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Table 3 Designs with optimal pool size for various prevalences

From: Effective matrix designs for COVID-19 group testing

m

Prev.

N

M

G

Desc.

3

0.14

7

5

1.4

PP\(_{\text {PG}}\)(2,2,1) (1 singl.)

4

0.071

14

8

1.8

PP(4,2,1)

5

0.043

23

10

2.3

PP(5,2,1)

6

0.031

32

15

2.1

PP\(_{\text {PG}}\)(5,2,1) (5 singl.)

7

0.024

42

14

3

PP(7,2,1)

8

0.017

58

16

3.6

PP(8,2,1)

9

0.015

66

16

4.1

PP\(_{\text {PG}}\)(8,2,1)

10

0.01

96

31

3.1

PP\(_{\text {PG}}\)(9,2,1) (13 singl.)

11

0.0083

121

22

5.5

PP(11,2,1)

12

0.0073

137

36

3.8

PP\(_{\text {PG}}\)(11,2,1) (14 singl.)

13

0.0059

169

26

6.5

PP(13,2,1)

16

0.0039

256

32

8

PP(16,2,1)

18

0.0031

318

61

5.2

PP\(_{\text {PG}}\)(17,2,1) (27 singl.)

32

0.00098

1024

64

16

PP(32,2,1)

  1. Number of singleton pools added to projective geometry. This ensures that each sample is tested in the case \(k < q\) as described in section “Projective Geometry”. Optimal pool sizes and prevalences are from [10]