Cyclic Polygonal Designs with Block Size 3 and λ = 1 for Joint Distance α = 6 to 16

References

• Bhattacharyya , G. , Hegeman , J. , Kim , J. , Langford , J. and Song , S. Y. 2008 . Some existence and construction results of polygonal designs . European Journal of Combinatorics , 29 : 1396 – 1407 .
   Google Scholar
• Bryant , J. D. , Chang , Y. , Rodger , C. A. and Wei , R. 2002 . Two-dimensional balanced sampling plans excluding contiguous units . Communications in Statistics - Theory & Methods , 31 : 1441 – 1455 .
   Web of Science ®Google Scholar
• Christman , M. C. 1997 . Efficiency of some sampling designs for spatially clustered populations . Environmetrics , 8 : 145 – 166 .
   Web of Science ®Google Scholar
• Colbourn , C. J. and Ling , A. C.H. 1998 . A class of triple systems with applications in survey sampling . Communications in Statistics - Theory & Methods , 27 : 1009 – 1018 .
   Web of Science ®Google Scholar
• Colbourn , C. J. and Ling , A. C.H. 1999 . Balanced sampling plans with block size four excluding contiguous units . Australasian Journal of Combinatorics , 20 : 37 – 46 .
   Google Scholar
• Frank , D. C. and O'Shughnessy , C. D. 1974 . Polygonal designs . Canadian Journal of Statistics , 2 : 45 – 59 .
   Google Scholar
• Dukes , P. J. and Ling , A. C.H. 2009 . Existence of balanced sampling plans avoiding cyclic distances . Metrika , 70 : 131 – 140 .
   Web of Science ®Google Scholar
• Hedayat , A. S. , Rao , C. R. and Stufken , J. 1988a . Sampling plans excluding contiguous units . Journal of Statistical Planning and Inference , 19 : 159 – 170 .
   Web of Science ®Google Scholar
• Hedayat , A. S. , Rao , C. R. and Stufken , J. 1988b . “ Designs in survey sampling avoiding contiguous units ” . In Handbook of Statistics 6: Sampling , Edited by: Krishnaiah , P. R. and Rao , C. R. 575 – 583 . Amsterdam : Elsevier .
   Google Scholar
• Hedayat , A. S. and Stufken , J. 1998 . Sampling designs to control selection probabilities of contiguous units . Journal of Statistical Planning and Inference , 72 : 333 – 345 .
   Web of Science ®Google Scholar
• Iqbal , I. 1991 . Construction of Experimental Designs Using Cyclic Shifts , Ph.D. thesis UK : University of Kent at Canterbury .
   Google Scholar
• Iqbal , I. and Tahir , M. H. 2008 . Construction of test-control treatment designs when k > v . Aligarh Journal of Statistics , 28 : 55 – 73 .
   Google Scholar
• Iqbal , I. and Tahir , M. H. 2009 . Circular strongly balanced repeated measurements designs . Communications in Statistics - Theory & Methods , 38 ( 20 ) : 3686 – 3696 .
   Web of Science ®Google Scholar
• Iqbal , I. , Tahir , M. H. and Ghazali , S. S.A. 2009 . Circular neighbor-balanced designs using cyclic shifts . Science in China Series A: Mathematics , 52 ( 10 ) : 2243 – 2256 .
   Google Scholar
• Iqbal , I. , Tahir , M. H. , Akhtar , M. , Ghazali , S. S.A. , Shabbir , J. and Bukhari , N. S. 2009 . Generalized polygonal designs with block size 3 and λ = 1 . Journal of Statistical Planning and Inference , 139 ( 9 ) : 3200 – 3219 .
   Web of Science ®Google Scholar
• Iqbal , I. , Tahir , M. H. and Ghazali , S. S.A. 2010 . Circular first- and second-order balanced repeated measurements designs . Communications in Statistics - Theory & Methods , 39 ( 2 ) : 228 – 240 .
   Web of Science ®Google Scholar
• Kong , H. , Lei , J. and Zhang , Y. 2008 . On constructions for two dimensional balanced sampling plan excluding contiguous units with block size four . Discrete Mathematics , 308 : 3729 – 3743 .
   Google Scholar
• Mandal , B. N. , Parsad , R. and Gupta , V. K. 2008a . Computer-aided construction of balanced sampling plans excluding contiguous units . Journal of Statistics and Applications , 3 : 67 – 93 .
   Google Scholar
• Mandal , B. N. , Parsad , R. and Gupta , V. K. 2008b . IPPS sampling plans excluding adjacent units . Communications in Statistics - Theory & Methods , 37 : 2532 – 2550 .
   Web of Science ®Google Scholar
• Mandal , B. N. , Parsad , R. , Gupta , V. K. and Sud , U. C. 2009 . A family of distance balanced sampling plans . Journal of Statistical Planning and Inference , 139 : 860 – 874 .
   Web of Science ®Google Scholar
• See , K. , Song , S. Y. and Stufken , J. 1997 . On a class of partially incomplete block designs with applications in survey sampling . Communications in Statistics - Theory & Methods , 26 : 1 – 13 .
   Web of Science ®Google Scholar
• See , K. , Song , S. Y. , Stufken , J. and Bailer , A. J. 2000 . Relative efficiencies of sampling plans for selecting a small number of units from a rectangular region . Journal of Statistical Computation and Simulation , 66 : 273 – 294 .
   Web of Science ®Google Scholar
• Stufken , J. 1993 . Combinatorial and statistical aspects of sampling plans to avoid the selection of adjacent units . Journal of Combinatorics and Information System Sciences , 18 : 149 – 160 .
   Google Scholar
• Stufken , J. , Song , S. Y. , See , K. and Driessel , K. R. 1999 . Polygonal designs: Some existence and non-existence results . Journal of Statistical Planning and Inference , 77 : 155 – 166 .
   Web of Science ®Google Scholar
• Stufken , J. and Wright , J. H. 2001 . Polygonal designs with blocks of size k ⩽ 10 . Metrika , 54 : 179 – 184 .
   Web of Science ®Google Scholar
• Tahir , M. H. , Iqbal , I. , Akhtar , M. and Shabbir , J. 2009 . “ Cyclic polygonal designs with block size 3 and λ = 1 for joint distance a α = 2,3,4,5. Under Review ” . In Science in China Series A: Mathematics
   Google Scholar
• Wei , R. 2002 . Cyclic BSEC of block size 3 . Discrete Mathematics , 250 : 291 – 298 .
   Web of Science ®Google Scholar
• Wright , J. H. 2008 . Two-dimensional balanced sampling plans excluding adjacent units . Journal of Statistical Planning and Inference , 138 : 145 – 153 .
   Google Scholar
• Wright , J. H. and Stufken , J. 2008 . New balanced sampling plans excluding adjacent units . Journal of Statistical Planning and Inference , 138 : 3326 – 3335 .
   Web of Science ®Google Scholar
• Zhang , J. and Chang , Y. 2005a . The spectrum of cyclic BSEC with block size three . Discrete Mathematics , 305 : 312 – 322 .
   Web of Science ®Google Scholar
• Zhang , J. and Chang , Y. 2005b . The spectrum of cyclic BSA(v,3,λ;α) with α = 2,3 . Journal of Combinatorial Designs , 13 : 313 – 335 .
   Web of Science ®Google Scholar
• Zhang , J. and Chang , Y. 2006 . Existence of BSAs and cyclic BSAs of block size three . Journal of Statistical Planning and Inference , 137 : 1496 – 1511 .
   Google Scholar
• Zhang , J. and Chang , Y. 2007 . The spectrum of BSA(v,3,λ;α) with α—2,3 . Journal of Combinatorial Designs , 15 : 61 – 76 .
   Web of Science ®Google Scholar
• Zhang , J. and Chang , Y. 2009 . Partitionable sets and cyclic BSECs with block size four . Journal of Statistical Planning and Inference , 139 : 1974 – 1979 .
   Web of Science ®Google Scholar