There's no need to calculate all the permutations or combinations. Think people, think! You have 48 players, arrange them in a 6 x 8 matrix:

    0    6   12   18   24   30   36   42
    1    7   13   19   25   31   37   43
    2    8   14   20   26   32   38   44
    3    9   15   21   27   33   39   45
    4   10   16   22   28   34   40   46
    5   11   17   23   29   35   41   47

Then you can create teams by going around horizontally, vertically, and diagonally. You just have to skip to a different column or row whenever to cross an edge. Or, in other words, we're going to tile the plane with the above matrix, but each time we put down another time, we shift a bit. We shift a row if a place a tile to the right, and a column if we place a tile above. We can then start any place and either go to the right, go down, or go up-right and make a team from each of the next 6 numbers; repeating that 8 times.

This boils down to the following program:

#!/usr/bin/perl

use strict;
use warnings 'all';

my @people = (0 .. 47);  

my @data;
my @z     = (0, 0,  0);
my @inc   = (1, 6,  5);
my @skew  = (0, 1,  0);
my @drift = (0, 0, 12);
for (my $x = 0; $x < 8; $x ++) {
    for (my $y = 0; $y < 6; $y ++) {
        for (my $z = 0; $z < @z; $z ++) {
            push @{$data [$z] [$x]} => $people [$z [$z]];
            $z [$z] += $inc [$z];
            $z [$z] += $drift [$z] if 5 == $z [$z] % 6;
            $z [$z] -= @people - $skew [$z] if $z [$z] >= @people;
        }
    } 
}

my $r = 0;
foreach my $info (@data) {
    printf "Round %d\n", ++ $r;
    my $t = 0;
    foreach my $team (@$info) {
        printf "Team %d: ", ++ $t;
        map {printf "%2d " => $_} @$team;
        print "\n";
    } 
    print "\n";
}
__END__
Round 1
Team 1:  0  1  2  3  4  5
Team 2:  6  7  8  9 10 11
Team 3: 12 13 14 15 16 17
Team 4: 18 19 20 21 22 23
Team 5: 24 25 26 27 28 29
Team 6: 30 31 32 33 34 35
Team 7: 36 37 38 39 40 41
Team 8: 42 43 44 45 46 47

Round 2
Team 1:  0  6 12 18 24 30
Team 2: 36 42  1  7 13 19
Team 3: 25 31 37 43  2  8
Team 4: 14 20 26 32 38 44
Team 5:  3  9 15 21 27 33
Team 6: 39 45  4 10 16 22
Team 7: 28 34 40 46  5 11
Team 8: 17 23 29 35 41 47

Round 3   
Team 1:  0 17 22 27 32 37 
Team 2: 42 11 16 21 26 31
Team 3: 36  5 10 15 20 25
Team 4: 30 47  4  9 14 19
Team 5: 24 41 46  3  8 13
Team 6: 18 35 40 45  2  7
Team 7: 12 29 34 39 44  1
Team 8:  6 23 28 33 38 43
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Abigail