Doesn't a 96 person tournament need the top 32 seeds to get a 1st round bye?

Otherwise:

R1 96
R2 48
R3 24
R4 12
R5 6
R6 3

With the top 32 getting byes:

R1 Bottom 64 of the 96 play; top 32 seeds get byes
R2 Winners of R1 plus top 32 seeds = 64
R3 32
R4 16
R5 8
R6 4
R7 2


If you want seven rounds with no byes, you need a 128 person tournament.