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Note 11 - Employee Benefit Plans (Details Textual) - USD ($)	12 Months Ended
	Sep. 27, 2025	Sep. 28, 2024	Sep. 30, 2023
Supplemental Employee Retirement Plan [Member]
Supplemental Retirement Benefit Period	15 years
Defined Benefit Plan Percent of Highest Average Salary Base	50.00%
Defined Benefit Plan Number of Years in Average Annual Base Salary (Year)	5 years
Defined Benefit Plan Number of Years Preceding Retirement for Average Annual Base Salary Calculation (Year)	10 years
Defined Benefit Plan, Accumulated Benefit Obligation	$ 11,300,000	$ 11,400,000
Supplemental Employee Retirement Plan [Member] | Minimum [Member]
Defined Benefit Plan, Employment Term (Year)	30 years
Reduced SERP [Member]
Defined Benefit Plan Retirement Age	55
Defined Benefit Plan, Reduction for Each Month	0.28%
Reduced SERP [Member] | Minimum [Member]
Defined Benefit Plan, Employment Term (Year)	10 years
Retirement Savings Plan [Member]
Defined Contribution Plan, Maximum Annual Contributions Per Employee, Percent	75.00%
Defined Contribution Plan, Employer Matching Contribution, Percent of Match	50.00%
Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay	5.00%
Defined Contribution Plan, Cost	$ 1,900,000	1,700,000	$ 1,700,000
Retirement Savings Plan, First 1% of Employee Contribution [Member]
Defined Contribution Plan, Employer Matching Contribution, Percent of Match	100.00%
Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay	1.00%
VEBA [Member]
Self-insured Health Insurance Plan, Contribution Cost	$ 10,000,000	$ 6,500,000	$ 6,500,000
Healthcare Coverage Claims in Excess of	$ 200,000

X

- Definition

The number of years of continuous service required to receive the maximum benefit under the SERP.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanEmploymentTerm
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The number of consecutive years used to determine a Participant's highest average annual base salary in a supplemental employee retirement plan.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanNumberOfYearsInAverageAnnualBaseSalary
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Defined benefit plan number of years preceding retirement for average annual base salary calculation

+ References

No definition available.

+ Details

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Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The percentage of a Participant's highest average base salary that will be paid out to the Participant as supplemental retirement benefits if they meet the continuous service requirement.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanPercentOfHighestAverageSalaryBase
Namespace Prefix:	iiin_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The benefit will be reduced by a certain percentage for each month short of 30 years that the Participant was employed by the Company assuming the minimum continuous service and age requirements.

+ References

No definition available.

+ Details

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Namespace Prefix:	iiin_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

X

- Definition

The minimum age that an employee may retire at to receive benefits.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanRetirementAge
Namespace Prefix:	iiin_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Represents the amount at which stop-loss insurance covers the remainder of the claim.

+ References

No definition available.

+ Details

Name:	iiin_HealthcareCoverageClaimsInExcessOf
Namespace Prefix:	iiin_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Represents contribution cost for self-insured health plan.

+ References

No definition available.

+ Details

Name:	iiin_SelfinsuredHealthInsurancePlanContributionCost
Namespace Prefix:	iiin_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

The maximum period of time that a Participant will be paid supplemental retirement benefits if they are eligible for full benefits.

+ References

No definition available.

+ Details

Name:	iiin_SupplementalRetirementBenefitPeriod
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of actuarial present value of benefits attributed to employee service rendered, excluding assumptions about future compensation level.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 715
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480506/715-20-50-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 715
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480506/715-20-50-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of cost for defined contribution plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 715
-SubTopic 70
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480794/715-70-50-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Percentage of employees' gross pay for which the employer contributes a matching contribution to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage employer matches of the employee's percentage contribution matched.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Maximum percentage of employee gross pay the employee may contribute to a defined contribution plan.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
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X

- Details

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Namespace Prefix:
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Balance Type:
Period Type:

X

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

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Namespace Prefix:
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Period Type: