Lease - Additional Information (Details) $ in Millions	1 Months Ended	3 Months Ended
Feb. 28, 2021 ft²	Mar. 31, 2022 USD ($) ft²	Mar. 31, 2021 USD ($)
Lessee, Lease, Description [Line Items]
Lease agreement termination date		2021-09
Rent expense \| $		$ 0.2	$ 0.1
Crossing Holdings, LLC
Lessee, Lease, Description [Line Items]
Area of lease space \| ft²	12,370	4,900
Lease commencement date	2021-09
Lease term	72 months
Option to renew lease term ends, year	2027	2027
Lessee, Operating Lease, Existence of Option to Extend [true false]	true
Lease term, option to extend period	three years
Percentage of annual increase in lease payments	3.00%
Operating lease remaining lease term		5 years 4 months 24 days
Operating lease right-of-use asset discount rate		7.15%

Area of leased property.

No definition available.

Name:	dsgn_AreaOfLeasedProperty
Namespace Prefix:	dsgn_
Data Type:	dtr-types:areaItemType
Balance Type:	na
Period Type:	instant

- Definition

Lease agreement termination date.

+ References

No definition available.

+ Details

Name:	dsgn_LeaseAgreementTerminationDate
Namespace Prefix:	dsgn_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Lease commencement date.

+ References

No definition available.

+ Details

Name:	dsgn_LeaseCommencementDate
Namespace Prefix:	dsgn_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Lessee, Operating Lease, Term of expiration year

+ References

No definition available.

+ Details

Name:	dsgn_LesseeOperatingLeaseTermOfExpirationYear
Namespace Prefix:	dsgn_
Data Type:	xbrli:gYearItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of annual increase in lease payments.

+ References

No definition available.

+ Details

Name:	dsgn_PercentageOfAnnualIncreaseInLeasePayments
Namespace Prefix:	dsgn_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_LesseeLeaseDescriptionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Discount rate used by lessee to determine present value of operating lease payments.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)(3)
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918673-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseDiscountRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Indicates (true false) whether lessee has option to extend operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918673-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend
Namespace Prefix:	us-gaap_
Data Type:	xbrli:booleanItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of terms and conditions of option to extend lessee's operating lease. Includes, but is not limited to, information about option recognized as part of right-of-use asset and lease liability.

+ References

+ Details

Name:	us-gaap_LesseeOperatingLeaseOptionToExtend
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Remaining lease term of operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918673-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseRemainingLeaseTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Term of lessee's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918673-209980

+ Details

Name:	us-gaap_LesseeOperatingLeaseTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of single lease cost, calculated by allocation of remaining cost of lease over remaining lease term. Includes, but is not limited to, single lease cost, after impairment of right-of-use asset, calculated by amortization of remaining right-of-use asset and accretion of lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 55
-Paragraph 53
-URI http://asc.fasb.org/extlink&oid=123414884&loc=SL77918982-209971

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123408670&loc=SL77918686-209980

+ Details

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

- Details

Name:	srt_CounterpartyNameAxis=dsgn_CrossingHoldingsLLCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: