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Circular binary block second- and higher-order neighbor designs. (English) Zbl 1169.05009
A neighbor design with $$v$$ treatments is a collection of circular blocks of constant size, $$k$$, such that any 2 treatments appear in a block equally often as neighbors. They can be used for estimating treatment effects and nearest neighbor effects. If any 2 treatments also occur together equally often and 2nd order neighbors, 3rd order neighbors …$$p$$th order neighbors, the design is called a $$p$$th order neighbor design. The authors provide new examples of 2nd, 3rd and 4th order neighbor designs, mostly with $$k$$ in $$\{v,v-1,(v-1)/2\}$$, that are either cyclic or 1-rotational. Some statistical models applicable to these designs are also given.

##### MSC:
 05B05 Combinatorial aspects of block designs 62K10 Statistical block designs 62K05 Optimal statistical designs
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##### References:
 [1] DOI: 10.2307/2532269 · doi:10.2307/2532269 [2] DOI: 10.1214/009053604000000481 · Zbl 1045.62074 · doi:10.1214/009053604000000481 [3] DOI: 10.1016/S0378-3758(99)00004-X · Zbl 0939.62076 · doi:10.1016/S0378-3758(99)00004-X [4] Filipiak K., Listy Biometryczne & # 8211; Biometrical Letters 42 (2) pp 133– (2005) [5] Ipinyomi , R. A. ( 1985 ). Equineighbored Experimental Designs . PhD thesis , UK : University of Southampton . [6] Iqbal I., Journal of Research (Science) 17 (3) pp 191– (2006) [7] DOI: 10.1007/s11425-007-0035-2 · Zbl 1121.62070 · doi:10.1007/s11425-007-0035-2 [8] DOI: 10.2307/2528428 · doi:10.2307/2528428
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