Code details
best found code with parameters
q=16 k=3 n=18
minimum distance = 16
this is new optimal code
the previous bounds were 1/16
this is a projective code
We used the prescribed group of automorphisms with the following generators
This group makes 25 orbits of sizes:
3

18

9

3

9

9

9

9

3

9

9

9

9

3

9

9

9

9

18

18

18

18

18

18

18

The solution of the corresponding linear system of equations was found after less than 500 seconds:
0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

2

2

0

0

0

2

0

0

2

2

0

2

0

2

2

2

2

2

0

2

0

2

0

0

This produces the following generator matrix
15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

1

14

4

5

9

10

11

6

15

1

14

4

5

9

10

11

6

15

10

9

4

6

14

1

15

5

11

1

15

10

9

5

4

6

11

14

Which is a code with the following weight distribution
1y^{18}+2295x^{16}y^{2}+1800x^{18}