The construction of replaceable (q+3)-nests of reguli in PG(3,q)

We describe a construction of (q+3)-nests of reguli in PG(3,q) for q odd, q⩾5, and examine the replacement question. Two examples, a replaceable 10-nest in PG(2,7) and a replaceable 14-nest in PG(3,11), are of particular interest since there is no replacement set consisting of a union of opposite half-reguli. For all previously known examples of replaceable nests, there is a replacement set consisting of a union of opposite half-reguli.