Skip to main content

Table 1 Choosing the optimal value for the number of pools per layer, q

From: A new pooling strategy for high-throughput screening: the Shifted Transversal Design

q

Γ

k

v

gain

≤ 13

≥ 3

≥ 16

k > q+1, can't use these values

17

3

16

272

36.8

19

3

16

304

32.9

23

2

11

253

39.5

29

2

11

319

31.3

...

2

11

...

...

97

2

11

1067

9.4

101

1

6

606

16.5

  1. This table shows the gains obtained with various q values, when the total number of variables to be tested is n = 10000 and the number of expected positives is t = 5, in a noiseless experiment (E = 0). Γ is the compression power (i.e. logarithm of n in base q, see Preliminaries in Results(1) section), k is the number of layers, v is the number of pools (i.e. k·q), and the gain is defined as n/v. By construction, STD requires k ≤ q+1; and to guarantee the identification of t positives while correcting E errors, section 3.3 showed that we must choose k = t·Γ+2·E+1; in this example, k = 5Γ+1. Often, the smallest useable q (i.e., satisfying k ≤ q+1), qmin, yields the highest gain, but this is not always the case. In this example, qmin = 17, but q = 23 (smallest q such that Γ = 2) yields the highest gain: 39.5.