Data generated using script https://pastebin.com/rzsdVGp2
This data assumes that all SV distributions with sum(svs) >= min_sv_constraint are equally likely.

Number of ways to get N perfect SVs if minimum total SV is 0:
0: 678223072849
1: 96889010407
2: 5931980229
3: 201768035
4: 4117715
5: 50421
6: 343
7: 1
Total: 781250000000
Probability of 1+ perfect SV: 0.131874

Number of ways to get N perfect SVs if minimum total SV is 147:
0: 524149344545
1: 90850650345
2: 5903194395
3: 201768035
4: 4117715
5: 50421
6: 343
7: 1
Total: 621109125800
Probability of 1+ perfect SV: 0.156107

Number of ways to get N perfect SVs if minimum total SV is 168:
0: 391848702376
1: 79590036883
2: 5730069261
3: 201684735
4: 4117715
5: 50421
6: 343
7: 1
Total: 477374661735
Probability of 1+ perfect SV: 0.179159