Ok Roman, that is a shame, I bought 10 of those a while ago & now can't find them anywhere.
I searched at mouser.com, and found this part that will do nicely instead.
http://se.mouser.com/ProductDetail/NXP-Semiconductors/PSMN035-150P127/?qs=sGAEpiMZZMvKM5ialpXrmoKPBF94BAPg
Your schematic is not quite correct.
Make sure to connect up like I have shown - 20V is the top of LEDs in series, finish with the resister going to the Drain pin of the MOSFET, with the Source pin to ground. With this MOSFET you are opening & closing the circuit on the Ground side, and not on the high voltage side.
Connect the Arduino pin to the gate thru a 1K resistor, with a 10K to ground.
Mouser also has 7406's in stock
Your resister choices look okay.