[1084]*1084SILER, Circuit Judge.
Rafael Cruz-Escoto appeals his jury conviction and sentence for being a deported alien found in the United States without permission, in violation of 8 U.S.C. § 1326. He presents six arguments on appeal: (1) the evidence was insufficient to support the verdict; (2) the district court improperly instructed the jury; (3) the district court violated his Fifth and Sixth Amendment rights by excluding the testimony of an impeachment witness; (4) the introduction of evidence that he twice illegally entered the United States violated Federal Rules of Evidence 401, 403, and 404(b); (5) the government violated Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986); and (6) the district court impermissibly increased his sentence above the statutory maximum. We AFFIRM.
I. BACKGROUND
In 2004, Border Patrol Agent Jason Viau conducted surveillance of an area along the Mexico-United States border known as the “Channel.” The Channel, located in California just north of Tijuana, is a cement river bed that runs north from Mexico into the United States, where it eventually empties into the Pacific Ocean. There are no fences where the Channel enters into the United States;1 however, a painted yellow line on the bottom of the Channel marks the international border. The Border Patrol has a permanent post located at this vulnerable section of the Channel. This permanent post is not a designated port of entry, and consists of a uniformed agent in a marked car who conducts a twenty-four hour surveillance of the area, which is illuminated by large lights.2
During his midnight shift, Agent Viau saw Cruz-Escoto running northbound in the Channel in front of the Ballard Fence, approximately 100-150 yards inside the United States. Agent Viau drove his Jeep into the Channel and, after a brief scuffle, arrested Cruz-Escoto. Cruz-Escoto admitted to Agent Viau that he was a citizen of Mexico and did not have proper documentation to permit him to enter the United States. He was subsequently indicted for being a deported alien found in the United States, in violation of 8 U.S.C. § 1326.
At trial, Agent Viau testified that he did not see Cruz-Escoto cross the border and could not say how or where Cruz-Escoto entered the United States. The government also introduced evidence that Cruz-Escoto had twice been removed from the United States and that he had never applied for permission to re-enter. Cruz-Escoto was convicted of violating § 1326.
At Cruz-Escoto’s sentencing hearing, the district court increased his sentence above the two-year statutory maximum to eighty-four months because it found that he had previously been deported following a felony conviction.
II. STANDARD OF REVIEW
Claims of insufficient evidence are reviewed de novo. United States v. Duran, [1085]*1085189 F.3d 1071, 1078 (9th Cir.1999). Whether jury instructions adequately cover the theory of the defense is reviewed de novo as well. United States v. Fejes, 232 F.3d 696, 702 (9th Cir.2000). Whether particular evidence falls within the scope of a rule of evidence is also reviewed de novo. United States v. Smith, 282 F.3d 758, 768 (9th Cir.2002). A district court’s decision to admit or exclude evidence is reviewed for an abuse of discretion. United States v. Castillo, 181 F.3d 1129, 1134 (9th Cir.1999). The district court’s findings regarding purposeful discrimination in jury selection are findings of facts entitled to great deference and will be set aside only if clearly erroneous. United States v. Power, 881 F.2d 733, 739 (9th Cir.1989). Claims that a defendant’s sentence violates Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), are reviewed de novo. Smith, 282 F.3d at 771.
III. DISCUSSION
A. Sufficiency of the Evidence
Cruz-Eseoto’s first argument is that the evidence was insufficient to find him guilty of violating § 1326. Specifically, he argues that he was never free from official restraint because he was apprehended before he passed Agent Viau’s permanent post.
To prove a violation of § 1326, the prosecution must show that a deported alien entered, attempted to enter, or was found in, the United States without official permission of the government. See 8 U.S.C. § 1326. Physical presence alone is insufficient to sustain a conviction of being “found in” the United States. See, e.g., United States v. Gonzalez-Torres, 309 F.3d 594, 598 (9th Cir.2002); United States v. Pacheco-Medina, 212 F.3d 1162, 1163-64 (9th Cir.2000). The government must also prove that the individual “entered the United States free from official restraint at the time officials discovered or apprehended him.” United States v. Ruiz-Lopez, 234 F.3d 445, 448 (9th Cir.2000). “The burden is on the government to establish lack of official restraint.” United States v. Bello-Bahena, 411 F.3d 1083, 1087 (9th Cir.2005).
