This is answered by the PDF specification (PDF 32000-1:2008):
(Optional) An array specifying the characteristics of the annotation's
border, which shall be drawn as a rounded rectangle.
(PDF 1.0) The array consists of three numbers defining the horizontal
corner radius, vertical corner radius, and border width, all in
default user space units. If the corner radii are 0, the border has
square (not rounded) corners; if the border width is 0, no border is
(PDF 1.1) The array may have a fourth element, an optional dash array
defining a pattern of dashes and gaps that shall be used in drawing
the border. The dash array shall be specified in the same format as in
the line dash pattern parameter of the graphics state (see 22.214.171.124,
"Line Dash Pattern").
Border value of [ 0 0 1 [ 3 2 ] ] specifies a
unit wide, with square corners, drawn with 3-unit
dashes alternating with 2-unit gaps.
NOTE (PDF 1.2) The dictionaries for some annotation types
as free text and polygon annotations) can include the
entry. That entry specifies a border style dictionary that has
more settings than the array specified for the
If an annotation dictionary includes the
BS entry, then the
Border entry is ignored.
Default value: [ 0 0 1 ].