Polygonal designs: some existence and non-existence results

Balanced Sampling Plans Excluding Adjacent Units for One Dimentional Population

“…Proofs of the results in Theorem 1 can be found in [2], [12] and [13]. For certain parametric combinations, the necessary conditions are also sufficient.…”

“…[10] and [11] provided solution of cBSA for n = 4 and α = 1. [12]; [13] and [14] presented interesting existence results for cBSA for n ≥ 4 and α ≥ 1. The following theorem gives an existence result.…”

Generalized polygonal designs with block size 3 and

“…It is important to mention here that Stufken et al (1999) coined the name PDs for BSEC and BSA plans. Other exact titles on PDs are Stufken and Wright (2001) and Bhattacharyya et al (2008).…”

“…Other exact titles on PDs are Stufken and Wright (2001) and Bhattacharyya et al (2008). Stufken et al (1999) showed that a PD (v, k, ; m) is equivalent to BSA(v, k, ; m). Also, it is very easy to show that BSEC (v, k, ) is equivalent to BSA(v, k, ; 1) (Wei, 2002).…”

“…Also, it is very easy to show that BSEC (v, k, ) is equivalent to BSA(v, k, ; 1) (Wei, 2002). Thus, in the context of block designs (in the form of either BSEC, BSA or PBIBD), the work with limited distance m appeared in Hedayat et al (1988a, b), See et al (1997), Ling (1998, 1999), Stufken et al (1999), Stufken and Wright (2001), Wei (2002), Zhang and Chang (2005a, b, 2006, 2007, Bhattacharyya et al (2008), Dukes and Ling (2008) and Mandal et al (2008aMandal et al ( , b, 2009.…”