“An alien is under ‘official restraint’ if, after crossing the border without authorization, he is ‘deprived of [his] liberty and prevented from going at large within the United States.’ ” Gonzalez-Torres, 309 F.3d at 598 (alteration in original) (quoting United States v. Pacheco-Medina, 212 F.3d 1162, 1164 (9th Cir.2000)). Because the concept of official restraint is interpreted broadly, an alien need not be in physical custody of authorities to be officially restrained. See Ruiz-Lopez, 234 F.3d at 448. “[T]he restraint may take the form of surveillance, unbeknownst to the alien....” Id. (alteration in original) (quoting Pacheco-Medina, 212 F.3d at 1164).
Whether an alien crosses the border at a designated point of entry or elsewhere also weighs on the consideration of official restraint. “An alien who crosses the border at a designated location and proceeds directly in the manner designated by the government to the border station where he then presents himself to the authorities has not [yet] been ‘found in’ the United States.... ” United States v. Zavala-Mendez, 411 F.3d 1116, 1121 (9th Cir.2005). Aliens who climb fences, raft canals, “or otherwise sneak[ ] across the border in some illegitimate manner,” id. at 1120, are under official restraint only if they are under constant governmental observation “from the moment [they] set foot in this country until the moment of [their] arrest.” United States v. Castellanos-Garcia, 270 F.3d 773, 775 (9th Cir.2001).
Another rule applies to this latter class of aliens: those who evade government observation while crossing the bor[1086]*1086der are deemed to be free from official restraint, regardless of the distance they travel between entry and arrest. See Bello-Bahena, 411 F.3d at 1087-88 (no official restraint when defendant first observed after he crossed the border); Castellanos-Garcia, 270 F.3d at 774-75 (no official restraint even though defendant captured only 100 yards beyond border because Border Patrol agent did not see defendant cross the border). The rule of these cases is that the distance traveled between entry and apprehension is not determinative; rather, the focus is on whether the alien is able to exercise his free will once he has entered this country.
Cruz-Escoto contends that he was never free from official restraint because although he crossed the border, he never made it past the permanent post. He argues that this permanent post is analogous to a designated point of entry because “unless the person succeeds in getting past this post, that person has not successfully and freely entered the United States.” Therefore, he reasons, this case falls between the port of entry cases and the other “sneaky entry” cases.
Despite his attempt to portray this case as falling between a port of entry case and a surreptitious entry case, we have never established a middle ground. In Zavala-Mendez, we specifically noted only two lines of authority for “found in” cases: the first where aliens present themselves at designated points of entry, and the second where aliens enter surreptitiously. Zavala-Mendez, 411 F.3d at 1118. Here, analysis under the designated point of entry cases is inappropriate because Cruz-Esco-to neither entered at a designated point of entry nor proceeded in a manner designated by the United States government.
Although the geography involved in this case presents a unique situation, the jury heard sufficient evidence to decide that Cruz-Escoto was free from official restraint. Agent Viau’s testimony that he never saw Cruz-Escoto cross the border is significant, but not dispositive, in our inquiry. Under our “surreptitious entry” precedent, his arrest only 100-150 yards from the border is of no consequence since the distance traveled once inside the United States is not the ultimate consideration. See, e.g., Bello-Bahena, 411 F.3d at 1087; United States v. Vela-Robles, 397 F.3d 786, 789 (9th Cir.2005); Castellanos-Garcia, 270 F.3d at 775. Rather, whether Cruz-Escoto could exercise his free will once inside the United States is the focus of our analysis.
A complicating fact in this case is that the geography of the Channel might prevent someone crossing the border from exercising his own free will inside the United States until he passes the permanent post. However, we need not consider that situation here, because there was no evidence that Cruz-Escoto did, in fact, cross the border immediately preceding his arrest. Because he did not testify, the jury might well have determined that Cruz-Escoto was already in this country and had the ability to exercise his free will inside the United States. We are simply unable to say that there was insufficient evidence for a rational jury to conclude that Cruz-Escoto was free from official restraint.
B. Adequacy of the Jury Instructions
Cruz-Escoto’s next argument is that the district court erred when: (1) it failed to give his proposed jury instruction with respect to official restraint; and (2) it instructed the jury based on an erroneous reading of the law.
