# series3: This function constructs five-associate class PBIB designs In PBIBD: Partially Balanced Incomplete Block Designs

## Description

Let us consider a module M of residue class mod(5) having elements 0, 1, 2, 3, 4 and all the elements of M are assigned to each of the n >= 2 classes. This function constructs PBIB designs with the following parameters:

v = 5n, b = 5n, r = 2(n + 1), k = 2(n + 1)

lambda 1 = n + 2, lambda 2 = n + 2, lambda 3 = 3, lambda 4 = 2, lambda 5 = 2n

## Usage

 `1` ```series3(n) ```

## Arguments

 `n` n is the number of classes to which the elements of Module M are assigned

## Value

The function returns the required PBIB design with specified parameters

## Author(s)

Parneet Kaur, Davinder Kumar Garg

## Examples

 `1` ```series3(5) ```

### Example output

```     [,1] [,2] [,3] [,4] [,5]
[1,]    1    6   11   16   21
[2,]    2    7   12   17   22
[3,]    3    8   13   18   23
[4,]    4    9   14   19   24
[5,]    5   10   15   20   25
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,]    1    2    3    4    7   12   17   22    8    13    18    23
[2,]    6    7    8    9    2   12   17   22    3    13    18    23
[3,]   11   12   13   14    2    7   17   22    3     8    18    23
[4,]   16   17   18   19    2    7   12   22    3     8    13    23
[5,]   21   22   23   24    2    7   12   17    3     8    13    18
The Parameters of the design are:
v =  25 b =  25 r =  12 k =  12
lambda[ 1 ] =  7 	lambda[ 2 ] =  7 	lambda[ 3 ] =  3 	lambda[ 4 ] =  2 	lambda[ 5 ] =  10
The developed blocks are:
( 1 2 3 4 7 8 12 13 17 18 22 23 )
( 2 3 4 5 8 9 13 14 18 19 23 24 )
( 3 4 5 1 9 10 14 15 19 20 24 25 )
( 4 5 1 2 10 6 15 11 20 16 25 21 )
( 5 1 2 3 6 7 11 12 16 17 21 22 )
( 6 7 8 9 2 3 12 13 17 18 22 23 )
( 7 8 9 10 3 4 13 14 18 19 23 24 )
( 8 9 10 6 4 5 14 15 19 20 24 25 )
( 9 10 6 7 5 1 15 11 20 16 25 21 )
( 10 6 7 8 1 2 11 12 16 17 21 22 )
( 11 12 13 14 2 3 7 8 17 18 22 23 )
( 12 13 14 15 3 4 8 9 18 19 23 24 )
( 13 14 15 11 4 5 9 10 19 20 24 25 )
( 14 15 11 12 5 1 10 6 20 16 25 21 )
( 15 11 12 13 1 2 6 7 16 17 21 22 )
( 16 17 18 19 2 3 7 8 12 13 22 23 )
( 17 18 19 20 3 4 8 9 13 14 23 24 )
( 18 19 20 16 4 5 9 10 14 15 24 25 )
( 19 20 16 17 5 1 10 6 15 11 25 21 )
( 20 16 17 18 1 2 6 7 11 12 21 22 )
( 21 22 23 24 2 3 7 8 12 13 17 18 )
( 22 23 24 25 3 4 8 9 13 14 18 19 )
( 23 24 25 21 4 5 9 10 14 15 19 20 )
( 24 25 21 22 5 1 10 6 15 11 20 16 )
( 25 21 22 23 1 2 6 7 11 12 16 17 )
```

PBIBD documentation built on May 1, 2019, 7:31 p.m.