MinT - Information on Result #1004079

Information on Result #1004079

Linear OOA(5⁵⁸, 252, F₅, 3, 19) (dual of [(252, 3), 698, 20]-NRT-code), using extracting embedded OOA based on digital (39, 58, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 29, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [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(5⁵⁸, 252, F₅, 3, 18) (dual of [(252, 3), 698, 19]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(5⁶¹, 253, F₅, 3, 19) (dual of [(253, 3), 698, 20]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(5⁶⁴, 254, F₅, 3, 19) (dual of [(254, 3), 698, 20]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(5⁵⁹, 252, F₅, 3, 19) (dual of [(252, 3), 697, 20]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(5⁶⁷, 258, F₅, 3, 19) (dual of [(258, 3), 707, 20]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
6	Linear OOA(5⁶⁸, 262, F₅, 3, 19) (dual of [(262, 3), 718, 20]-NRT-code)	[i]
7	Linear OOA(5⁶⁹, 264, F₅, 3, 19) (dual of [(264, 3), 723, 20]-NRT-code)	[i]
8	Linear OOA(5⁷⁰, 268, F₅, 3, 19) (dual of [(268, 3), 734, 20]-NRT-code)	[i]
9	Linear OOA(5⁷¹, 270, F₅, 3, 19) (dual of [(270, 3), 739, 20]-NRT-code)	[i]
10	Linear OOA(5⁷², 272, F₅, 3, 19) (dual of [(272, 3), 744, 20]-NRT-code)	[i]
11	Linear OOA(5⁷³, 273, F₅, 3, 19) (dual of [(273, 3), 746, 20]-NRT-code)	[i]