“A defendant is entitled to have the judge instruct the jury on his theory of the defense, provided that it is supported by law and has some foundation in the evidence.” United States v. Mason, 902 F.2d [1087]*10871434, 1438 (9th Cir.1990). An instruction is proper “ ‘even though the evidence may be weak, insufficient, inconsistent, or of doubtful credibility.’ ” United States v. Sotelo-Murillo, 887 F.2d 176, 178 (9th Cir.1989) (quoting United States v. Yarbrough, 852 F.2d 1522, 1541 (9th Cir.1988), cert. denied, 488 U.S. 866, 109 S.Ct. 171, 102 L.Ed.2d 140 (1988)).
The instructions given to the jury mostly coincided with Cruz-Escoto’s proposed instructions. However, the last line of one of Cruz-Escoto’s proposed instructions was not included in the final jury instructions:
Furthermore, when an alien attempts to enter the United States, the mere fact that he may have eluded the gaze of law enforcement, or eluded arrest, for a brief period of time after having come upon United States territory is insufficient, in and of itself, to establish “freedom from official restraint.”
Rather, the district court instructed the jury:
If an alien is under constant surveillance by immigration officers when he entered the United States and the entire time he is inside the United States, he may not be free from official restraint. On the other hand, if an immigration official did not see the Defendant cross into the United States, then the Defendant would not be under official restraint.
Cruz-Escoto’s first assignment of error is the district court’s refusal to give the last line of his proposed instruction. While his proposed instruction is an accurate statement of the law, see, e.g., Gonzalez-Torres, 309 F.3d at 598, Pacheco-Medina, 212 F.3d at 1163-64, it is inapplicable to this case. There was never a question of whether the government surveillance amounted to constructive official restraint resulting from brief periods of interruption. Apparently, Cruz-Escoto believes that because a period of time elapsed from the moment he crossed the border until he was first detected, this case is similar to the “interruption” cases such as Gonzalez-Torres and Pacheco-Medina. However, the rule of those cases applies only where the defendant was observed crossing the border. The rule is inapplicable in this case because Cruz-Escoto was not seen crossing the border.
It is for this reason that Cruz-Escoto’s second assignment of error is also incorrect. He argues that the last sentence of the final jury instructions misstates the law because it contradicts Pacheco-Medina and its progeny, including Ruiz-Lopez. However, nothing in Pacheco-Medina or subsequent cases has changed the settled rule that if an alien sneaks across the border undetected, he is generally deemed to be free from official restraint regardless of the distance he travels in the United States. See Bello-Bahena, 411 F.3d at 1087-88; Castellanos-Garcia, 270 F.3d at 775-76.
His contention that Ruiz-Lopez is a case where the defendant was not observed crossing the border is misguided. Although the immigration officer in that case could not specifically recall observing the defendant cross the border, his general practice of closely monitoring the border and immediately interviewing suspected illegal aliens provided sufficient testimony of habitual practice to permit the inference that the defendant was monitored while crossing the border. Ruiz-Lopez, 234 F.3d at 448-49.
C. Exclusion of Opinion Testimony
Cruz-Escoto argues that the district court violated his Fifth and Sixth Amendment rights when it excluded the testimony of a defense witness that would have impeached the government’s central witness.
[1088]*1088The Constitution provides an accused with “a meaningful opportunity to introduce relevant evidence on his behalf.” Menendez v. Terhune, 422 F.3d 1012, 1033 (9th Cir.2005); see also Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986). However, “a trial judge may exclude or limit evidence to prevent excessive consumption of time, undue prejudice, confusion of the issues, or misleading the jury.” Menendez, 422 F.3d at 1033. In considering whether the exclusion of evidence violates due process, this court considers “the probative value of the evidence on the central issue.... ” Miller v. Stagner, 757 F.2d 988, 994 (9th Cir.1985).
Cruz-Escoto sought to impeach Agent Viau’s testimony that his vehicle was facing south, but that he was continually looking west. He argues that this testimony enabled the government to argue that Agent Viau did not see Cruz-Escoto cross the border and therefore was never free from “official restraint” because he was not continually under surveillance.
