DCC: d16, d24 and d30 Free

Remember the d66?

If you've played Traveller, then you remember the d66, or rolling two six-sided dice reading the first result as 10's and the second as 1's. The d66 equals to a d36, in which on any other roll you have 36 possible combinations (6 times 6.) See the point? 16 is 4 times 4, thus a d44. 24 is 4 times 6 (or 6 times 4), thus a d46 or a d64. 30 is 6 times 5 (or 5 times 6), thus a d65 or a d56. You can also generates numbers between 1 and 30 by rolling 1d6 (or 1d3) and 1d10 reading 1-2 (1) as +0, 3-4 (2) as +10 and 5-6 (3) as +20. Use the following tables as in-game reference:

16-sided Die Conversion Chart

d44	d16
11	1
12	2
13	3
14	4
21	5
22	6
23	7
24	8
31	9
32	10
33	11
34	12
41	13
42	14
43	15
44	16

24-sided Die Conversion Chart

d46	d24
11	1
12	2
13	3
14	4
15	5
16	6
21	7
22	8
23	9
24	10
25	11
26	12
31	13
32	14
33	15
34	16
35	17
36	18
41	19
42	20
43	21
44	22
45	23
46	24

The d7 can't just be obtained this way. Why?