MinT - Information on Result #1831883

Information on Result #1831883

OOA(27¹⁰², 9943, S₂₇, 2, 29), using (u,Â u+v)-construction based on

OOA(27²⁰, 100, S₂₇, 2, 14), using
- extracting embedded OOA [i] based on (6, 20, 100)-net in base 27, using
  - base change [i] based on digital (1, 15, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
linear OOA(27⁸², 9843, F₂₇, 2, 29) (dual of [(9843, 2), 19604, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁸², 19686, F₂₇, 29) (dual of [19686, 19604, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
    1. linear OA(27⁸², 19683, F₂₇, 29) (dual of [19683, 19601, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(27⁷⁹, 19683, F₂₇, 28) (dual of [19683, 19604, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive.

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	OOA(27¹⁰³, 9943, S₂₇, 2, 29)	[i]		OOA Duplication