Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this paper, we discuss these designs having cyclic automorphisms. We use Langford sequence to construct all admissible cyclic BSEC (or CBSEC) of block size 3. As consequent we obtain that the existence spectrum of a CBSEC(v, 3, ) are either v ∈ {1, 3}, or v 9 and (v − 3) ≡ ...

The cardinality of the minimal pairwise balanced designs on v elements with largest block size k is denoted by g(k)(v). It is known that 31 ≤ g(4)(18) ≤ 33. In this paper we show that g(4)(18) 6= 31.

We find the graphs of valency at most 7 with the property that any two nonadjacent vertices have either 0 or 2 common neighbours. In particular, we find all semibiplanes of block size at most 7.

By an FGDRP(3, g), we mean a uniform frame (X,G,A) of block size 3, index 2 and type g, where the blocks of A can be arranged into a gu/3× gu array. This array has the properties: (1) the main diagonal consists of u empty subarrays of sizes g/3×g; (2) the blocks in each column form a partial parallel class partitioning X \G for some G ∈ G, while the blocks in each row contain every element of X...

Introduction

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...

A holey perfect Mendelsohn design of type h n 1 1 h n 2 2 h n k k (HPMD(h n 1 1 h n 2 2 h n k k) with block size four is equivalent to a frame idempotent quasigroup satisfying Stein's third law with the same type, where a frame quasigroup of type h n 1

It is proved in this paper that for m ≡ 0; 2; 6; 10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v ≡ 0 (mod 4), v ≡ 0 (modm), v − m ≡ 0 (mod 3), except when (3; 12) and except possibly when (3; 264); (3; 372); (8; 80); (8; 104), (9; 396) (40; 400) or (40; 520). c © 2002 Elsevier Science B.V. All rights reserved.

We find the 302 graphs of valency 8 with the property that any two nonadjacent vertices have 0 or 2 common neighbours, and, in particular, the 104 semibiplanes of block size 8.