sun, Fasheng; Liu, Min-Qian; Lin, Dennis K. J.
Construction of orthogonal Latin hypercube designs with flexible run sizes.
J. Statist. Plann. Inference 140 (2010), no. 11, 3236–3242.

MR3183676
Georgiou, Stelios D.; Efthimiou, Ifigenia
Some classes of orthogonal Latin hypercube designs.
Statist. Sinica 24 (2014), no. 1, 101–120.

MR3377513
Cao, Rui-Yuan; Liu, Min-Qian
Construction of second-order orthogonal sliced Latin hypercube designs.
J. Complexity 31 (2015), no. 5, 762–772.

MR3254915
Georgiou, S. D.; Stylianou, S.; Drosou, K.; Koukouvinos, C.
Construction of orthogonal and nearly orthogonal designs for computer experiments.
Biometrika 101 (2014), no. 3, 741–747.

MR3183339
Huang, Hengzhen; Yang, Jian-Feng; Liu, Min-Qian
Construction of sliced (nearly) orthogonal Latin hypercube designs.
J. Complexity 30 (2014), no. 3, 355–365.

MR3183681
Yang, Jinyu; Liu, Min-Qian; Lin, Dennis K. J.
Construction of nested orthogonal Latin hypercube designs.
Statist. Sinica 24 (2014), no. 1, 211–219.

MR2933184
Yang, Jinyu; Liu, Min-Qian
Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs.
Statist. Sinica 22 (2012), no. 1, 433–442.

MR2861300 (2012j:05072)

Sun, FaSheng; Pang, Fang; Liu, MinQian
Construction of column-orthogonal designs for computer experiments.
Sci. China Math. 54 (2011), no. 12, 2683–2692.