Although Virginia does not seem to be listed as having reciprocity with South Dakota yet, any state that meets or exceeds our requirements can have reciprocity with us, and our requirements are not that stringent:
18 years-of age or older;
never pled guilty to, nolo contendere to, or been convicted of a crime of violence;
not habitually intoxicated or drugged;
no history of repeated acts of violence; and
has not been found in the previous ten years to be a "danger to others" or a "danger to self" as defined in § 27A-1-1 or is not currently adjudged mentally incompetent.
has been a resident of the county or municipality where the application is being made for at least thirty days.
has had no violations of chapter 23-7, firearms control, 22-14, unlawful use of weapons, or 22-42, controlled substances, marijuana, in the five years preceding the date of application.
Interestingly, our secretary of state page on concealed carry in SD has a link to Packing.org
http://www.state.sd.us/sos/Firearms/index.htm