WOLLMAN, Circuit Judge.
Shirley Harvell and other voters in the Blytheville School District appeal from the judgment dismissing the complaint in their suit alleging violations of the Voting Rights Act. The defendants cross-appeal from the district court’s denial of their motion for Rule 11 sanctions. We affirm the denial of sanctions, reverse the judgment dismissing the complaint, and remand to the district court for further findings.
I.
The Blytheville School District is a large one, encompassing the city of Blytheville and its adjacent rural areas. The District has a population of 23,500, of which 64% are white and 35% are black. The voting [228]*228age population, which for Voting Rights Act purposes is the pertinent population, is 14,500, of which 70% are white and 29% are black.1
The Blytheville School Board consists of eight members. Each member serves a four-year term, and two terms expire each year. Under the election scheme that was in place until 1987, the candidate who received the most votes was elected to the Board, whether or not that candidate received a majority vote. When several candidates would run for one slot, only one of them black, the white vote would be split among the white candidates, while the black vote would concentrate on the black candidate, and the black candidate would be elected.2 In 1987, pursuant to a new Arkansas statute, this voting scheme was changed, so that now a candidate can be elected only after receiving a majority of the votes. Thus, even if more than one white candidate runs for a position, there will ultimately be a run-off election between the black candidate and the white candidate who receives the highest number of votes.
Historically, blacks have rarely been able to elect a representative to the Blytheville School Board. For the last sixteen years, however, there have consistently been two black members on the eight member board, representation roughly proportional to the percentage of blacks in the voting age population. All but two of the black members were seated on the Board through unopposed races or through bullet voting. Dr. Helen Nunn defeated a white candidate in 1982, then was reseated in unopposed races in 1986 and 1990. Norvell Moore was elected through, bullet voting in 1975 (there were four white candidates). He was reseated in unopposed races in 1979 and 1983. As a three-term incumbent, he defeated a white by only twenty-three votes in 1987.3
Harvell, who is black, an unsuccessful candidate for the Board of Directors of the District, and four black citizens of the District brought suit under section 2 of the Voting Rights Act in the fall of 1989, after two elections under the new scheme. They challenged the election of school board members at large from such a large district. They proposed an eight-district scheme to replace the at-large scheme, under which one member of the Board would be elected from each district. The district court found that plaintiffs had not shown a violation of the Voting Rights Act and entered judgment in favor of the defendants.
Plaintiffs contend on appeal that the district court erred in finding that sustained minority presence on the Blytheville School Board precluded a finding of a violation of the Act. Plaintiffs further contend that the district court failed to make sufficiently detailed findings to satisfy the requirements of Buckanaga v. Sisseton Independent School District No. 54-5, 804 F.2d 469, 472 (8th Cir.1986). Defendants cross-appeal, contending that the district court erred in denying their motion for sanctions and in refusing to dismiss the case on the basis of laches and equitable principles.
II.
The Voting Rights Act prohibits any state or political subdivision from using any “voting qualification or prerequisite to voting or standard, practice, or procedure ... which results in a denial or abridgement of the right of any citizen ... to vote on account of race or eolor[.]” 42 U.S.C. § 1973. In determining whether a violation of the Act has been established, a court must determine whether, based on the totality of the circumstances, “members [of a protected class] have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their [229]*229choice.” 42 U.S.C. § 1973(b). In making that determination, “[t]he extent to which members of a protected class have been elected to office in the State or political subdivision is one circumstance which may be considered[.]” Id.
A plaintiff alleging a violation of the Act due to multi-member districts must show: first, that the minority group is large enough and geographically compact enough that it would be a majority in a single-member district; second, that the minority group is politically cohesive; and third, that the white majority votes sufficiently as a bloc to enable it, in the absence of special circumstances, usually to defeat the minority’s preferred candidate. Thornburg v. Gingles, 478 U.S. 30, 50-51, 106 S.Ct. 2752, 2766, 92 L.Ed.2d 25 (1986).
