A recurring theme of this blog is that in order to get relief from an appellate court trial court error must be properly preserved. Although members of the panel from which a jury is selected can generally be struck from the jury list for any reason, it is illegal to strike panelists solely on account of their race (Batson error) or their sex (J.E.B. error). It is not merely illegal in criminal cases, but also in civil ones per Edmonson v. Leesville Concrete Co., 500 U.S. 614 (1991).
So what should you do when you think that the other side has made such an improper strike? Before the panel is dismissed and the trial commences, make a prima facie case that the strike was made solely for an impermissible reason or reasons--race or sex. At that point, the burden of proof shifts to the striker to show that the strikes were made for acceptable reasons. That is not the end of the process for you. You must then object to or dispute what opposing counsel says, showing that your adversary's explanations are not supported by the facts or are just pretexts for race or sex and ask for a ruling.
In the course of preparing this post I ran across an excellent continuing legal education article on trial error preservation by Southern District of Texas assistant public defender Timothy Crooks (What a surname for a public defender!). I recommend it highly for any criminal defense practitioner in the federal trial courts subject to the Fifth Circuit.