Table 1 The Weyl groups \(B_{7}\), \(D_{8}\), \(E_{7}\), \(B_{8}\): level sizes and total runtime of the extended Snow’s algorithm

0, 49

1

0, 56

1

0, 63

1

0, 64

1

1, 48

7

1, 55

8

1, 62

7

1, 63

8

2, 47

27

2, 54

35

2, 61

27

2, 62

35

3, 46

77

3, 53

112

3, 60

77

3, 61

112

4, 45

181

4, 52

293

4, 59

182

4, 60

293

5, 44

371

5, 51

664

5, 58

378

5, 59

664

6, 43

686

6, 50

1350

6, 57

713

6, 58

1350

7, 42

1170

7, 49

2520

7, 56

1247

7, 57

2520

8, 41

1869

8, 48

4388

8, 55

2051

8, 56

4389

9, 40

2827

9, 47

7208

9, 54

3205

9, 55

7216

10, 39

4082

10, 46

11,263

10, 53

4975

10, 54

11,298

11, 38

5662

11, 45

16,848

11, 52

6909

11, 53

16,960

12, 37

7581

12, 44

24,248

12, 51

9632

12, 52

24,541

13, 36

9835

13, 43

33,712

13, 50

13,040

13, 51

34,376

14, 35

12,399

14, 42

45,425

14, 49

17,194

14, 50

46,775

15, 34

15,225

15, 41

59,480

15, 48

22,134

15, 49

62,000

16, 33

18,242

16, 40

75,853

16, 47

27,874

16, 48

80,241

17, 32

21,358

17, 39

94,384

17, 46

34,398

17, 47

101,592

18, 31

24,464

18, 38

114,766

18, 45

41,657

18, 46

126,029

19, 30

27,440

19, 37

136,544

19, 44

49,567

19, 45

153,392

20, 29

30,162

20, 36

159,125

20, 43

58,009

20, 44

183,373

21, 28

32,150

21, 35

181,800

21, 42

66,831

21, 43

215,512

22, 27

34,376

22, 34

203,777

22, 41

75,852

22, 42

249,201

23, 26

35,672

23, 33

224,224

23, 40

84,868

23, 41

283,704

24, 25

36,336

24, 32

242,318

24, 39

93,659

24, 40

318,171

25, 31

257,295

25, 38

101,997

25, 39

351,680

26, 30

268,504

26, 37

109,655

26, 38

383,270

27, 29

275,440

27, 36

116,417

27, 37

411,984

28

277,788

28, 35

122,087

28, 36

436,913

29, 34

126,497

29, 35

457,240

30, 33

129,514

30, 34

472,281

31, 32

131,046

31, 33

481,520

32

484,636