MinT - Information on Result #1112762

Information on Result #1112762

Linear OOA(3¹⁸⁴, 688, F₃, 5, 39) (dual of [(688, 5), 3256, 40]-NRT-code), using extracting embedded OOA based on digital (145, 184, 688)-net over F₃, using

trace code for nets [i] based on digital (7, 46, 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(3¹⁸⁴, 688, F₃, 5, 38) (dual of [(688, 5), 3256, 39]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁸⁹, 689, F₃, 5, 39) (dual of [(689, 5), 3256, 40]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁹⁴, 690, F₃, 5, 39) (dual of [(690, 5), 3256, 40]-NRT-code)	[i]
4	Linear OOA(3¹⁹⁹, 691, F₃, 5, 39) (dual of [(691, 5), 3256, 40]-NRT-code)	[i]
5	Linear OOA(3¹⁸⁵, 688, F₃, 5, 39) (dual of [(688, 5), 3255, 40]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3¹⁸⁶, 688, F₃, 5, 39) (dual of [(688, 5), 3254, 40]-NRT-code)	[i]
7	Linear OOA(3¹⁸⁷, 688, F₃, 5, 39) (dual of [(688, 5), 3253, 40]-NRT-code)	[i]
8	Linear OOA(3²⁰³, 692, F₃, 5, 39) (dual of [(692, 5), 3257, 40]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
9	Linear OOA(3²⁰⁴, 695, F₃, 5, 39) (dual of [(695, 5), 3271, 40]-NRT-code)	[i]
10	Linear OOA(3²⁰⁵, 696, F₃, 5, 39) (dual of [(696, 5), 3275, 40]-NRT-code)	[i]
11	Linear OOA(3²⁰⁶, 698, F₃, 5, 39) (dual of [(698, 5), 3284, 40]-NRT-code)	[i]
12	Linear OOA(3²⁰⁷, 700, F₃, 5, 39) (dual of [(700, 5), 3293, 40]-NRT-code)	[i]