MAX743 unstable with load (5 to +/- 15V)
1) A vector board with 3 holes per pad plus ground and power traces is what I built 90% of all my test fixtures with. It forces you to use DIP and SIP packages but I managed to force-fit a 64 pin PLCC package one time. It was a PITB. Better to use adaptors now days. This 9" x 6" board is about $60 USD.

2) Cut it in half and save the rest for another project. Teaches important lessons before making the big leap to having a board house do a custom board for you.

3) The part number is from Digi-Key. V1019-ND. The part number on the board is 3677 Plugbord. Mfg is Vector Electronics and Technology, inc. Board is 4.5" x 9.6". 0.062 thk with 3-hole solder pads plus wide power and ground traces.

4) You can cut off the plug board end if not needed. Holes are 0.042" diameter and are NOT plated through, so solder both sides when you need to. I had some spares on hand to get the part numbers.

5) Follow the advice of @MarkU and keep caps and Schottky diodes very close to the IC package, as well as the 100uF caps. You can use 1N5817 thru 1N5822, depending on bulk vs. single price.

6) I would use the 1N5822 if possible as it is rated for 50 volts. A 15 volt supply puts 15 volts on the diode output but when the polarity changes the transformer hits it with -16 volts, so the diodes actually have 32 volts p-p across them. The 1N5822 gives you a 40% safety margin.

7) The 100 uF capacitors are supposed to filter out noise, but their leads need to be very short to the IC body. I am surprised that there no filter inductors after the diodes. You can add tiny .1 uF SMD caps across the +VO and -VO lines and ground the caps close to the IC body. A single 100 uF capacitor will not filter out all RF noise due to lead inductance (ESR). A better design (like if you bought a ready made power supply) would have the output inductors and .1 uF caps already installed to meet FCC requirements for noise emission.