Cruz-Escoto attempted to introduce testimony of Robert Castillo, a defense witness trained in surveillance. Cruz-Esco-to’s counsel proffered that Castillo “would testify that, when you’re doing surveillance, it’s very difficult to have your vehicle pointed in one direction and then to constantly be looking in another, which was essentially the testimony of the agent.” Thus, Cruz-Escoto argues, Agent Viau must have been looking toward the gap in the border fences, which was the direction his vehicle was pointing, and he must have seen Cruz-Escoto cross the border.
The district court did not violate Cruz-Escoto’s Fifth or Sixth Amendment rights by excluding Castillo’s testimony. The court decided that the evidence was irrelevant because it was within the understanding of a common juror. See Fed.R.Evid. 702. Moreover, this ruling was not an abuse of discretion under Fed.R.Evid. 403.
D. Evidence of Prior Removals
Cruz-Escoto’s next argument is that the district court improperly admitted evidence of his previous illegal entries and removals. He argues that this evidence violates Federal Rules of Evidence 401, 403, and 404(b).
While Rule 404(b) does prohibit the admission of “other crimes, wrongs, or acts” to prove the propensity of a defendant, evidence that is a necessary element of the crime charged is not considered “[e]vi-dence of other crimes, wrong, or acts” within the meaning of the Rule. United States v. Campbell, 774 F.2d 354, 356 (9th Cir.1985) (alteration in original) (quoting Fed.R.Evid. 404(b)). Therefore, evidence showing that Cruz-Escoto had previously been deported is not Rule 404(b) evidence because the government had to prove this element of the crime. See 8 U.S.C. § 1326(a)(1).
Cruz-Escoto argues that the government’s use of multiple prior deportations, when proof of only one was necessary, constitutes reversible error. We find no error in permitting this evidence because in other contexts we have permitted the introduction of more than one predicate act to establish an element of the crime. See United States v. Weiland, 420 F.3d 1062, 1078 (9th Cir.2005) (finding harmless error in the use of four prior felony convictions to establish defendant’s status as a felon under 18 U.S.C. § 922(g)(1)), cert. denied, — U.S.-, 126 S.Ct. 1911, 164 L.Ed.2d 667 (2006).
Moreover, the district court gave two limiting instructions to minimize the potential prejudice. See United States v. Ba-singer, 60 F.3d 1400, 1408 (9th Cir.1995). The first limiting instruction informed the jury that it could only use the 2000 deportation to show citizenship, absence of mis[1089]*1089take or accident, and for deportation, which was an element of the offense. The second limiting instruction was given after closing arguments and informed the jury again of the limited purpose of the “other acts” evidence.
E. Batson Allegations
Cruz-Escoto contends that the government violated the Equal Protection Clause because it impermissibly used peremptory challenges to exclude two Hispanic potential jurors.
The Fourteenth Amendment prohibits racial discrimination in the jury selection process. See Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986). A defendant who objects to the use of peremptory challenges carries the burden of establishing a prima facie showing of unconstitutional discrimination. Id. at 93-96, 106 S.Ct. 1712. To make such a showing, the defendant must first show that: (1) he is a member of a cognizable racial group; (2) the government used peremptory challenges to remove members of that racial group; and (3) the “facts and any other relevant circumstances raise an inference” that the peremptory challenge was motivated by an impermissible factor, such as race. Id. at 96, 106 S.Ct. 1712.
If a defendant makes a prima facie showing of discrimination, the burden shifts to the government to offer race-neutral reasons for exclusion of a particular race. Id. at 94, 106 S.Ct. 1712. “The prosecutor’s explanation, to satisfy Batson, need only be facially valid, it need not be persuasive or even plausible so long as it is race-neutral.” United States v. Gillam, 167 F.3d 1273, 1278 (9th Cir.1999); see also Purkett v. Elem, 514 U.S. 765, 767-68, 115 S.Ct. 1769,131 L.Ed.2d 834 (1995) (per curiam). Finally, “[i]f a race-neutral explanation is tendered, the trial court must then decide ... whether the opponent of the strike has proved purposeful racial discrimination.” Purkett, 514 U.S. at 767, 115 S.Ct. 1769.
