Table 3 Summary of the best and worst-performing MH sequences across 20 runs of the HH process for cardinalities two and three. The table includes the sequences (Seq) and their corresponding performance (Perf).

1

\([h_3, h_{14}, h_8]\)

0.0065

\([h_1, h_{2}, h_6]\)

0.0114

\([h_{15}, h_{10}]\)

0.00571

\([h_{11}, h_{10}]\)

0.0276

2

\([h_{26}, h_{25}, h_{27}]\)

0.0030

\([h_{16}, h_{1}, h_{17}]\)

0.0121

\([h_{15}, h_{17}]\)

0.00525

\([h_{4}, h_{5}]\)

0.0139

3

\([h_{26}, h_{16}, h_{5}]\)

0.0054

\([h_{14}, h_{24}, h_{21}]\)

0.0108

\([h_{7}, h_{20}]\)

0.00800

\([h_{16}, h_{14}]\)

0.0227

4

\([h_{3}, h_{9}, h_{23}]\)

0.0046

\([h_{0}, h_{6}, h_{16}]\)

0.0112

\([h_{14}, h_{26}]\)

0.0057

\([h_{8}, h_{14}]\)

0.0499

5

\([h_{15}, h_{12}, h_{11}]\)

0.0029

\([h_{23}, h_{14}, h_{9}]\)

0.0222

\([h_{15}, h_{5}]\)

0.0064

\([h_{1}, h_{0}]\)

0.0455

6

\([h_{23}, h_{16}, h_{15}]\)

0.0061

\([h_{1}, h_{4}, h_{9}]\)

0.0119

\([h_{15}, h_{27}]\)

0.0049

\([h_{1}, h_{12}]\)

0.0133

7

\([h_{19}, h_{15}, h_{11}]\)

0.0050

\([h_{14}, h_{15}, h_{16}]\)

0.0372

\([h_{15}, h_{27}]\)

0.0053

\([h_{8}, h_{11}]\)

0.0215

8

\([h_{19}, h_{17}, h_{3}]\)

0.0058

\([h_{17}, h_{21}, h_{14}]\)

0.0272

\([h_{15}, h_{9}]\)

0.0064

\([h_{1}, h_{0}]\)

0.0381

9

\([h_{3}, h_{1}, h_{15}]\)

0.0029

\([h_{17}, h_{21}, h_{2}]\)

0.0118

\([h_{22}, h_{13}]\)

0.0062

\([h_{23}, h_{22}]\)

0.0124

10

\([h_{5}, h_{0}, h_{9}]\)

0.0029

\([h_{17}, h_{1}, h_{14}]\)

0.0288

\([h_{9}, h_{17}]\)

0.0070

\([h_{23}, h_{11}]\)

0.0171

11

\([h_{14}, h_{26}, h_{5}]\)

0.0030

\([h_{0}, h_{12}, h_{18}]\)

0.0114

\([h_{7}, h_{15}]\)

0.0069

\([h_{0}, h_{16}]\)

0.0185

12

\([h_{15}, h_{27}, h_{5}]\)

0.0029

\([h_{1}, h_{4}, h_{21}]\)

0.0117

\([h_{3}, h_{15}]\)

0.0052

\([h_{6}, h_{1}]\)

0.0128

13

\([h_{27}, h_{26}, h_{3}]\)

0.0029

\([h_{16}, h_{1}, h_{0}]\)

0.0149

\([h_{27}, h_{24}]\)

0.0061

\([h_{1}, h_{23}]\)

0.0189

14

\([h_{26}, h_{5}, h_{23}]\)

0.0029

\([h_{10}, h_{8}, h_{5}]\)

0.0125

\([h_{27}, h_{16}]\)

0.0060

\([h_{11}, h_{4}]\)

0.0127

15

\([h_{17}, h_{22}, h_{16}]\)

0.00600

\([h_{14}, h_{13}, h_{21}]\)

0.0213

\([h_{5}, h_{15}]\)

0.0065

\([h_{14}, h_{1}]\)

0.0261

16

\([h_{14}, h_{10}, h_{3}]\)

0.0030

\([h_{9}, h_{8}, h_{0}]\)

0.0126

\([h_{5}, h_{25}]\)

0.0076

\([h_{3}, h_{11}]\)

0.0127

17

\([h_{16}, h_{1}, h_{11}]\)

0.0044

\([h_{16}, h_{17}, h_{12}]\)

0.0105

\([h_{15}, h_{8}]\)

0.0059

\([h_{23}, h_{19}]\)

0.0107

18

\([h_{15}, h_{26}, h_{1}]\)

0.0029

\([h_{4}, h_{20}, h_{17}]\)

0.0106

\([h_{19}, h_{17}]\)

0.0074

\([h_{13}, h_{11}]\)

0.0121

19

\([h_{22}, h_{10}, h_{14}]\)

0.0033

\([h_{4}, h_{20}, h_{2}]\)

0.0103

\([h_{14}, h_{27}]\)

0.0055

\([h_{1}, h_{23}]\)

0.0189

20

\([h_{26}, h_{23}, h_{0}]\)

0.0058

\([h_{3}, h_{4}, h_{15}]\)

0.0103

\([h_{3}, h_{15}]\)

0.0054

\([h_{13}, h_{10}]\)

0.0121