#JavaScript (ES7), 216 ... 205 201 199 bytes
Takes input as (block)(double), where block is either \$-2\$ (top right), \$-1\$ (bottom left), \$1\$ (bottom right) or \$2\$ (top left) and double is a Boolean value.
b=>d=>(g=x=>y<31?`+-| =OTF
`[X=x-19,Y=y-15,p=X*Y*b<0,q=Y>0^b&1,X*=X,Y*=Y,i=x*24%35>2|~16>>Y%62%6&2,x<39?Y?p*X|(d?Y:X-87)>169?3:i?X-1|Y-16|q?i:7:q*(d?X-87:Y)%169&&6:x%38?4:5:++y&&8]+g(-~x%40):'')(y=0)
###How?
We iterate from \$y=0\$ to \$y=30\$ and from from \$x=0\$ to \$x=39\$ for each value of \$y\$.
We first define \$X=x-19\$ and \$Y=y-15\$.
The variables p = X * Y * b < 0 and q = Y > 0 ^ b & 1 are used to determine what do draw in each quarter according to the block \$b\$.
From now on, both \$X\$ and \$Y\$ are squared in order to easily test absolution positions within each quarter of the field.
The expression x * 24 % 35 > 2 yields false if \$x\$ belongs to \$\{0, 3, 19, 35, 38\}\$ (the positions of the vertical lines) or true otherwise.
The expression ~16 >> Y % 62 % 6 & 2 yields \$0\$ if \$y\$ belongs to \$\{0, 2, 12, 18, 28, 30\}\$ (the positions of the horizontal lines, excluding the net) or \$2\$ otherwise.
The variable \$i\$ is defined as the result of a bitwise OR between the two values above, and is therefore interpreted as:
- 3: space
- 2:
| - 1:
- - 0:
+orT
The expression (d ? Y : X - 87) > 169 is used to crop the field according to the game type \$d\$ (single or double). The similar expression (d ? X - 87 : Y) % 169 is used to draw the T's at the appropriate positions.