A new method to construct maximal partial spreads of smallest size in 𝑃𝐺(3,𝑞)

A computer search of maximal partial spreads in PG(3,q)

“…Moreover, we found new density results for q = 8, 9, 16, 19, 25, 27 and the size 149 for q = 23, which is the missing value between the minimum found in [20] and the minimum of the density result found in the same article.…”

“…This work is the natural continuation of the paper "A new method to construct maximal partial spreads in PG(3, q)" [20], where we found new minimums for the sizes of maximal partial spreads of PG (3, q), with q = 11, 13, 17, 19, 23. Moreover in [20], for q = 11, 13, 17, we constructed maximal partial spreads (in the following Mps) having all the cardinalities between our minimums and those of the density results found by O. Heden. In the cases q = 19 and q = 23 we did not fill the previous gap, but we do it here.…”

“…The first program, identified by "max-intersection program", it is much more efficient version than the one used in [20], and it works in the following way.…”