The first 2 SPSSs of this order were found by Ian Gambini in the late 1990s, up to 2013 Stephen Johnson had found 41. In 2013 Milla and Anderson found 4010 and in the same year James Williams found 21852. In 2014 Brian Trial found 71.
It is estimated that there are approximately 2.6 x 10^6 SPSSs in order 35.
UPDATE! Jim Williams has enumerated order 35 SPSS in April 2016. There are 2578081 SPSSs in this order, Jim has found the remaining 2552105 SPSSs for a total of 2573957 discoveries in this order.
The full listings of this order, including postscript graphics of the dissections can be downloaded from the links above.