MinT - Information on Result #1004184

Information on Result #1004184

Linear OOA(5⁷⁰, 252, F₅, 3, 25) (dual of [(252, 3), 686, 26]-NRT-code), using extracting embedded OOA based on digital (45, 70, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 35, 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(5⁷⁰, 252, F₅, 3, 24) (dual of [(252, 3), 686, 25]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(5⁷³, 253, F₅, 3, 25) (dual of [(253, 3), 686, 26]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(5⁷⁶, 254, F₅, 3, 25) (dual of [(254, 3), 686, 26]-NRT-code)	[i]
4	Linear OOA(5⁷⁹, 255, F₅, 3, 25) (dual of [(255, 3), 686, 26]-NRT-code)	[i]
5	Linear OOA(5⁷¹, 252, F₅, 3, 25) (dual of [(252, 3), 685, 26]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(5⁸², 258, F₅, 3, 25) (dual of [(258, 3), 692, 26]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
7	Linear OOA(5⁸³, 262, F₅, 3, 25) (dual of [(262, 3), 703, 26]-NRT-code)	[i]
8	Linear OOA(5⁸⁴, 264, F₅, 3, 25) (dual of [(264, 3), 708, 26]-NRT-code)	[i]
9	Linear OOA(5⁸⁵, 268, F₅, 3, 25) (dual of [(268, 3), 719, 26]-NRT-code)	[i]
10	Linear OOA(5⁸⁶, 270, F₅, 3, 25) (dual of [(270, 3), 724, 26]-NRT-code)	[i]
11	Linear OOA(5⁸⁷, 272, F₅, 3, 25) (dual of [(272, 3), 729, 26]-NRT-code)	[i]
12	Linear OOA(5⁹⁴, 304, F₅, 3, 25) (dual of [(304, 3), 818, 26]-NRT-code)	[i]