# Code details

best found code with parameters
q=16 k=3 n=157
minimum distance = 146

## this is new optimal code

the previous bounds were -1/146
this is a projective code

We used the prescribed group of automorphisms with the following generators

 15 0 0 0 0 15 0 15 0

 9 0 0 0 6 0 0 0 12

This group makes 37 orbits of sizes:

 2 10 5 1 10 5 10 10 10 5 10 10 10 5 10 5 5 5 10 10 10 10 10 5 10 10 5 5 10 5 5 10 10 5 5 5 5

The solution of the corresponding linear system of equations was found after less than 500 seconds:

 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 11 9 7 11 11 9 9 11 7 9 11 3 11 9 11 11 11 11 11 11 9 11 7 9 9 11 11 7 11 11 11 11 11 11 11 11

This produces the following generator matrix

 0 0 0 0 0 0 0 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 0 15 15 15 15 15 15 1 8 14 4 5 7 2 13 10 11 1 4 7 9 13 10 3 6 12 15 9 3 6 12 15 8 14 5 9 2 3 11 6 12 15 1 4 7 9 13 10 3 6 12 15 8 14 5 9 2 3 11 6 12 15 9 3 6 12 15 9 3 6 12 15 8 14 5 9 2 3 11 6 12 15 8 14 5 9 2 3 11 6 12 15 1 4 7 9 13 10 3 6 12 15 8 14 5 2 11 1 8 14 4 5 7 2 13 10 11 1 8 14 4 5 7 2 13 10 11 8 14 5 2 11 1 8 14 4 5 7 2 13 10 11 1 4 7 13 10 1 4 7 13 10 1 4 7 13 10 15 0 9 3 6 12 15 2 10 4 14 13 11 1 5 8 7 6 3 15 13 9 12 4 1 10 7 15 6 3 12 9 9 3 12 8 15 14 6 11 5 2 12 9 6 4 15 3 10 7 1 13 3 12 6 2 9 8 15 5 14 11 12 3 15 9 6 6 12 9 3 15 6 15 9 5 12 11 3 8 2 14 15 9 3 14 6 5 12 2 11 8 15 12 9 7 3 6 13 10 4 1 14 8 2 5 11 5 13 7 2 1 14 4 8 11 10 8 1 10 5 4 2 7 11 14 13 2 11 5 8 14 11 4 13 8 7 5 10 14 2 1 7 4 1 10 13 1 13 10 4 7 13 10 7 1 4

Which is a code with the following weight distribution
1y157+2475x146y11+1125x148y9+315x150y7+150x154y3+30x156y1