In 1999 Ian Gambini found the first 3 SPSSs of order 58, 1100A, 1100A and 1297A. 1297A has a square of size 5 on the perimeter of the SPSS. Five is the smallest size square that can appear on the perimeter of a Perfect Squared Square (PSS).
In 2014 Brian Trial found 5558 order 58 SPSSs.
In 2018 Bernard Moss found 958 order 58 SPSSs using a transform applied to Brian Trial's discoveries.
In 2019, 2020 Bernard Moss found 7157 SPSSs in order 58, some quite small, including the seven smallest found so far with sides of 628, 814, 968, 976, 990, 1080 and 1084. These are shown below.
There are 13819 known SPSSs of Order 58. Files provided as;