What is the test for deliberate omissions of material facts from an affidavit for a search warrant?

This court has applied the rule in Franks to deliberate omissions of material facts from an affidavit for a search warrant: "A defendant can challenge a search warrant by showing that the affiant deliberately or recklessly omitted material facts that negate probable cause when added to the affidavit." (People v. Eubanks (2011) 53 Cal.4th 110, 136, 134 Cal.Rptr.3d 795, 266 P.3d 301.) We have recognized that a claim that material facts were omitted from an affidavit differs from a claim that the affidavit contains

[62 Cal.4th 410]

falsehoods: "Though similar for many purposes, omissions and misstatements analytically are distinct in important ways. Every falsehood makes an affidavit inaccurate, but not all omissions do so. An affidavit need not disclose every imaginable fact however irrelevant. It need only furnish the magistrate with information, favorable and adverse, sufficient to permit a reasonable, common sense determination whether circumstances which justify a search are probably present. [Citations.]" (People v. Kurland (1980) 28 Cal.3d 376, 384, 168 Cal.Rptr. 667, 618 P.2d 213.) "[A]n affiant's duty of disclosure extends only to material or relevant adverse facts." (Ibid. ) "[F]acts are material and hence must be disclosed if their omission would make the affidavit substantially misleading. On review under section 1538.5, facts must be deemed material for this purpose if, because of their inherent probative force, there is a substantial possibility they would have altered a reasonable magistrate's probable cause determination." (Id. at p. 385, 168 Cal.Rptr. 667, 618 P.2d 213.)