On constructions for two dimensional balanced sampling plan excluding contiguous units with block size four

Balanced sampling plans excluding contiguous units (BSEC) were first introduced in 1988 by Hedayat, Rao and Stufken [A.S. Hedayat, C.R. Rao, J. Stufken, Sampling plans excluding contiguous units, J. Statist. Plann. Inference 19 (1988) 159–170]. These designs can be used for survey sampling when the contiguous units provide similar information. In this paper, we show some recursive constructions for two dimensional BSECs with block size four, and give the existence of some infinite classes.