MinT - Information on Result #1112483

Information on Result #1112483

Linear OOA(3¹⁶⁸, 688, F₃, 5, 35) (dual of [(688, 5), 3272, 36]-NRT-code), using extracting embedded OOA based on digital (133, 168, 688)-net over F₃, using

trace code for nets [i] based on digital (7, 42, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁶⁸, 688, F₃, 5, 34) (dual of [(688, 5), 3272, 35]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁷³, 689, F₃, 5, 35) (dual of [(689, 5), 3272, 36]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁷⁸, 690, F₃, 5, 35) (dual of [(690, 5), 3272, 36]-NRT-code)	[i]
4	Linear OOA(3¹⁸³, 691, F₃, 5, 35) (dual of [(691, 5), 3272, 36]-NRT-code)	[i]
5	Linear OOA(3¹⁶⁹, 688, F₃, 5, 35) (dual of [(688, 5), 3271, 36]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3¹⁷⁰, 688, F₃, 5, 35) (dual of [(688, 5), 3270, 36]-NRT-code)	[i]
7	Linear OOA(3¹⁷¹, 688, F₃, 5, 35) (dual of [(688, 5), 3269, 36]-NRT-code)	[i]