Relying on the Senate Report accompanying the Voting Rights Act, the Court also set out factors by which plaintiffs may establish a violation of the Act. These include 1) the extent of a history of official discrimination in the state which touched voting rights; 2) the extent to which voting is racially polarized; 3) the extent to which the state has used voting practices or procedures which would enhance opportunities for discrimination against minorities; 4) whether minority candidates had been denied access to the slating process; 5) the extent to which minorities have borne the effects of discrimination in relation to education, employment, and health; 6) whether political campaigns have had overt or subtle racial appeals; 7) the extent to which minorities have been elected to public office in the jurisdiction; 8) whether there is a significant lack of responsiveness on the part of elected officials to the needs of minorities; and 9) whether the policy underlying the use of voting qualifications is tenuous. Thornburg v. Gingles, 478 U.S. at 36-37, 106 S.Ct. at 2758-59; see also Buckanaga, 804 F.2d at 471 (setting out same factors); S.Rep. No. 417, 97th Cong., 2d Sess. 28-29 (1982), reprinted in 1982 U.S.C.C.A.N. 177, 206-07. The Senate Report accompanying the amendment, from which the Court drew these factors, emphasizes that this list is not exclusive. S.Rep. No. 417 at 28-29, 1982 U.S.C.C.A.N. at 206-207. These factors are not to be used, however, as a “mechanical ‘point-counting’ device.” Id. n. 118. Instead, the court should, based on the totality of the circumstances and guided by the factors, determine whether the voting strength of the minority group is “minimized or cancelled out.” Id.
A district court’s decision as to whether a Voting Rights Act violation occurred is a finding of fact, which we review for clear error. Thornburg v. Gingles, 478 U.S. at 78, 106 S.Ct. at 2780.
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WOLLMAN, Circuit Judge.
Shirley Harvell and other voters in the Blytheville School District appeal from the judgment dismissing the complaint in their suit alleging violations of the Voting Rights Act. The defendants cross-appeal from the district court’s denial of their motion for Rule 11 sanctions. We affirm the denial of sanctions, reverse the judgment dismissing the complaint, and remand to the district court for further findings.
I.
The Blytheville School District is a large one, encompassing the city of Blytheville and its adjacent rural areas. The District has a population of 23,500, of which 64% are white and 35% are black. The voting [228]*228age population, which for Voting Rights Act purposes is the pertinent population, is 14,500, of which 70% are white and 29% are black.1
The Blytheville School Board consists of eight members. Each member serves a four-year term, and two terms expire each year. Under the election scheme that was in place until 1987, the candidate who received the most votes was elected to the Board, whether or not that candidate received a majority vote. When several candidates would run for one slot, only one of them black, the white vote would be split among the white candidates, while the black vote would concentrate on the black candidate, and the black candidate would be elected.2 In 1987, pursuant to a new Arkansas statute, this voting scheme was changed, so that now a candidate can be elected only after receiving a majority of the votes. Thus, even if more than one white candidate runs for a position, there will ultimately be a run-off election between the black candidate and the white candidate who receives the highest number of votes.
Historically, blacks have rarely been able to elect a representative to the Blytheville School Board. For the last sixteen years, however, there have consistently been two black members on the eight member board, representation roughly proportional to the percentage of blacks in the voting age population. All but two of the black members were seated on the Board through unopposed races or through bullet voting. Dr. Helen Nunn defeated a white candidate in 1982, then was reseated in unopposed races in 1986 and 1990. Norvell Moore was elected through, bullet voting in 1975 (there were four white candidates). He was reseated in unopposed races in 1979 and 1983. As a three-term incumbent, he defeated a white by only twenty-three votes in 1987.3
Harvell, who is black, an unsuccessful candidate for the Board of Directors of the District, and four black citizens of the District brought suit under section 2 of the Voting Rights Act in the fall of 1989, after two elections under the new scheme. They challenged the election of school board members at large from such a large district. They proposed an eight-district scheme to replace the at-large scheme, under which one member of the Board would be elected from each district. The district court found that plaintiffs had not shown a violation of the Voting Rights Act and entered judgment in favor of the defendants.
Plaintiffs contend on appeal that the district court erred in finding that sustained minority presence on the Blytheville School Board precluded a finding of a violation of the Act. Plaintiffs further contend that the district court failed to make sufficiently detailed findings to satisfy the requirements of Buckanaga v. Sisseton Independent School District No. 54-5, 804 F.2d 469, 472 (8th Cir.1986). Defendants cross-appeal, contending that the district court erred in denying their motion for sanctions and in refusing to dismiss the case on the basis of laches and equitable principles.
II.
The Voting Rights Act prohibits any state or political subdivision from using any “voting qualification or prerequisite to voting or standard, practice, or procedure ... which results in a denial or abridgement of the right of any citizen ... to vote on account of race or eolor[.]” 42 U.S.C. § 1973. In determining whether a violation of the Act has been established, a court must determine whether, based on the totality of the circumstances, “members [of a protected class] have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their [229]*229choice.” 42 U.S.C. § 1973(b). In making that determination, “[t]he extent to which members of a protected class have been elected to office in the State or political subdivision is one circumstance which may be considered[.]” Id.
A plaintiff alleging a violation of the Act due to multi-member districts must show: first, that the minority group is large enough and geographically compact enough that it would be a majority in a single-member district; second, that the minority group is politically cohesive; and third, that the white majority votes sufficiently as a bloc to enable it, in the absence of special circumstances, usually to defeat the minority’s preferred candidate. Thornburg v. Gingles, 478 U.S. 30, 50-51, 106 S.Ct. 2752, 2766, 92 L.Ed.2d 25 (1986).
Relying on the Senate Report accompanying the Voting Rights Act, the Court also set out factors by which plaintiffs may establish a violation of the Act. These include 1) the extent of a history of official discrimination in the state which touched voting rights; 2) the extent to which voting is racially polarized; 3) the extent to which the state has used voting practices or procedures which would enhance opportunities for discrimination against minorities; 4) whether minority candidates had been denied access to the slating process; 5) the extent to which minorities have borne the effects of discrimination in relation to education, employment, and health; 6) whether political campaigns have had overt or subtle racial appeals; 7) the extent to which minorities have been elected to public office in the jurisdiction; 8) whether there is a significant lack of responsiveness on the part of elected officials to the needs of minorities; and 9) whether the policy underlying the use of voting qualifications is tenuous. Thornburg v. Gingles, 478 U.S. at 36-37, 106 S.Ct. at 2758-59; see also Buckanaga, 804 F.2d at 471 (setting out same factors); S.Rep. No. 417, 97th Cong., 2d Sess. 28-29 (1982), reprinted in 1982 U.S.C.C.A.N. 177, 206-07. The Senate Report accompanying the amendment, from which the Court drew these factors, emphasizes that this list is not exclusive. S.Rep. No. 417 at 28-29, 1982 U.S.C.C.A.N. at 206-207. These factors are not to be used, however, as a “mechanical ‘point-counting’ device.” Id. n. 118. Instead, the court should, based on the totality of the circumstances and guided by the factors, determine whether the voting strength of the minority group is “minimized or cancelled out.” Id.
A district court’s decision as to whether a Voting Rights Act violation occurred is a finding of fact, which we review for clear error. Thornburg v. Gingles, 478 U.S. at 78, 106 S.Ct. at 2780. Additionally, in a voting rights case, the district court must “explain with particularity the reasoning and the subsidiary factual conclusions underlying [its] reasoning.” Buckanaga, 804 F.2d at 472. We require the district court to discuss “not only the evidence that supports its decision but also all the substantial evidence contrary to its opinion.” Id.
III.
Plaintiffs first argue that the district court did not make the detailed findings required in a Voting Rights Act case and did not discuss all substantial evidence contrary to its decision. We agree. In order to review a district court’s findings of fact and conclusions of law, a court of appeals must have before it sufficient detail to enable it to determine the factual and legal bases for the district court’s judgment. Fed.R.Civ.P. 52(a); Buckanaga, 804 F.2d at 472.
Because the resolution of a voting dilution claim requires close analysis of unusually complex factual patterns, and because the decision in such a case has the potential for serious interference with state functions, we have strictly adhered to the Rule 52(a) requirements in voting dilution cases and have required district courts to explain with particularity the reasoning and the subsidiary factual conclusions underlying their reasoning.
Buckanaga, 804 F.2d at 472 (quoting Velasquez v. City of Abilene, Tex., 725 F.2d 1017, 1020 (5th Cir.1984)).
[230]*230In making its findings, the district court should keep in mind that the question to be answered in a voting rights case is whether, under the totality of the circumstances, and “ ‘as a result of the challenged practice or structure^] plaintiffs do not have an equal opportunity to participate in the political processes and to elect candidates of their choice.’ ” Thornburg v. Gingles, 478 U.S. at 44, 106 S.Ct. at 2762 (quoting S.Rep. No. 417 at 28, 1978 U.S.C.C.A.N. at 206).
There was evidence at trial regarding all of the factors listed in Thornburg v. Gingles. The district court, however, made findings with respect to only factors seven and eight listed above. In the face of sustained proportional representation, the plaintiffs in a voting rights case may show “special circumstances,” such as the minority candidate running unopposed, bullet voting, or incumbency. Thornburg v. Gingles, 478 U.S. at 57 and n. 25, 106 S.Ct. at 2769 and n. 25. This list of special circumstances, the Court stated, was meant to be illustrative and not exclusive. Id. at 57 n. 26, 106 S.Ct. at 2770 n. 26.
Here, no black candidate has been elected to the Board in the four years since the election scheme was changed in 1987, though Dr. Nunn was reseated in 1990 in an unopposed election. Only two blacks have ever been elected in contested races, and one of those races involved an incumbent. Thus, representation, while proportional, comes essentially from blacks who ran unopposed. We agree with plaintiffs that successes prior to the 1988 majority vote requirement do not necessarily reflect the black voters’ present ability to elect representatives of their choice under the current election scheme. The district court made no findings, however, with respect to the special circumstances that might explain the proportional black representation. The absence of such findings leaves us with an inadequate record to review. Accordingly, we remand this case to the district court for further findings, taking into account the factors set out in Thornburg v. Gingles and Buckanaga.
Because we remand for further findings, we do not reach plaintiffs’ claim that the district court was clearly erroneous in finding that sustained proportional black representation precluded a finding that defendants had violated the Voting Rights Act.
IV.
The district court found that plaintiffs had not brought a frivolous lawsuit and denied defendants’ motion for Rule 11 sanctions. We find no error in this ruling. Plaintiffs raised allegations in their complaint that were “well grounded in fact and ... warranted by existing law.” Fed. R.Civ.P. 11. They alleged that their rights under the Act had been violated by the new majority vote requirement and by at-large elections, and they had sufficient knowledge of voting practices within the District to make their claim non-frivolous.
Defendants also claim that the district court erred in refusing to dismiss the case based on laches and equitable principles. Because it found against plaintiffs on the merits of the complaint, the district court found it unnecessary to reach the issue of laches. The district court, not this court, must be the first to decide this issue. We note, however, that plaintiffs brought suit after only two elections under the new voting scheme and eighteen months before any new census data would be available.
The denial of sanctions is affirmed; the judgment dismissing the complaint is reversed, and the ease is remanded to the district court for entry of further findings in accordance with the views set forth in this opinion.