Existence of simple BIBDs from a prime power difference family with minimum index

2019 ◽  
Vol 18 (09) ◽  
pp. 1950166
Author(s):  
Hsin-Min Sun
Keyword(s):  
Simple Formula ◽  
Prime Power ◽  
Block Designs ◽  
Incomplete Block ◽  
Difference Family ◽  
Balanced Incomplete Block Designs ◽  
Extensive Analysis ◽  
Power Difference ◽  
Balanced Incomplete Block ◽  
Minimum Index

We show that under certain technical conditions that simple [Formula: see text] balanced incomplete block designs (BIBDs) exist for all allowable values of [Formula: see text], where [Formula: see text] is an odd prime power. Our primary technique is to argue for the existence of difference families in finite fields, in the flavor of Wilson [J. Number Theory 4 (1972) 17–47]. We provide an extensive analysis in the cases, where [Formula: see text] and also for [Formula: see text].

Some Series of SGDD's with the Dual Property, BOD's and BIBD's

1981 ◽  
Vol 30 (3-4) ◽  
pp. 115-122
Author(s):  
A. C. Mukhopadhyay
Keyword(s):  
Prime Number ◽  
Infinite Series ◽  
Prime Power ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Dual Property ◽  
Group Divisible ◽  
Symmetrical Group ◽  
Balanced Incomplete Block

In the present paper an infinite series of Ba1am:ed ortbozonal designs (BOD's) is constructed for each s, an odd prime number or prime power and hence some infinite series of balanced incomplete block designs (BIBD's) and symmetrical group divisible designs (SGDD's) witb dual Ptoperty. Following Bose (1977), equivalences of some series of SGDD's with dual property are cstablished and their equivalence with corresponding series of BOD's is pointed out.

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Petteri Kaski ◽  
Patric Östergård
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Doctoral Thesis ◽  
Parallel Class ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block

AbstractApproaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points.

Sign in / Sign up

Export Citation Format

Share Document