Two 16. 5" pieces of 2x2 Two 37" pieces of 2x2 Two 14" pieces of 1x4 One 14" piece of 1x4, then split that lengthwise into two long pieces.
Drill 1/4" holes half-way into the 16. 5" posts, 1 1/6" from the top and then 2 1/3" from the top. Cut identically spaced 1/4" holes into both ends of the 1x4 boards. Drill 1/4" holes half-way into the 37" posts, 15 1/3" from the bottom, then 14 1/6" from the bottom. Glue and then insert dowels into the holes. Then you can fit all of the pieces together to form the two sides of the chair. The side pieces should be flush with the tops of the short posts. Slide the split 1x4s 4" up from the bottom on either side piece and screw them into place with decking screws.
Cut three pieces of 14" 1x4, and cut a 12" piece of 1x4 into 3 pieces. Cut a 17x17" square from the plywood for the seat. Then cut 1. 5"x1. 5" notches out of two of the corners of the board, to make room for the back posts. Drill 1/4" dowel holes into one of the 1x4s at the edge on one of the long sides (one hole centered and the other two 4 1/3" from each end of the board). Line up this piece with the seat piece on the side that has the notches. Mark the locations of the dowel holes from the 1x4 onto the seat piece between the two notches. Drill 1/4" dowel holes there as well. Drill 1/4" dowel holes, centered, into each of your 3 pieces created from the 1x4. Drill centered pilot holes in your posts for your decking screws 1 3/4" from the top of the short posts and 14 3/4 from the bottom of your tall posts.
Glue and slide the two final aprons (front and back), and then screw them into place through the pilot holes you made earlier (passing through the posts and into the side of the apron). Then insert two more decking screws going through the seat and into the back apron, with the screw place in between the 3 vertical bars. You can create an even stronger connect with corner brackets on the inside of the chair, if you want to.
Do not overstuff the bag. . . . it needs to be comfy!
All pieces should be dry fit before doing any trimming. Your end shape should be a rectangle. If your pieces aren’t fitting together right, they can be trimmed down. The long side T joints should be facing into the inside of the rectangle. The upper T joint will need to be adjusted but will likely be around a 45 degree angle from the line of the long side.