The government contends that Cruz-Escoto did not make a prima facie showing of discrimination because he failed to produce any facts or other relevant circumstances that could raise an inference of impermissible discrimination. In his objection, Cruz-Escoto stated that “[t]here are two hispanics who were stricken by the government, number 23 and 24,” and that “I don’t think that’s the reason they struck her.” The government argues that this is insufficient to establish a prima facie showing. However, the district court requested and accepted the government’s reasons for excluding the two Hispanic jurors. Thus, the issue of whether Cruz-Escoto made a prima facie showing of discrimination is moot. See Kesser v. Cambra, 465 F.3d 351, 381 (9th Cir.2006) (“ '[0]nce a prosecutor has offered a race-neutral explanation for the peremptory challenges and the trial court has ruled on the ultimate question of intentional discrimination, the preliminary issue of whether the defendant has made a prima facie showing becomes moot.’ ”) (quoting Hernandez v. New York, 500 U.S. 352, 359, 111 S.Ct. 1859, 114 L.Ed.2d 395 (1991) (plurality opinion)).
Assuming, as the district court did, that Cruz-Escoto made a prima facie showing of discrimination, his claim still fails because the government articulated a valid, race-neutral justification for excluding the potential jurors. The government rationalized excluding the two Hispanic jurors because they — or their sons, depending on which version of transcript is accurate3— [1090]*1090were unemployed. Cruz-Escoto argues that this reason is insufficient to rebut a prima facie Batson showing. However, our precedent contradicts this contention. See Gillam, 167 F.3d at 1278 (finding that unemployment for one year was a race-neutral explanation).
Moreover, ample evidence supports the district court’s conclusion that Cruz-Escoto did not establish purposeful racial discrimination. The seated jury included two Hispanics who were not struck by the government. See Turner v. Marshall, 121 F.3d 1248, 1254 (9th Cir.1997) (finding fact that jury included minorities to be indicative, but not dispositive, of nondiscriminatory motive); United States v. Chinchilla, 874 F.2d 695, 698 n. 4 (9th Cir.1989) (noting that “the willingness of a prosecutor to accept minority jurors weighs against the findings of a prima facie case”). Also, the challenges at issue only constituted two of the government’s six peremptory challenges. See United States v. Vasquez-Lopez, 22 F.3d 900, 902 (9th Cir.1994) (considering that the “government’s other peremptory challenges did not suggest a general pattern of discrimination against racial minorities” in the Batson analysis). Finally, the defense also struck one of the two jurors in dispute.
F. Apprendi Challenge to Sentence
Cruz-Escoto’s final claim is that the district court improperly increased his sentence above the statutory maximum. Pursuant to 8 U.S.C. § 1326(b)(2), the district court sentenced Cruz-Escoto above the two-year statutory maximum because it found that he had previously been convicted of two felonies — a 1994 drug trafficking charge and a 1996 sale of cocaine charge. According to Cruz-Escoto, this increase violates the Supreme Court’s ruling in Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), because he did not admit that he had previously been convicted nor did the jury make such a finding.
Any fact that increases a sentence above the statutory maximum must be admitted by the defendant or proved to a jury beyond a reasonable doubt. Apprendi, 530 U.S. at 490, 120 S.Ct. 2348. However, Cruz-Escoto’s argument fails because Ap-prendi specifically exempts recidivism enhancements based on prior convictions from its holding. Id. at 490,120 S.Ct. 2348 (“Other than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.” (emphasis added)).
Cruz-Escoto’s contention that Almendarez-Torres v. United States, 523 U.S. 224, 118 S.Ct. 1219, 140 L.Ed.2d 350 (1998), requires a defendant’s admission of prior conviction to trigger a § 1326 recidivism enhancement is contrary to both the history of the recidivism enhancement and our precedent. See id. at 227, 118 S.Ct. 1219 (noting that recidivism “is a traditional, if not the most traditional, basis for a sentencing court’s increasing an offender’s sentence”); United States v. Yanez-Saucedo, 295 F.3d 991, 993 (9th Cir.2002) (“[N]o-where does Apprendi limit Almendarez-Torres to cases where a defendant admits prior aggravated felony convictions on the record.”) (quotation and citation omitted).
Moreover, we have repeatedly upheld statutory maximum increases based on the same recidivism enhancement in this case. [1091]*1091See, e.g., United States v. Cortez-Arias, 403 F.3d 1111, 1114 n. 8 (9th Cir.2005).
AFFIRMED.
Dissent by Judge TASHIMA.